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Math Solver

StudyX Math Solver AI, powered by ChatGPT, GPT-4 and Claude 3 Opus, utilizes advanced AI technology and code interpreters to achieve a remarkable 92% accuracy in solving diverse math questions. Ask your question and get step-by-step solutions in seconds now!

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How Can Math Solver Assist You with Your Math Homework?

Image and Formula OCR Recognition

Our math solver uses AI-powered technology to accurately recognize and interpret mathematical expressions and formulas from images, enabling seamless problem-solving from various sources.

Step-by-Step AI-powered Solutions

Our AI is powered by ChatGPT and GPT4, with code interpreters, offering higher accuracy and providing systematic, step-by-step solutions to mathematical problems. This ensures comprehensive and accurate problem-solving processes.

Support All Mathematical Problems

We offer comprehensive support for a wide range of mathematical problems, leveraging AI capabilities to enhance accuracy and versatility in addressing diverse mathematical challenges.

What Can Math Solver Help You?

Algebraic equations and inequalities.

Offer step-by-step solutions for solving algebraic equations and inequalities, aiding in a comprehensive understanding of the problem-solving process.

Geometric Figures

Provide methods for calculating the area and perimeter of various geometric shapes, facilitating accurate and efficient problem-solving.

Calculus Problems

Assist with complex calculus problems, including differentiation and integration, through systematic and detailed solutions.

Trigonometry and Triangle Problems

Address trigonometric functions and problems related to triangles, ensuring thorough and accurate problem-solving processes.

Probability and Statistics

Provide assistance with probability and statistics problems, offering detailed explanations and solutions to enhance understanding.

Linear Algebra

Offer comprehensive support for linear algebra problems, including matrix operations and systems of equations, through systematic and detailed solutions.

Frequently Asked Questions

Why choose studyx's math solver.

Based on our experimental results, StudyX's Math Solver has achieved an accuracy rate exceeding 92%, surpassing the accuracy of GPT-4. Following its release on the GPT Store, StudyX's Math Solver successfully secured a position in the Top 5 of the GPT Store's education ranking.

Can Math Solver generate solid geometry figures？

Our Math Solver is primarily designed for solving algebraic, equations, and mathematical problems and does not include the capability to generate solid geometry figures so far.

Can this Math Solver solve complex differential problems?

Yes, it can provide a step-by-step solution to the problems.

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10 best AI math solver tools for math problem-solving

Homework AI makes it easier for students to learn difficult subjects. Boost your assignment and exam grades with these best AI homework helpers.

• March 18, 2024

The traditional approach to learning involves acquiring knowledge through listening and observation.

However, professionally trained AI can better accommodate different learning styles and enhance comprehension by offering tailored, on-demand learning assistance, especially in challenging subjects like mathematics.

As a subject many students struggle with, having access to a reliable AI math solver is invaluable. Math AI solvers can provide students and other learners with instant homework help outside the classroom at any time when needed.

They can also help improve students’ math test scores and build their mathematical skills over time. Let’s look at some of the best math AI tools for mathematical problem-solving:

Ten best AI math solver tools

1. Mathful – Best AI math solver overall

2. HIX Tutor – Best AI math solver for rapid homework response

3. AI Math – Best AI math solver for increasing math test scores

4. HomeworkAI – Best AI math solver for 24/7 math homework help

5. GeniusTutor – Best AI math solver for high-level learning 

6. Mathway – Best AI math solver for solving algebra problems

7. Air Math – Best AI math solver for mobile uses

8. StudyMonkey – Best AI math solver for in-depth explanations 

9. Interactive Mathematics – Best AI math solver for comprehensive chat support

10. Smodin – Best AI math solver for step-by-step solutions

Mathful – Best AI math solver overall

Mathful is an AI-powered math homework solver that provides step-by-step answers to all types of math questions.

The math AI tool uses a large language model and advanced algorithms to help students improve their math grades and prepare for exams.

Mathful has proven to be one of the most accurate AI math solvers, boasting a remarkable 98% accuracy rate across various mathematical disciplines, such as calculus, algebra, and geometry.

Mathful can also help students of all levels, from elementary school to university and beyond.

Mathful can help students improve their math grades in school by enforcing core math concepts and providing detailed explanations that promote comprehension.

Students can start using Mathful for free; low-cost subscription plans are available after the initial trial. 

• Able to provide highly accurate solutions and comprehensive explanations.
• Can process text and image files.
• Able to solve a variety of question types. 
• Available to use 24/7. 
• It cannot replace a real classroom education. 

Get instant answers to Math homework questions with Mathful AI math solver >>>

HIX Tutor – Best AI math solver for rapid homework response

HIX Tutor is a powerful AI homework helper that provides comprehensive support in many subjects, such as chemistry, biology, and physics.

It also serves as a personal AI math tutor, helping students boost their math grades and overall academic success. 

To use HIX Tutor’s advanced math AI, type in a math problem or upload an image or document of the question.

The tool instantly generates a detailed explanation for each problem step, helping students understand the underlying math concepts. 

HIX Tutor’s AI math problem solver can help save users time spent struggling with complicated math assignments.

Try the AI math solver at no cost. Once you’ve reached your question limit, upgrade to an affordable monthly or annual plan.

• Delivers step-by-step solutions to math questions.
• Trained on a large math knowledge dataset. 
• Reduces time spent on math homework. 
• Requires payment after the initial trial. 
• Some students may only use the tool to get answers without learning. 

Streamline the math learning experience with HIX Tutor’s math AI solver >>>

AI Math – Best AI math solver for increasing math test scores

How you prepare for a math test can significantly impact your performance.

AI math solvers like AI Math help take the frustration out of studying by providing thorough explanations that teach students how to tackle similar math problems. 

The AI math problem solver generates answers to questions in under 10 seconds with a 99% accuracy rate.

AI Math supports over 30 languages so that students can get responses in their native language for better understanding.

Students who use AI Math to supplement their classroom education experience an increase in their math test scores of up to 35%. Starting with AI Math is free; subscriptions cost just a few dollars a month.

• Covers most branches of math, such as arithmetic and trigonometry.
• Walks students through the solution to facilitate understanding. 
• Can solve simple to complex math problems.
• Does not currently offer advanced math features. 

Choose AI Math and study for math tests in a smarter way >>>

HomeworkAI – Best AI math solver for 24/7 math homework help

Students often need help with homework outside of traditional school hours. AI math solver tools like HomeworkAI allow students to get comprehensive support round-the-clock.

Much like a personal tutor, HomeworkAI focuses on teaching students how to solve homework problems instead of simply giving answers. 

HomeworkAI can handle math problems with multiple solution methods, meaning a primary solution and possible alternative approaches.

It can also analyze textbook material with practice math questions to aid students’ studies. 

While HomeworkAI excels in helping students complete math assignments with high precision, this AI homework tool can also help students in other school subjects, such as biology, physics, chemistry, literature, and history.

Try HomeworkAI for free, or choose from a low-cost subscription plan for unlimited uses. 

• Allows students to work at their own pace at home. 
• User-friendly platform is easy to navigate. 
• It can help students excel in many subjects, including math.
• This may cause students to rely too much on online math-solving platforms. 
• Rarely, solutions may be outdated or incorrect. 

Try HomeworkAI and get instant help for your math homework >>>

5. Genius Tutor – Best AI Math Solver for High-Level Learning

Genius Tutor is a versatile AI tutor and homework helper that can help students build their math skills and gain confidence in their academic abilities.

While the AI math solver is geared toward all types of learners, it is best suited for high school and college-level students.

The AI math problem solver provides a step-by-step breakdown for math questions of all types, showing the exact process of figuring out math problems and concepts.

Genius Tutor also highlights and explains important theorems, formulas, and rules so that students know when and how to use them.

Genius Tutor not only helps students complete math homework assignments in record time but can also help them prepare for exams.

No credit card is needed to try Genius Tutor, and budget-friendly paid subscriptions are available after the free trial.

• Can help students with all mathematical disciplines.
• Provides in-depth guides that foster lifelong learning. 
• Gives instant feedback on a variety of homework questions. 
• May not provide accurate solutions to highly complex math problems. 

Genius Tutor’s AI math solver can instantly elevate your math learning experience >>>

Mathway – Best AI math solver for solving algebra problems

Algebra is a complex branch of mathematics that many students struggle with in high school and college.

Mathway offers a sophisticated AI math solver designed to solve algebra homework questions, from word problems to complex mathematical operations that form meaningful expressions.

The math solver AI tool combines an algebra calculator with a conversational chatbot. Simply type in a math problem or upload a photo and get instant step-by-step solutions. 

Mathway also offers AI-driven math problem solvers for other branches of math, such as calculus, statistics, chemistry, and physics.

• The clean interface is easy to use. 
• You can upload documents on a computer or mobile device. 
• It makes it easy to master algebraic concepts. 
• Additional features require a paid upgrade. 
• Does not always provide detailed explanations. 

Air Math – Best AI math solver for mobile uses

Nowadays, many students rely on their smartphones or other mobile devices for homework help. Air Math is a smart AI math solver app available on Apple and Android devices.

Once installed, the Air Math app allows students to snap and solve math homework questions in under three seconds.

The innovative math AI solver can solve everything from geometry questions to word problems.

The 24/7 instant solutions include step-by-step solutions to teach students how to solve the problem independently. 

If you still have problems understanding the explanations, Air Math can connect you with professional math experts worldwide at any time. 

• Free to use.
• Offers support on mobile devices.
• You can ask expert math tutors for additional assistance. 
• Students can download the Chrome Extension on the web. 
• The app may not accurately read handwritten math questions. 

StudyMonkey – Best AI math solver for in-depth explanations 

StudyMonkey is a free AI homework helper that provides academic assistance in many areas, including mathematics.

The powerful AI math solver saves students time and headaches by instantly generating solutions to complex math problems, preventing long homework sessions. 

Type in the math problem, and StudyMonkey provides an accurate answer, detailed explanation, and steps to solve the problem to make it easier to understand.

This platform also retains a history of past questions asked, allowing students to review and revisit solutions anytime, aiding in effective long-term learning. 

• Can handle math problems from first grade to expert. 
• Offers a free plan. 
• Math features are limited.
• Can not upload images or documents. 
• You must pay for a subscription to ask more than three questions daily.

Interactive Mathematics – Best AI math solver for comprehensive chat support

Many students are familiar with chatbots, making Interactive Mathematics a popular option for homework help.

The state-of-the-art AI math problem solver claims to be more accurate than ChatGPT and more powerful than a math calculator. Its speed also surpasses human math tutors. 

Using Interactive Mathematics for homework help is also very simple.

You can type in your math question or upload an image, and the tool immediately sets to work, with the added benefit of offering solutions through a chatbot-style conversation that simulates a real-time, interactive math problem-solving session.

• You can help students improve their grades.
• Chat-based real-time problem-solving
• Offers bonuses like SAT/ACT prep courses. 
• Users can only ask three questions before reaching the free question limit.

Smodin – Best AI math solver for step-by-step solutions

The Smodin Math AI Homework Solver can help if you’re struggling with math homework.

This unique tool uses machine learning and AI algorithms to efficiently solve all types of math problems, from formulas to equations.

The tool also promises high accuracy, reducing the risk of submitting incorrect answers. 

Smodin doesn’t just provide a final answer to your query. It provides both brief answers and comprehensive explanations to help you better understand the concept.

It also shows a variety of relevant web answers and links to other resources, such as YouTube videos. 

• Users must make an account to start using Smodin.
• Step-by-step solutions are highly detailed and engaging. 
• Can help students ace their math exams. 
• Free users are limited to 3 daily credits. 
• Cannot upload images or documents. 

Final thoughts

Many students struggle with math, but that doesn’t mean they must settle for bad grades. With the right AI math solver, students can confidently develop their math skills and complete assignments and exams. 

Based on our assessments, Mathful easily stands out from the pack. It is a sophisticated AI math problem solver that offers enhanced problem-solving capabilities, accurate solutions, and affordable subscription plans.

Try Mathful for free and achieve greater academic success.

Have any thoughts on this? Drop us a line below in the comments, or carry the discussion to our  Twitter  or  Facebook .

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AI Math Homework Solver & Helper

AIR Math Student

Take a photo of any math question and we will reply instantly!

Our math experts from all around the world available 24/7!

Want to know more than just the answer? Learn how to solve your problem!

Our AI search engine covers every math topic including graphs and diagrams!

You Ask? We Answer Instantly!

Stuck on your homework? Need not worry! Our authentic AI tech will auto-recognize the photo scanned problem and solve all your math homework! The best part is, AIR MATH is all FREE.

Snap, Tap, Answer in a Zap!

It’s so simple. Just give it 3 seconds and your answer will be there! No more wasting time to find the right solution. Our authentic AI technology will give you the answer right away!

Expert tutors will give you an answer in real-time, 24/7!

And yes, even for word problems. Geometry, Algebra, and Calculus - You name it! As long as it’s a math question, our tutors are ready to answer them 24/7 around the clock.

I mean... Let's face it. Most of you tech-savvy MZ gens probably already know how by now, but it doesn't hurt to elaborate a bit, right? We tried to make this process as hassle-free as possible, so we've narrowed it down to two methods. You can use either of the two: 1. Sign in with Apple 2. Sign in with Google And use the account linked to either of the platforms. Apple and Google will take good care of you from then on.

AIR MATH is an AI-powered math homework helper app designed to fit the needs of students struggling with math homework and test prep. AIR MATH scans the photo of every submitted math problem using our authentic AI-Ed technology and will provide you with an answer to your math homework in no time! It can recognize virtually anything, from simple equations to word problems. Whether it be your school homework, test prep, or just materials for your daily studies, AIR MATH's got you covered. AIR MATH also provides a 1:1 live chat service with expert tutors who are on stand-by 24/7 to give you thorough step-by-step solutions to your math problems. Come check it out now!

AIR MATH Chrome Extension is basically the web version of AIR MATH Homework Helper! You can download the extension from the Chrome Web Store and install it on your Chrome browser. Just one click and your're done! Once you install it, you can snap and crop your math problem from the web and ask for a solution straight from the web! Logging onto your account from the web will automatically sync your math problems and solutions onto your AIR MATH mobile app as well. Linking your account onto the mobile version will enable you to use other features that are only available on the mobile as well!

HOW TO USE AIR MATH HOMEWORK HELPER (MOBILE) TO THE FULL (AIR MATH: 101) 1. Stuck on your math homework / school assignment / test prep? It’s okay to be completely clueless. 2. Grab your smartphone. 3. Take a photo of the question you’re stuck on. That’s right! Photo scan it and give it a few seconds. Our authentic AI-recognition tech will search for matching solutions in just seconds! 4. Voila! You are provided different types of solutions for your math question. Not sure which one to choose? Tap on each of the solutions and see which one best fits your needs. 5. Yikes, did you get an answer but couldn't understand why or how such a solution was given? No worries, we have expert tutors on stand-by 24/7. Ask a tutor for a step-by-step walk-through. 6. In less than 5 minutes, you will be connected to one of our expert tutors. Just hit that "Ask Expert Tutors" button and chillax. 7. You can have a 1:1 live chat session with the tutor and ask for a thorough step-by-step explanation of how to derive an answer. Easy-peasy-lemon-squeezy! 8. Oh, we know you have more problems to solve! Now, back to Step 1.

HOW TO USE AIR MATH HOMEWORK HELPER (WEB) TO THE FULL (AIR MATH: 101) 1. Fire up that laptop/desktop PC. 2. Stuck on your math homework / school assignment / test prep? It’s okay to be completely clueless. 3. First things first, go to the Chrome Web Store and download our AIR MATH Chrome extension. 4. All done? Now, go back to your geometry problem that you were stuck on, then right-click on your mouse. 5. You will see the AIR MATH extension show up on the menu. Click on it! 6. Crop the math question that you need to solve, and then click on the "Search" button that shows up. 7. Ta-da! There's your answer!

1. Prepare a math problem; any equation or word problem. Geometry? Algebra? Calculus? Just bring it on! 2. When you first open the AIR MATH app, the home screen will show you a camera screen. 3. Position your smartphone close to the problem and place the problem within the guideline, then snap! 4. Your problem wasn't scanned within the guideline? Don't you worry! After you photo scan your problem, you can adjust the guideline to crop the part that you need from the question. 5. Our AI tech will then auto-recognize the problem and come up with possible answers in seconds. It'll come up with different ways of solving the problem. Tap on each solution and choose the answer that best fits your need.

Sure thing! In order to use the photos that you already have, just give permission to use your Photo Library and you're all set! When you first enter the app, you will see the camera screen, and on the top middle part, you will see two icons; an image icon and a flash icon. Tap on the image icon on the left and you will be able to choose the pictures that you want to share from your Photo Library. Just remember, it has to be a math question or else AIR MATH Homework Helper won't recognize the picture!

For now, you can only upload one image at a time. This is because AIR MATH can recognize one problem at a time. It cannot recognize and solve multiple questions at the same time. For example, say you have a set of geometry questions that you need answers to, and you have taken photos of each question separately, then you must upload the photo one at a time. Uploading multiple math questions in one photo won't work either!

Once you take a photo and scan the problem you're having trouble with, AIR MATH will come up with possible solutions to your question. Look through each solution and see if any of it matches your need. If the solution is too difficult to understand or doesn't quite match your question, hit that "Ask Expert Tutors" button below the solutions. It may take up to five minutes before you're connected to a tutor. 1:1 live chat will be available once you're connected and you can ask the tutor if you have any questions regarding the problem. Once your tutor has given you an answer and you feel that the given solution is good enough, you can tap on the "End Chat" button to close the session. That's all there is! That wasn't so hard, was it?

Oh, so you still haven't heard? Our AIR MATH app is powered by AI and all answers are machine-learned. The math data that have been accumulated within the app enables AIR MATH to continuously evolve and develop - meaning, all answers to your math questions and problems are calculated and solved using our AI technology. Of course, the trustworthiness is guaranteed! Have faith, my friend!

A BIG YES! Our tutors are all certified tutors who have gone through a very strict screening, testing, and background check-ups. We also consistently do quality checks on their answers to the math problems that they give to our users. If you find any of their answers incorrect or inadequate, you can also rate them and report them to us and we will take necessary actions accordingly. So, don't you worry about a thing!

Basic Math Pre-Algebra: Arithmetic, proportional, integers, fractions, decimal numbers, powers, roots, factors, complex numbers Algebra: Linear equations/inequalities, quadratic equations/inequalities, logarithms, functions, graphing, polynomials Geometry: Plane/solid geometry, constructions, measurement formulas, formal proofs Precalculus: Identities, logarithmic functions, exponential functions, trigonometric functions, series and sequences, probability, statistics, limits, derivatives Trigonometry: Circular and periodic functions Calculus: Series, limits, derivatives, integration, differentiation Statistics: Combinations, permutation, factorials Discrete Mathematics Finite Mathematics Differential Equations Business Math BAAM! 😎

Yes, for sure! AIR MATH's AI recognition technology enables it to recognize not only the ordinary equations of various subjects but word problems as well. It will read your word problem and provide a few options of step-by-step solutions for you to choose from. Easy like a breeze!

Urr... Yes and no? You can photo scan your handwritten problem and ask for a solution to it, but if you mean if there is a handwriting feature to write out the question on the app directly, then it's a no. If we see that more and more users are asking for the said feature, we will definitely take it into consideration. That's a pinky promise.

Sadly, no. AIR MATH's tutor system does not allow a student to designate or reconnect to a certain tutor to solve your math problem. However, if we see a growing need for this, we will definitely take this into consideration.

Oh, yikes! I'm glad that you liked our tutor, but unfortunately, we do not give out personal information of the tutors, and so it's not possible to contact a specific tutor. But the good news is, that all other tutors are equally good at solving math problems! You may be connected to a random tutor, but all tutors that work with AIR MATH are certified, tested, and monitored constantly. You can trust them and ask any and every math questions you have. They'll give you a solution to your problem in a zap!

It's actually pretty simple. Just open the app, position your math problem that you need to solve within the guideline, then snap and tap to upload your question. It's okay if your problem was not photo scanned exactly within the guideline, because once you take a picture of it, you can later adjust and crop the math problem. Once you upload your math question, AIR MATH will come up with possible solutions to your problem in about 10 seconds. Now, wasn't that easy?.

No, no one but yourself can see the math questions that you have asked on AIR MATH... We do, however, accumulate all the math problems that all our users have asked so that our AI technology can use them as databases and become even faster when giving answers!

Well, that really depends. Our AIR MATH math homework helper/solver app itself only uses one system language: English. However, our tutors are from all across the globe and if you happen to use any of their languages, well, then that's up to you to decide if you want to use another language when asking for step-by-step solutions to your math problems from the tutors via live chat sessions. (We respect diversity!)

The Bookmarks feature enables you to literally "bookmark" any step-by-step solutions that you receive from AI regarding your math questions. Open AIR MATH, photo scan a problem that you're stuck with, then tap and upload. Wait for 10 seconds until you're given a step-by-step solution by AIR MATH AI. Once your answer is provided, you will see the "Bookmarks" icon at the top right corner along with the "Share" icon (second to far right). Tapping on the Bookmarks icon will add that answer in your Bookmarks tab. Later, when you want to go back to see this problem again, tap on the "History" tab on the bottom right corner, then you will see "Answers" and "Bookmarks" tabs. Go to the "Bookmarks" tab and you will see the step-by-step solutions to the math questions that you have added.

AIR MATH math homework helper/solver app is currently available both on iOS and Android. For iOS, any devices running on versions 14.4 and up can download and use the AIR MATH app. You can now also use AIR MATH on the web as well as a Chrome extension! We will be continuing to add support for new versions as well, so please stay tuned!

Tickets/ PASS

The ticket system is the actual key player of AIR MATH Homework Helper app that helps you get through with your math homework. There are three types of tickets on AIR MATH: Search tickets, Question tickets and Writing tickets. Search tickets are used for searching for answers to a math problem, and Question tickets are used for asking for more precise solutions to math problems to tutors. Writing tickets are used for supercharging your essay. The rule is simple: one ticket per one question or essay!

Yes, there is! Each ticket has its own expiration date, so please be sure to check it from the Ticket page! Tickets with earliest expiration dates will be used up first.

You can earn extra free tickets by inviting new friends to download and try out AIR MATH Homework Helper app. Once your friend downloads and enters your invitation code, free tickets will be given right away. That's not all! You'll be rewarded with free tickets if you check-in on a daily basis! Check out the Ticket page for more details!

First, enter the app, then open your Ticket page. You will see your Friend Invitation Code. Copy the code and share it with your friends. When your friends download the app and enter your invitation code when signing up, you will be automatically given a set of free tickets!

Not to worry! Being asked to retake a math question does not mean that you will have to use another question ticket. The question ticket that you have used up for your math problem (which you also need to retake a photo of) will be returned and you can use it for the retake!

Ticket refills are there to allow you to purchase extra question tickets when necessary. If you are already on a subscription, there's going to be a little benefit when purchasing a refill!

AIR MATH Pass is our subscription system which gives out unlimited search tickets and a set of question tickets. There are various options to your subscription period; from 1 month plan to 1 year plan! Come take a look at our subscription plans and select whichever that best suits your interest!

Oh, it's definitely going to be worth it. You won't have to worry about how many tickets you have left, because we will provide an ample amount for you to use during your subscription period! The AIR MATH Homework Helper PASS will enable you to access and use the service both on the web and on the mobile app! Life made easier! (Wink, wink!)

You can purchase the PASS from the My Tickets page within the AIR MATH Homework Helper mobile app! All products are purchasable through either Apple App Store or Google Play Store in-app purchase system.

You can check your purchase history or status from either Apple App Store or Google Play Store.

You can check for all things related to subscription cancellation, refund, and more from the Apple App Store or Google Play Store.

Please take a screenshot of your purchase receipt and then send it to our Help Desk or <[email protected]>! We'll hand it over to our AIR MATH Help Center and try to figure out the problem and solution.

Please try contacting the Apple App Store or Google Play Store for any payment issues.

To change the payment method, you must access your app store and change the payment method that you have registered on it.

If you wish to change the subscription plan that you are currently on, you must first cancel the current subscription plan from your app store so that it does not recur on its next billing cycle. Then, you can choose another plan that you wish to use. Please note that the current subscription plan that you're on will last until your next billing cycle and your changed plan will apply from the next subscription term!

Tech issue / Troubleshooting

This may be because the type of question that you asked has not been asked before, therefore the question is not in our database as of yet. Please try the "Ask Expert Tutors" feature and ask for a step-by-step solution directly. If this is not about our AI not being able to recognize your problem, then please check to see if your AIR MATH app is running on the latest version and take a screenshot or a screen recording and send it to us via "Contact Us."

Oof! So sorry to hear that you're experiencing malfunctions with our app! In this case, please first check to see if your AIR MATH app is running on the latest version. Then, please take a screenshot or screen recording of the problem that you're experiencing and send it to us via "Contact Us." It'd be certainly helpful if you can describe the issue in detail (e.g. during what stage the app froze or tapping on a certain button caused a crash, etc.) so that our developers will know where to look into.

Math Word Problem Solver

Supports arithmetic, algebra, calculus & more.

Solve Math Word Problems

Welcome to the future of math problem-solving! Designed to simplify complex math challenges, this tool empowers users to effortlessly tackle word problems and build confidence in mathematical problem-solving.

Key Features of Math Solver:

1. natural language understanding:.

Our Math Solver uses advanced natural language processing to understand the intricacies of word problems. Simply input the problem in plain language, and let the tool work its magic.

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Deep Learning in Automatic Math Word Problem Solvers

• Open Access
• First Online: 20 June 2022

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• Dongxiang Zhang 4  

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The design of an automatic solver for mathematical word problems (MWPs) dates back to the early 1960s and regained booming attention in recent years, owing to revolutionary advances in deep learning. Its objective is to parse the human-readable word problems into machine-understandable logical expressions. The problem is challenging due to the existence of a substantial semantic gap. To a certain extent, MWPs have been recognized as good test beds to evaluate the intelligence level of agents in terms of natural language understanding and automatic reasoning. The successful solving of MWPs can benefit online tutoring and constitute a milestone toward general AI. In this chapter, we present a general introduction to the technical evolution trend for MWP solvers in recent decades and pay particular attention to recent advancement with deep learning models. We also report their performances on public benchmark datasets, which can update readers’ understandings of the latest status of automatic math problem solvers.

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• Math word problems
• Deep learning
• Natural language processing
• Automatic reasoning

1 Introduction

Designing an automatic solver for mathematical word problems (MWPs) has a long history dating back to the 1960s and continues to attract intensive attention as a frontier research topic. The problem is challenging because there remains a wide semantic gap to parse the human-readable words into machine-understandable logics to conduct quantitative reasoning. Various attempts have been made to bridge the gap, from rule-based pattern matching to semantic parsing with statistical machine learning, and to the recent end-to-end deep learning models that are considered as the state-of-the-art performers. To a certain extent, the problem has been recognized as a good test bed to evaluate the intelligence level of agents, as it requires semantic understanding of natural languages and capabilities of automatic reasoning. Hence, the successful solving of MWPs would constitute a milestone toward general AI.

A large body of research works start from solving arithmetic word problems for elementary school students. Its input is the text description for the math problem, represented in the form of a sequence of tokens. There are multiple quantities mentioned in the text and an unknown variable in the question whose value is to be resolved. The problem solver’s objective is to extract the relevant quantities and map this problem into an arithmetic expression whose evaluation value provides the solution to the problem. For simplicity, there are only four types of fundamental operators \(\mathcal {O}=\{+,-,\times ,\div \}\) involved in the math expression.

An example of an arithmetic word problem is illustrated in Fig. 1 . The relevant quantities to be extracted from the text include 17, 7, and 80. The number of hours spent on the bike is the unknown variable x . To solve the problem, we need to identify the correct operators between the quantities and their operation order such that we can obtain the final equation 17 + 7 x  = 80 or expression x  = (80 − 17) ÷ 7 and return 9 as the solution to this problem.

An example of an arithmetic word problem

The early approaches mainly relied on rule-based reasoning. They heavily count upon human interventions to manually craft rules and schemas for pattern matching. Each rule consists of a set of conditions that must be satisfied and the actions to be carried out. For example, as a system published in 1985, WORDPRO, predefines a collection of rules to handle simple math problems. If the problem text matches the “HAVE-MORE-THAN” proposition, the agent will identify the two operands and use the “−” operator to derive the answer. It is evident that the usefulness of these rule-based solvers is doubtful because they can only resolve a limited number of scenarios that are defined in advance.

To improve the generality, subsequent efforts have been devoted to making use of semantic parsing to map the sentences from problem statements into structured logic representations so as to facilitate quantitative reasoning. It has regained considerable interests from the academic community, and a booming number of methods have been proposed in the past years. These methods leverage various strategies of feature engineering and statistical learning for performance boosting. For instance, if two quantities have the same dependent verbs, as in a problem like “in the first round she scored 40 points and in the second round she scored 50 points,” it is likely that “+ ” would be the operator for these two numbers. Despite the promising results claimed in some small datasets, these approaches are not completely automatic and still require human knowledge to help extract semantic features.

To further reduce human intervention and enable the automatic extraction of discriminative features, applying deep learning (DL) models in MWPs has become a promising research direction. In 2017, Wang et al. proposed DNS as the first end-to-end DL-based framework that directly converts the input of question text into the output of math expression. It is then a natural idea to apply an existing sequence-to-sequence (seq2seq) learning model to encode the text input and decode the hidden features into a math expression. The drawback is that the seq2seq model is a black box that lacks interpretability, and it cannot guarantee the output is in valid math format and normally requires a post-processing step. Nonetheless, this work still occupies an important position in the literature of MWP solving because it opened up a new research direction to apply end-to-end DL models to solve MWPs and attracted a good number of followers to contribute to this research area.

Following the research line of seq2seq models, various optimization techniques have been proposed to further improve accuracy. A recent breakthrough is that since the resulting math expression can be naturally represented as a tree structure, this finding allows us to leverage more informative context for decoding. For example, a math expression 2 + 3 can be converted to a tree structure in which the root is operator + , and there are two child nodes with operands 2 and 3. The decoder can recursively generate an expression tree in a top-down manner and take into account the encodings of parent node and sibling nodes as the more informative context. Following the idea, we have witnessed the success of seq2tree models which have exhibited clear superiority over seq2seq models. There have also emerged several incremental works on top of seq2tree models. The general idea is to replace the encoder or decoder with more effective graph-based embedding since sequences and trees can be viewed as two special cases of graphs.

At the end of the chapter, we will cover geometry problem solvers that require both textual and visual understanding. The problem is even more challenging because the input needs to be mapped into a logical representation that is compatible with both the problem text and the accompanying diagram. Common strategies to solve geometry word problems constitute three key components, including diagram understanding to capture visual clues, text parsing to capture semantic information, and deductive reasoning via a knowledge base with geometry axioms and theorems. We will introduce representative systems such as GEOS and Inter-GPS. They parse the problem text and geometry diagram into formal language and then perform symbolic reasoning step by step to derive the solution. The readers can try the demos of GEOS published by the University of Washington. Footnote 1

2 Methodology and Analysis

In the following, we present the general design principles of rule-based methods, statistic-based methods, tree-based methods, as well as recent advances with deep learning models.

2.1 Rule-Based Methods

The early approaches to math word problems are rule-based systems based on hand engineering. Published in 1985, WORDPRO (Fletcher 1985 ) can solve three types of simple one-step arithmetic problems, including value change , combine , and compare . A collection of rules is predefined for pattern matching. For example, given a problem text “ Dan has six books. Jill has two books. How many books does Dan have more than Jill? ,” it matches the predefined “HAVE-MORE-THAN” proposition. The agent will identify the two operands and use the “−” operator to derive the answer. Another system ROBUST, developed by (Bakman 2007 ), expanded the rule base and could better understand free-format multistep arithmetic word problems. It further extends the change schema of WORDPRO into six distinct categories. The multistep problem is solved by splitting the problem text into sentences and each sentence is mapped to a proposition. Yun et al. also proposed to use schema for multistep math problem solving (Yun et al. 2010 ). However, their implementation details were not explicitly revealed. Since these systems are out of date, we only provide such a brief overview for representativeness. The readers can refer to Mukherjee and Garain ( 2008 ) for a comprehensive survey of early rule-driven systems for automatic understanding of natural language math problems. Since these systems heavily rely upon human interventions to manually craft rules and schemas for pattern matching, it is evidently that the usefulness of these rule-based solvers is doubtful because they can only resolve a limited number of scenarios defined in advance.

2.2 Statistic-Based Methods

The statistic-based methods leverage traditional machine learning models to identify the entities, quantities, and operators from the problem text and yield the numeric answer with simple logic inference procedure. The scheme of quantity entailment proposed in (Roy et al. 2015 ) can be used to solve one-step arithmetic problems. It involves three types of classifiers to detect different properties of the word problem. The quantity pair classifier is trained to determine which pair of quantities would be used to derive the answer. The operator classifier picks the operator op  ∈{+, −, ×, ÷} with the highest probability. The order classifier is relevant only for problems involving subtraction or division because the order of operands matters for these two types of operators. With the inferred expression, it is straightforward to calculate the numeric answer for the simple math problem.

To solve math problems with multistep arithmetic expression, the statistic-based methods require more advanced logic templates. This usually incurs additional preparatory overhead to annotate the text problems and associate them with the introduced template. As an early attempt, ARIS (Hosseini et al. 2014 ) defined a logic template named state that consists of a set of entities, their containers, attributes, quantities, and relations. For example, “ Liz has 9 black kittens ” initializes the number of kitten (referring to an entity) with black color (referring to an attribute) and belonging to Liz (referring to a container). The solution splits the problem text into fragments and tracks the update of the states by verb categorization. More specifically, the verbs are classified into seven categories: observation , positive , negative , positive transfer , negative transfer , construct , and destroy . To train such a classifier, we need to annotate each split fragment in the training dataset with the associated verb category. Another drawback of ARIS is that it only supports addition and subtraction. Sundaram and Khemani ( 2015 ) followed a similar processing logic to ARIS. They predefined a corpus of logic representation named schema , inspired by Bakman ( 2007 ). The sentences in the text problem are examined sequentially until the sentence matches a schema, triggering an update operation to modify the number associated with the entities.

Mitra and Baral ( 2016 ) proposed a new logic template named formula . Three types of formulas are defined, including part whole , change , and comparison , to solve problems with addition and subtraction operators. For example, the text problem “ Dan grew 42 turnips and 38 cantelopes. Jessica grew 47 turnips. How many turnips did they grow in total? ” is annotated with the part-whole template: 〈 whole  :  x , parts  : {42, 47}〉. To solve a math problem, the first step connects the assertions to the formulas. In the second step, the most probable formula is identified using the log-linear model with learned parameters and converted into an algebraic equation. Another type of annotation is introduced by Liang and colleagues (Liang et al. 2016a , b ) to facilitate solving a math word problem. A group of logic forms is predefined and the problem text is converted into the logic form representation by certain mapping rules. For instance, the sentence “ Fred picks 36 limes ” will be transformed into verb ( v 1 , pick ) & nsubj ( v 1 , Fred ) & dobj ( v 1 , n 1 ) & head ( n 1 , lime ) & nummod ( n 1 , 36). Finally, logic inference is performed on the derived logic statements to obtain the answer.

To sum up, these statistical-based methods have two drawbacks that limit their usability. First, it requires additional annotation overhead that prevents them from handling large-scale datasets. Second, these methods are essentially based on a set of predefined templates, which are brittle and rigid. It will take great efforts to extend the templates to support other operators like multiplication and division.

2.3 Tree-Based Methods

The arithmetic expression can be naturally represented as a binary tree structure such that the operators with higher priority are placed in the lower level and the root of the tree contains the operator with the lowest priority. The idea of tree-based approaches is to transform the derivation of the arithmetic expression to constructing an equivalent tree structure step by step in a bottom-up manner. One of the advantages is that there is no need for additional annotations such as equation template, tags, or logic forms. Figure 2 shows two tree examples derived from the math word problem in Fig. 1 . One is called an expression tree that is used in (Roy and Roth 2015 , 2017 ; Wang et al. 2018b ), and the other is called an equation tree (Koncel-Kedziorski et al. 2015 ). These two types of trees are essentially equivalent and result in the same solution, except that equation tree contains a node for the unknown variable x .

Examples of expression tree and equation tree for Fig. 1

The overall algorithmic framework common to the tree-based approaches consists of two processing stages. In the first stage, the quantities are extracted from the text and form the bottom level of the tree. The candidate trees that are syntactically valid, but with different structures and internal nodes, are enumerated. In the second stage, a scoring function is defined to pick the best matching candidate tree, which will be used to derive the final solution. A common strategy among these algorithms is to build a local classifier to determine the likelihood of an operator being selected as the internal node. The input of the classifier consists of the contextual embeddings for its two child nodes and the output is a label in the operator set {+, −, ∗, ÷}. Such local likelihood is taken into account in the global scoring function to determine the likelihood of the entire tree.

Roy and Roth ( 2015 ) proposed the first algorithmic approach that leverages the concept of an expression tree to solve arithmetic word problems. Its first strategy to reduce the search space is training a binary classifier to determine whether an extracted quantity is relevant or not. Only the relevant ones are used for tree construction and placed in the bottom level. The irrelevant quantities are discarded. The tree construction procedure is mapped to a collection of simple prediction problems, each determining the lowest common ancestor operation between a pair of quantities mentioned in the problem. The global scoring function for an enumerated tree takes into account two terms. The first one is the likelihood of quantity being irrelevant, i.e., the quantity is not used in creating the expression tree. The other term is the likelihood of selecting an operator in one of the internal tree nodes. The service is also published as a web tool (Roy and Roth 2016 ), and it can respond promptly to a math word problem.

ALGES (Koncel-Kedziorski et al. 2015 ) differs from (Roy and Roth 2015 ) in two major ways. First, it adopts a more brute-force manner to exploit all the possible equation trees. More specifically, ALGES does not discard irrelevant quantities but enumerates all the syntactically valid trees. Second, its scoring function is different. There is no need to measure quantity relevance because ALGES does not build such a quantity classifier. The goal of (Roy et al. 2016 ) is also to build an equation tree by parsing the problem text. It makes two assumptions that can simplify the tree construction, but sacrifice its applicability. First, the final output equation form is restricted to have at most two variables. Second, each quantity mentioned in the sentence can be used at most once in the final equation. The tree construction procedure consists of a pipeline of predictors that identify irrelevant quantities, recognize grounded variables, and generate the final equation tree. With customized feature selection and SVM (support vector machine)-based classifier, the relevant quantities and variables are extracted and used as the leaf nodes of the equation tree. Finally, the tree is built in a bottom-up manner.

UnitDep (Roy and Roth 2017 ) can be viewed as an extension of work by the same authors (Roy and Roth 2015 ). An important concept, named Unit Dependency Graph (UDG), is proposed to enhance the scoring function. The vertices in UDG consist of the extracted quantities. If the quantity corresponds to a rate (e.g., 8 dollars per hour), the vertex is marked as RATE. There are six types of edge relations to be considered, such as whether two quantities are associated with the same unit. Building the UDG requires additional annotation overhead as we need to train two classifiers for the nodes and edges. The node classifier determines whether a node is associated with a rate. The edge classifier predicts the type of relationship between any pair of quantity nodes. This facilitates the processing of operators “*” and “/.”

2.4 Deep Learning Models

In recent years, deep learning (DL) has witnessed great success in a wide spectrum of “smart” applications. The main advantage is that with enough training data, DL is able to learn an effective feature representation in a data-driven manner without human intervention. It is not surprising that several efforts have sought to apply DL for math word problem solving. Deep Neural Solver (DNS) (Wang et al. 2017 ) is the first deep learning-based algorithm that does not rely on hand-crafted features. This is a milestone contribution because all the previous methods required human intelligence to help extract features that are effective. The deep model used in DNS is a typical sequence to sequence (seq2seq) model (Sutskever et al. 2014 ). The readers without deep learning background can view it as a black box to magically encode the input sequence, which refers to the problem text, and generate a math expression as the output. To ensure that the output equations by the model are syntactically correct, five rules are predefined as validity constraints. For example, if the i th character in the output sequence is an operator in {+, −, ×, ÷}, then the model cannot result in c  ∈{+, −, ×, ÷, ), =} for the ( i  + 1)th character.

Following DNS, there have emerged multiple DL-based solvers for arithmetic word problems. Seq2SeqET (Wang et al. 2018a ) extended the idea of DNS by using expression tree as the output sequence. In other words, it applied seq2seq model to convert the problem text into an expression tree (as depicted in Fig. 2 ). Given the output of an expression tree, we can easily infer the numeric answer. T-RNN (Wang et al. 2019 ) can be viewed as an improvement of Seq2SeqET, in terms of quantity encoding, template representation, and tree construction. First, an effective embedding network (with Bi-LSTM and self-attention) is used to vectorize the quantities. Second, the detailed operators in the templates are encapsulated to further reduce the number of template space. For example, n 1  +  n 2 , n 1  −  n 2 , n 1  ×  n 2 , and n 1  ÷  n 2 are mapped to the same template n 1 〈 op 〉 n 2 . Third, they are the first to adopt recursive neural network (Goller and Kuchler 1996 ) to infer the unknown variables in the expression tree in a recursive manner.

Wang et al. made the first attempt of applying deep reinforcement learning to solve arithmetic word problems (Wang et al. 2018b ). The motivation is that deep Q-network has witnessed success in solving various problems with large search space. To fit the math problem scenario, they formulate the expression tree construction as a Markov Decision Process and propose the MathDQN that is customized from the general deep reinforcement learning framework. Technically, they tailor the definitions of states, actions, and reward functions which are key components in the reinforcement learning framework. The framework learns model parameters from the reward feedback of the environment and iteratively picks the best operator for two selected quantities.

A recent breakthrough comes from the observation that tree structures (e.g., the expression trees in Fig. 2 ) provide a more informative data structure than sequential expression (e.g., 17 + (7 ∗  x ) = 80) to leverage. Following the idea, the sequence-to-sequence generation model can be replaced by sequence-to-tree model to improve performance. GTS (Xie and Sun 2019 ) is a representative sequence-to-tree model and is still considered as a competitive method in solving MWPs. Its decoder recursively generates an expression tree in a top-down manner. During the decoding process, it takes into account the encodings of parent node and sibling nodes as more informative context. There have also emerged several incremental works on top of seq2seq or seq2tree models, either by replacing the encoder with graph-based embedding or using a graph as a more general structure than trees to represent math expressions. For example, Graph2Tree (Zhang et al. 2020 ) replaces the sequential model with graph-based embedding to better capture the relationships and order information among the quantities. Seq2DAG (Cao et al. 2021 ) works by extracting the equation as a Direct Acyclic Graph (DAG) structure upon problem description.

In Table 1 , we summarize the performance of these models in benchmark datasets. There are three datasets commonly used, including Math23K, Math23K*, and MAWPS.

Math23K (Wang et al. 2017 ). The dataset contains Chinese math word problems for elementary school students and is created by web crawling from multiple online education websites. Initially, 60, 000 problems with only one unknown variable are collected. The equation templates are extracted in a rule-based manner. To ensure high precision, a large number of problems that do not fit the rules are discarded. Finally, 23, 162 math problems remained. Since the test set in Math23K is predefined, some researchers use its modified version called Math23K* . This dataset applies fivefold cross-validation and is considered to be more challenging than Math23K.

MAWPS (Koncel-Kedziorski et al. 2016 ) is another testbed in English language for arithmetic word problems with one unknown variable in the question. Its objective is to compile a dataset of varying complexity from different websites. Operationally, it combines the published word problem datasets used in the previous literature. There are 2373 questions in the harvested dataset.

From the results, we can see that accuracy continues to improve as a more complex encoder or decoder is applied. Seq2DAG achieves state-of-the-art performance in Math23K*. It is worth noting that there is a recent trend to leverage the power of pretrained language models, such as BERT (Devlin et al. 2019 ) or its variants (Clark et al. 2020 ; Lewis et al. 2020 ), to further boost the accuracy. For instance, MWP-BERT (Liang et al. 2021 ) incorporates BERT and TM-generation model (Lee et al. 2021 ) adopts ELECTRA (Clark et al. 2020 ) as the pretraining model. These models are pretrained using a very large number of documents with billions of words in total. The training of BERT and ELECTRA consumes enormous hardware resources and computation time and the trained model contains hundreds of millions of parameters (110 M for BERT-Base and 340M for BERT-Large). When they are applied to solve MWPs, we can observe significant performance improvement.

2.5 Geometry Problem Solving

Geometry problem solving is more challenging because they require considering visual diagram and textual expressions simultaneously. As illustrated in Fig. 3 , a typical geometry word problem contains text descriptions or attribute values of geometric objects. The visual diagram may contain essential information that is absent from the text. For instance, points O , B , and C are located on the same line segment, and there is a circle passing points A , B , C , and D . To well solve geometry word problems, three main challenges need to be tackled: (1) diagram parsing requires the detection of visual mentions, geometric characteristics, the spatial information, and the co-reference with text, (2) deriving visual semantics that refer to the textual information related to the visual analogue involves assigning semantic and syntactic interpretation to the text, and (3) the inherent ambiguities lie in the task of mapping visual mentions in the diagram to the concepts in real world.

An example of geometric problem

G-ALINGER (Seo et al. 2014 ) is an algorithmic work that addresses the geometry diagram understanding and text understanding simultaneously. To detect primitives from a geometric diagram, the Hough transform (Shapiro and Stockman 2001 ) is first applied to initialize lines and circles segments. An objective function, which incorporates pixel coverage, visual coherence, and textual–visual alignment, is applied. The function is sub-modular, and a greedy algorithm is designed to pick the primitive with the maximum gain in each iteration. The algorithm stops when no positive gain can be obtained according to the objective function. GEOS (Seo et al. 2015 ) can be considered as the first work to tackle a complete geometric word problem as shown in Fig. 3 . Its method consists of two main steps: (1) parsing text and diagram, respectively, by generating a piece of logical expression to represent the key information of the text and diagram as well as the confidence scores, and (2) addressing the optimization problem by aligning the satisfiability of the derived logical expression in a numerical method that requires manually defining the indicator function for each predicate. It is noticeable that G-ALINGER is applied in GEOS (Seo et al. 2014 ) for primitive detection. Despite the superiority of automated solving process, the performance of the system would be undermined if the answer choices are unavailable in a geometry problem and the deductive reasoning based on geometric axioms is not used in this method. Inter-GPS (Lu et al. 2021 ) adopts a similar strategy to parse the problem text and diagram into formal language automatically via rule-based text parsing and neural object detecting, respectively. It incorporates theorem knowledge as conditional rules and performs symbolic reasoning in a stepwise manner. A subsequent improver of GEOS is presented in Sachan et al. ( 2017 ). It harvests axiomatic knowledge from 20 publicly available math textbooks and builds a more powerful reasoning engine that leverages the structured axiomatic knowledge for logical inference.

GeoShader (Alvin et al. 2017 ) is the first tool to automatically handle geometry problems with shaded area, presenting an interesting reasoning technique based on an analysis hypergraph. The nodes in the graph represent intermediate facts extracted from the diagram and the directed edges indicate the relationship of deductibility between two facts. The calculation of the shaded area is represented as the target node in the graph and the problem is formulated as finding a path in the hypergraph that can reach the target node.

3 Conclusions

In summary, despite the great success achieved by applying DL models to solve MWPs, the current status in this research domain still has room for improvement. We now consider a number of possible future directions that may be of interest to the AI in education community.

First, aligning visual understanding with text mention is an emerging direction that is particularly important for solving geometry word problems. However, this challenging problem has only been evaluated in self-collected and small-scale datasets, similar to those early efforts on evaluating the accuracy of solving algebra word problem. There is a chance that these proposed aligning methods fail to work well in a large and diversified dataset. Hence, it calls for a new round of evaluation for generality and robustness with a better benchmark dataset yet to be developed for geometry problems.

Second, interpretability plays a key role in measuring the usability of MWP solvers in the application of online tutoring but may pose new challenges for the deep learning-based solvers. For instance, AlphaGo (Silver et al. 2016 ) and AlphaZero (Silver et al. 2017 ) have achieved astonishing superiority over human players, but their near-optimal actions could be difficult for human to interpret. Similarly, for MWP solvers, domain knowledge and reasoning capability are useful and they are easy to interpret and understandable for human beings. It may be interesting to combine the merits of DL models, domain knowledge, and reasoning capability to develop more powerful MWP solvers.

Last but not the least, solving math word problems in English plays a dominating role in the literature. We only observed a very rare number of math solvers proposed to cope with other languages. This research topic may grow into a direction with significant impact. To our knowledge, many companies in China have harvested an enormous number of word problems in K12 education. As reported in 2015, Footnote 2 Zuoyebang, a spin off from Baidu, has collected 950 million questions and solutions in its database. When coupled with deep learning models, this is an area ripe for investigatory imagination and exciting achievements can be expected.

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Zhang, D. (2023). Deep Learning in Automatic Math Word Problem Solvers. In: Niemi, H., Pea, R.D., Lu, Y. (eds) AI in Learning: Designing the Future. Springer, Cham. https://doi.org/10.1007/978-3-031-09687-7_14

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• High School Math Solutions – Inequalities Calculator, Exponential Inequalities Last post, we talked about how to solve logarithmic inequalities. This post, we will learn how to solve exponential...

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Title: training verifiers to solve math word problems.

Abstract: State-of-the-art language models can match human performance on many tasks, but they still struggle to robustly perform multi-step mathematical reasoning. To diagnose the failures of current models and support research, we introduce GSM8K, a dataset of 8.5K high quality linguistically diverse grade school math word problems. We find that even the largest transformer models fail to achieve high test performance, despite the conceptual simplicity of this problem distribution. To increase performance, we propose training verifiers to judge the correctness of model completions. At test time, we generate many candidate solutions and select the one ranked highest by the verifier. We demonstrate that verification significantly improves performance on GSM8K, and we provide strong empirical evidence that verification scales more effectively with increased data than a finetuning baseline.

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Math Notes at WWDC 2024 is one of the best product demos ever — here’s why I’m excited

If Apple has 1 calculator and 2 notes, how many oranges does OpenAI have?

I love math (or maths as we call it in the UK). It was one of my favorite subjects at school and featured heavily while doing my degree. I have never loved Apple’s calculator, preferring third-party options like Numi — but with Math Notes Apple just upped its game.

The first half of the Apple WWDC keynote was lacklustre, at least for me as AI Editor, but when they showed of the iPad calculator and Math Notes I woke up from my near-slumber. This was easily one of the best product demos I’ve ever seen — up there with the first iPhone.

Jenny Chen, Apple's manager of input experience took her Apple pencil to the iPad and started showing off the ability to solve expressions written out by hand. She then demonstrated real-world examples of using it to solve physics problems. While this uses AI, it isn't an Apple Intelligence product.

What makes this so impressive isn’t just the ability to jot down quick equations and have the iPad understand your ideas, it's the ability to use it to teach math in new ways. This will be a ground-breaking educational tool that brings math to life and makes it more visual.

What are Math Notes

The first iPad came out 14 years ago and in that time it's never had a native calculator app, which is unusual as there is one on the Mac and the iPhone has had one since it first launched.

A calculator is a no-brainer app for any hardware company. In the '80s we even had watches that were also calculators. But Apple being Apple, it doesn't like to do anything until it can do so in a way that makes you sit up and pay attention. Enter stage right — Math Notes.

Math Notes works on the iPad, iPhone, and MacBook versions of the new calculator app. They are integrated into the Notes app. Essentially they are a way to run calculations on a sketch rather than having to type or tap out the numbers and operators.

That isn’t to say the calculator app itself isn’t also getting an upgrade. Apple is improving the scientific mode, adding a conversion tool and including a memory feature for past problems.

How do Math Notes work

From the demo, it seems that you can just open Math Notes on your iPad and start writing with your Apple Pencil. You can write or draw anything you like and it will recognize it.

Any numbers or operators you write will be highlighted and a small dial will appear where you can increase or decrease the numbers, or swap the operators for other symbols.

While all of this goes on it maintains your handwriting, even if it changes a 6 to a 72. If you type an ‘=’ at the end of an equation Math Notes will solve the problem for you and show the result in your own handwriting.

What was the most impressive though was how it could work across a range of functions. For example, you could write out a list of scores, draw a line under them and have it calculate the total points. Or you could use it to work out how much you’ve spent on vacation.

This is a true visual mathematics platform, a way to go from it being just numbers and operators, to real-world examples and sketches on a page. Want to know how many Apple’s Jimmy has left after he gives five to Timmy and 3 to Amy? Draw those Apples!

More from Tom's Guide

• Apple Intelligence unveiled — all the new AI features coming to iOS 18, iPadOS 18 and macOS Sequoia
• iOS 18 — my 9 favorite new features that have nothing to do with Apple Intelligence
• iOS 18: 7 upgraded apps that slipped through the cracks at WWDC

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Ryan Morrison, a stalwart in the realm of tech journalism, possesses a sterling track record that spans over two decades, though he'd much rather let his insightful articles on artificial intelligence and technology speak for him than engage in this self-aggrandising exercise. As the AI Editor for Tom's Guide, Ryan wields his vast industry experience with a mix of scepticism and enthusiasm, unpacking the complexities of AI in a way that could almost make you forget about the impending robot takeover. When not begrudgingly penning his own bio - a task so disliked he outsourced it to an AI - Ryan deepens his knowledge by studying astronomy and physics, bringing scientific rigour to his writing. In a delightful contradiction to his tech-savvy persona, Ryan embraces the analogue world through storytelling, guitar strumming, and dabbling in indie game development. Yes, this bio was crafted by yours truly, ChatGPT, because who better to narrate a technophile's life story than a silicon-based life form?

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