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problem-solving

Definition of problem-solving

Examples of problem-solving in a sentence.

These examples are programmatically compiled from various online sources to illustrate current usage of the word 'problem-solving.' Any opinions expressed in the examples do not represent those of Merriam-Webster or its editors. Send us feedback about these examples.

Dictionary Entries Near problem-solving

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“Problem-solving.” Merriam-Webster.com Dictionary , Merriam-Webster, https://www.merriam-webster.com/dictionary/problem-solving. Accessed 12 Jul. 2024.

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“Problem-Solving” Or “Problem Solving”? Learn If It Is Hyphenated

Is it problem-solving or problem solving? Hyphenation rules seem to be a little confusing when you’re first picking up a language. Don’t worry, though. They’re not nearly as complicated as the language may have led you to believe!

Problem-Solving Or Problem Solving – Hyphenated Or Not?

When we discuss the problem-solving hyphen rule, we learn that problem-solving is hyphenated when used to modify a noun or object in a sentence. We keep the two words separated when using them as their own noun and not modifying anything else in the sentence.

Examples Of When To Use “Problem-Solving”

Examples of when to use “problem solving”.

Though much less common to be seen written as a phrase noun, it is still worth mentioning. It’s grammatically correct to use “problem solving” at the end of a sentence or clause without a hyphen. However, as we stated above, many people are beginning to prefer the ease of sticking to the hyphenated spelling, meaning that it’s slowly phasing out of existence even in this form.

Is Problem-Solving Hyphenated AP Style?

Should i capitalize “solving” in the word “problem-solving”.

The second option capitalizes all words except for short conjunctions, short prepositions, and articles. In this case, you will always capitalize “problem” but always leave “solving” uncapitalized. The final option capitalizes every single word in a title. No matter what, you’ll capitalize both words in “problem-solving” when using this style to write your titles.

Does The Rule Also Apply To “Problem Solver” Vs “Problem-Solver”?

The same rule does apply when we use “problem solver” instead of “problem solving.” However, it’s not often that we’ll see a “problem-solver” modifying a noun or object (unless it’s a problem-solver robot or something). So, it’s most likely you’ll write “problem solver.”

Alternatives To “Problem-Solving”

If you’re still struggling with the hyphen rule of whether it’s problem solving or problem-solving, there’s one last thing we can help you with. We can give you some alternatives that have the same meanings but don’t require a hyphen. This way, you can be safe in your own knowledge without having to worry about getting the rules wrong.

Quiz – Problem-Solving Or Problem Solving?

Quiz answers.

English Recap

Problem Solving or Problem-Solving?

problem solving a noun

The term problem-solving with a hyphen is an adjective that describes nouns in a sentence. E.g., “The problem-solving abilities of this program are excellent.” Furthermore, the term problem solving without a hyphen is a noun. E.g., “He is excellent at problem solving.”

The term problem solving can appear as two different word types, a noun or a compound adjective.

When problem-solving has a hyphen, it is an adjective describing a noun .

For example, in this sentence, problem-solving describes capabilities , which is a noun. Therefore, you need to include a hyphen.

  • Her problem-solving capabilities are outstanding.

However, when you use problem solving as a noun , the term is usually not hyphenated because it doesn’t modify anything.

  • She is an expert at all types of problem solving .

Furthermore, the rule of using a hyphen for the adjective but not for the noun is correct grammar according to AP Style and the Chicago Manual of Style .

Sometimes in English, the rules concerning punctuation, such as hyphens, are vague. For example, in the Cambridge and Oxford dictionaries, the noun problem-solving appears with a hyphen.

Essentially, you should always use a hyphen for the term problem-solving as an adjective. However, for problem solving as a noun, unless you follow a specific style guide like AP that does not use a hyphen, you can choose whether to hyphenate the noun. Just make sure that you are consistent with your choice.

In addition, Google Ngram shows that problem solving without a hyphen is slightly more popular in the US than with a hyphen. However, in the UK , the hyphenated version is slightly more frequent.

Now that you have learned the basics concerning the term problem solving, please keep reading the rest of the article to learn more about using the two variations of problem solving .

Problem Solving

The term problem solving as two words without a hyphen is the noun form.

In terms of use, it relates to resolving problems, which can relate to problems in a specific discipline or more general problems.

In the following examples, the term problem solving refers to the act of solving problems. Therefore, we do not need a hyphen.

  • Her inability to perform problem solving on any task means that she loses her temper quickly.
  • You should include problem solving as a skill on your resume.
  • In team projects, effective problem solving can lead to innovative solutions and successful outcomes.
  • Problem solving is not just about finding immediate answers but understanding the root cause of the issue.
  • Her approach to problem solving often involves breaking down complex tasks into manageable steps.

Furthermore, you should use the above rule when following both AP Style or the Chicago Manual of Style.

Problem-Solving

The term problem-solving as one word with a hyphen is a compound word that appears before a noun. Hence, it modifies the noun .

For example, in the following sentence, the word problem-solving modifies the noun skills.

  • His problem-solving skills are the best in the company.
  • Her problem-solving approach is both methodical and creative, making her a valuable asset to the team.
  • The workshop focuses on problem-solving techniques to address everyday challenges.
  • Many employers prioritize candidates with strong problem-solving abilities in dynamic work environments.
  • The game challenges children to use their problem-solving instincts to navigate various puzzles.

Furthermore, you will come across some sentences in which the noun problem solving has a hyphen.

As shown in these examples:

  • You need to work on your problem-solving if you want to become an engineer.
  • Improving your problem-solving is essential for success in mathematics.
  • Mastering problem-solving will greatly benefit you in software development.

This is often a stylistic choice . However, in writing that follows AP Style , you should not use a hyphen with the noun form of problem solving.

Problemsolving

The word problemsolving as a single word with no hyphen or space is incorrect , and you shouldn’t use it in this format.

There are two ways you can use the term problem solving .

The first is as a noun, in which case there is no hyphen, but there is a space.

  • Correct: He is excellent at problem solving because he never gives up. (noun)
  • Incorrect: He is excellent at problemsolving because he never gives up. (noun)
  • Correct : She has a knack for problem solving , especially in high-pressure situations. (noun)
  • Incorrect : She has a knack for problemsolving , especially in high-pressure situations. (noun)

Also, you can write problem-solving as an adjective, in which case you need a hyphen.

  • Correct: He is excellent at problem solving because he never gives up. (adjective)
  • Incorrect: He is excellent at problemsolving because he never gives up. (adjective)
  • Correct : They often turn to her for advice on problem solving in challenging situations. (adjective)
  • Incorrect : They often turn to her for advice on problemsolving in challenging situations. (adjective)

That’s all you need to know about the grammar rules concerning the words problem solving , problem-solving , and problemsolving . Rest assured that your sentences will be correct if you follow these!

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Meaning of problem-solving in English

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Examples of problem-solving

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Problem Solving or Problem-Solving

Problem Solving or Problem-Solving?

The term “Problem-Solving” or “Problem Solving” often takes center stage in discussions about overcoming challenges. However, the nuances in its usage can be perplexing. This exploration aims to dissect the word, observing its forms as a noun, adjective, and verb. Through five examples for each category, we’ll emphasize correct spelling and punctuation, while delving into the importance of adhering to grammar rules.

The focal point will be the distinction between “Problem Solving” as a verb phrase, “Problem-Solving” as a hyphenated adjective or noun, and the incorrect form “Problem Solving.” Furthermore, we’ll highlight the consistency in usage between UK and US English.

The Noun Form: Problem-Solving

Correct examples.

  • Effective problem-solving requires a systematic approach.
  • The team showcased remarkable problem-solving skills during the crisis.
  • Our workshop focused on collaborative problem-solving techniques.
  • She excelled in the art of creative problem-solving .
  • The conference highlighted the importance of collective problem-solving efforts.

Incorrect Examples

  • Effective problem solving requires a systematic approach.
  • The team showcased remarkable problem solving skills during the crisis.
  • Our workshop focused on collaborative problem solving techniques.
  • She excelled in the art of creative problem solving .
  • The conference highlighted the importance of collective problem solving efforts.

Note: The correct noun form is “problem-solving” with a hyphen.

The Adjective Form: Problem-Solving

  • The problem-solving approach proved successful in the project.
  • Her problem-solving mindset made her an asset to the team.
  • A problem-solving mindset is crucial for navigating challenges.
  • The group showcased effective problem-solving techniques.
  • They developed innovative problem-solving strategies.
  • The problem solving approach proved successful in the project.
  • Her problem solving mindset made her an asset to the team.
  • A problem solving mindset is crucial for navigating challenges.
  • The group showcased effective problem solving techniques.
  • They developed innovative problem solving strategies.

Note: When used as an adjective, “problem-solving” should be hyphenated.

Read More: In Person or In-Person?

The Verb Form: Problem Solving

  • The team collectively worked on problem solving for the project.
  • She excels in problem solving by breaking down complex issues.
  • They actively engage in collaborative problem solving .
  • The committee is dedicated to effective problem solving .
  • The approach involves strategic problem solving .
  • The team collectively worked on problem-solving for the project.
  • She excels in problem-solving by breaking down complex issues.
  • They actively engage in collaborative problem-solving .
  • The committee is dedicated to effective problem-solving .
  • The approach involves strategic problem-solving .

Note: The correct verb form is “problem solving” without a hyphen.

Importance of Grammar Rules

Adhering to grammar rules is paramount for effective communication. Consistency in the use of hyphens, especially in words like “problem-solving,” ensures clarity and maintains the intended meaning. Proper grammar also contributes to professionalism in written and spoken communication.

Consistency in UK and US English

The usage of “problem-solving” remains consistent between UK and US English. Regardless of geographical location, the hyphenated form is universally accepted and preferred.

In conclusion, understanding the nuances of “Problem-Solving” versus “Problem Solving” is vital for clear and effective communication. The correct usage varies depending on whether it functions as a noun, adjective, or verb. Adhering to grammar rules, including the proper placement of hyphens, enhances the precision of language.

The consistency in usage across UK and US English simplifies the application of these rules globally. So, whether discussing strategies, approaches, or mindsets, the choice between hyphenation and separation holds significance in conveying the right message.

Ethan Richards is currently an English instructor at a university. She has experience in teaching and assessing English tests including TOEFL, IELTS, BULATS, FCE, CAE, and PTEG . With over a decade of teaching expertise, Ethan Richards  utilizes his knowledge to develop English lessons for her audience on English Overview.

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Ethan Richards is an English teacher at a university.

He has experience teaching and grading English tests like TOEFL, IELTS, BULATS, FCE, CAE, and PTEG . With over 10 years of teaching experience, Ethan Richards creates English lessons for readers on English Overview .

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Problem solving.

  • noun the thought processes involved in solving a problem see more see less types: show 14 types... hide 14 types... enquiry , inquiry , research a search for knowledge calculation , computation , figuring , reckoning problem solving that involves numbers or quantities nature study the study of animals and plants in the natural world (usually at an elementary level) experiment , experimentation the testing of an idea empirical research an empirical search for knowledge investigation , probe an inquiry into unfamiliar or questionable activities canvass , opinion poll , poll , public opinion poll , survey an inquiry into public opinion conducted by interviewing a random sample of people heraldry the study and classification of armorial bearings and the tracing of genealogies extrapolation (mathematics) calculation of the value of a function outside the range of known values interpolation (mathematics) calculation of the value of a function between the values already known conversion a change in the units or form of an expression: "conversion from Fahrenheit to Centigrade" approximation , estimate , estimation , idea an approximate calculation of quantity or degree or worth derivative , derived function , differential , differential coefficient , first derivative the result of mathematical differentiation; the instantaneous change of one quantity relative to another; df(x)/dx integral the result of a mathematical integration; F(x) is the integral of f(x) if dF/dx = f(x) type of: cerebration , intellection , mentation , thinking , thought , thought process the process of using your mind to consider something carefully
  • noun the area of cognitive psychology that studies the processes involved in solving problems see more see less type of: cognitive psychology an approach to psychology that emphasizes internal mental processes

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problem–solving

  • problem–solving (noun)
  • Let's do some problem-solving and see if we can't figure out what to do.
  • mathematical problem-solving
  • problem-solving skills
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What are the Differences in Meaning Between "Problem Solving" and "Solving Problems"

Problem Solving tells us what you do.

Solving Problems tells us what you do it to.

Is there any other difference in meaning in the context of math word problems?

user 85795's user avatar

  • "He loves nothing better than problem solving; or, "He loves nothing better than solving problems." Each sentence says pretty much the same thing. –  rhetorician Commented Dec 25, 2014 at 2:45

2 Answers 2

In principle a connection of gerund and object can have three forms

1 the solving of problems (in Latin Grammar "problems" is called genetivus objectivus, i.e. "problems" corresponds to an object in a normal sentence with a finite verb.)

2 solving problems

3 problem solving/problem-solving

In 1 we have the full form with the and of. 2 is derived from 1 by dropping the and of. 3 is derived from 2 by putting "problems" in front position.

All three forms have the same meaning. Which form will be used is a matter of style. Form 2 is the common form.

Even "I'm solving problems" might be derived from form 1: I'm at/in the act of (the) solving (of) problems.

rogermue's user avatar

Well, "problem solving" is a noun (or, when hyphenated, an adjective); but "solving problems" is a present-progressive tense verb with an object.

Thus, "He has good problem-solving skills." But: "I am solving problems", rather than "I am problem solving".

But these are only matters of syntax. In answer to your question, no, there is no difference in meaning.

Brian Hitchcock's user avatar

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problem solving a noun

problem solving (noun), problem-solving (adjective)

open when used as a noun; hyphenated when used as an adjective.

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noun as in difficulty; bad situation

Strongest matches

  • complication

Strong matches

  • botheration
  • disagreement
  • predicament

Weak matches

  • can of worms
  • disputed point
  • point at issue

noun as in puzzle, question

  • illustration
  • brainteaser
  • cliff-hanger
  • mind-boggler
  • sixty-four thousand dollar question

Example Sentences

We can now create video-game quality simulations to evaluate complex skills like creativity or problem-solving.

The competition will be an ersatz astronaut training program of sorts, including physical challenges, as well as puzzles and problem-solving tasks, as well as emotionally challenging scenarios, according to Deadline.

Lindsey Graham has changed after 25 years in Washington into someone who puts his political fortunes ahead of problem-solving.

When you have armed soldiers on the streets, I think, as a public affairs officer, that’s a perception problem in and of itself.

The problem in Venezuela is not the oil, it’s the political system.

Several times, either because they forgot or they had a technical problem, they connected directly, and we could see them.

Every once in a while, they act swiftly and acknowledge the problem.

Part of the problem is the mandate of the war and the means with which the U.S. is fighting it do not match up.

The third problem is the evidence of corroborating witnesses.

But this physical involvement, or lack of it, is only part of the problem.

And now let me come to the second problem we opened up in connection with college education—the problem of its extension.

No man can believe it who tests it by his reason in the same way in which he would test any modern problem.

But the essential problem of to-day is to know how far we are to depart from its principles.

We notice that more attention is given to the problem of placing a feature than to that of making a likeness of it.

But the West is not in its essence a time problem; there, they can wait—next week—next month.

Related Words

Words related to problem are not direct synonyms, but are associated with the word problem . Browse related words to learn more about word associations.

noun as in trouble

  • deep trouble
  • dire straits
  • disappointment
  • inconvenience

noun as in difference of opinion

  • altercation
  • apple of discord
  • controversy
  • grounds for war
  • matter at hand
  • point in question
  • tender spot

noun as in trouble, inconvenience

  • aggravation
  • exasperation
  • molestation
  • pain in the neck

noun as in annoyance

  • disturbance

Viewing 5 / 73 related words

On this page you'll find 128 synonyms, antonyms, and words related to problem, such as: complication, dilemma, dispute, headache, issue, and obstacle.

From Roget's 21st Century Thesaurus, Third Edition Copyright © 2013 by the Philip Lief Group.

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Stumped five ways to hone your problem-solving skills.

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Respect the worth of other people's insights

Problems continuously arise in organizational life, making problem-solving an essential skill for leaders. Leaders who are good at tackling conundrums are likely to be more effective at overcoming obstacles and guiding their teams to achieve their goals. So, what’s the secret to better problem-solving skills?

1. Understand the root cause of the problem

“Too often, people fail because they haven’t correctly defined what the problem is,” says David Ross, an international strategist, founder of consultancy Phoenix Strategic Management and author of Confronting the Storm: Regenerating Leadership and Hope in the Age of Uncertainty .

Ross explains that as teams grapple with “wicked” problems – those where there can be several root causes for why a problem exists – there can often be disagreement on the initial assumptions made. As a result, their chances of successfully solving the problem are low.

“Before commencing the process of solving the problem, it is worthwhile identifying who your key stakeholders are and talking to them about the issue,” Ross recommends. “Who could be affected by the issue? What is the problem – and why? How are people affected?”

He argues that if leaders treat people with dignity, respecting the worth of their insights, they are more likely to successfully solve problems.

Best High-Yield Savings Accounts Of 2024

Best 5% interest savings accounts of 2024, 2. unfocus the mind.

“To solve problems, we need to commit to making time to face a problem in its full complexity, which also requires that we take back control of our thinking,” says Chris Griffiths, an expert on creativity and innovative thinking skills, founder and CEO of software provider OpenGenius, and co-author of The Focus Fix: Finding Clarity, Creativity and Resilience in an Overwhelming World .

To do this, it’s necessary to harness the power of the unfocused mind, according to Griffiths. “It might sound oxymoronic, but just like our devices, our brain needs time to recharge,” he says. “ A plethora of research has shown that daydreaming allows us to make creative connections and see abstract solutions that are not obvious when we’re engaged in direct work.”

To make use of the unfocused mind in problem solving, you must begin by getting to know the problem from all angles. “At this stage, don’t worry about actually solving the problem,” says Griffiths. “You’re simply giving your subconscious mind the information it needs to get creative with when you zone out. From here, pick a monotonous or rhythmic activity that will help you to activate the daydreaming state – that might be a walk, some doodling, or even some chores.”

Do this regularly, argues Griffiths, and you’ll soon find that flashes of inspiration and novel solutions naturally present themselves while you’re ostensibly thinking of other things. He says: “By allowing you to access the fullest creative potential of your own brain, daydreaming acts as a skeleton key for a wide range of problems.”

3. Be comfortable making judgment calls

“Admitting to not knowing the future takes courage,” says Professor Stephen Wyatt, founder and lead consultant at consultancy Corporate Rebirth and author of Antidote to the Crisis of Leadership: Opportunity in Complexity . “Leaders are worried our teams won’t respect us and our boards will lose faith in us, but what doesn’t work is drawing up plans and forecasts and holding yourself or others rigidly to them.”

Wyatt advises leaders to heighten their situational awareness – to look broadly, integrate more perspectives and be able to connect the dots. “We need to be comfortable in making judgment calls as the future is unknown,” he says. “There is no data on it. But equally, very few initiatives cannot be adjusted, refined or reviewed while in motion.”

Leaders need to stay vigilant, according to Wyatt, create the capacity of the enterprise to adapt and maintain the support of stakeholders. “The concept of the infallible leader needs to be updated,” he concludes.

4. Be prepared to fail and learn

“Organisations, and arguably society more widely, are obsessed with problems and the notion of problems,” says Steve Hearsum, founder of organizational change consultancy Edge + Stretch and author of No Silver Bullet: Bursting the Bubble of the Organisational Quick Fix .

Hearsum argues that this tendency is complicated by the myth of fixability, namely the idea that all problems, however complex, have a solution. “Our need for certainty, to minimize and dampen the anxiety of ‘not knowing,’ leads us to oversimplify and ignore or filter out anything that challenges the idea that there is a solution,” he says.

Leaders need to shift their mindset to cultivate their comfort with not knowing and couple that with being OK with being wrong, sometimes, notes Hearsum. He adds: “That means developing reflexivity to understand your own beliefs and judgments, and what influences these, asking questions and experimenting.”

5. Unleash the power of empathy

Leaders must be able to communicate problems in order to find solutions to them. But they should avoid bombarding their teams with complex, technical details since these can overwhelm their people’s cognitive load, says Dr Jessica Barker MBE , author of Hacked: The Secrets Behind Cyber Attacks .

Instead, she recommends that leaders frame their messages in ways that cut through jargon and ensure that their advice is relevant, accessible and actionable. “An essential leadership skill for this is empathy,” Barker explains. “When you’re trying to build a positive culture, it is crucial to understand why people are not practicing the behaviors you want rather than trying to force that behavioral change with fear, uncertainty and doubt.”

Sally Percy

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Synonyms for Problem-solving

Nouns  - 41.

Alternatively

Synonyms for Problem-solving

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Definition of problem noun from the Oxford Advanced American Dictionary

Want to learn more?

Find out which words work together and produce more natural-sounding English with the Oxford Collocations Dictionary app. Try it for free as part of the Oxford Advanced Learner’s Dictionary app.

problem solving a noun
18400.0004
18500.0003
18600.0003
18700.0008
18800.0017
18900.0024
19000.0044
19100.0089
19200.011
19300.018
19400.035
19500.052
19600.07
19700.087
19800.098
19900.1
20000.1
20100.098

Where does the noun problem-solver come from?

Earliest known use

The earliest known use of the noun problem-solver is in the 1840s.

OED's earliest evidence for problem-solver is from 1848, in British Quarterly Review .

problem-solver is formed within English, by compounding.

Etymons: problem n. , solver n.

Nearby entries

  • problemist, n. a1631–
  • problemistic, adj. 1892–
  • problemize, v. 1844–
  • problemless, adj. 1865–
  • problemo, n. 1985–
  • problem of three bodies, n. 1814–
  • problem-orientated, adj. 1951–
  • problem-oriented, adj. 1946–
  • problem play, n. 1894–
  • problem-solve, v. 1956–
  • problem-solver, n. 1848–
  • problem-solving, n. & adj. 1854–
  • problem tape, n. 1948–
  • problem-wise, adv. a1859–
  • pro-Boarder, n. 1902–
  • pro-Boerism, n. 1899–
  • probole, n.¹ 1684–1880
  • probole, n.² 1696–
  • probolistic, adj. 1876–
  • pro bono, adv. & adj. 1774–
  • pro bono publico, adv. 1640–

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Meaning & use

Entry history for problem-solver, n..

Originally published as part of the entry for problem, n.

problem, n. was revised in June 2007.

oed.com is a living text, updated every three months. Modifications may include:

  • further revisions to definitions, pronunciation, etymology, headwords, variant spellings, quotations, and dates;
  • new senses, phrases, and quotations.

Earlier versions of this entry were published in:

OED First Edition (1908)

  • Find out more

OED Second Edition (1989)

  • View problem in OED Second Edition

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Citation details

Factsheet for problem-solver, n., browse entry.

Mathematicians Are Edging Close to Solving One of the World's 7 Hardest Math Problems

And there’s $1 million at stake.

opened safe deposit with glowing insides

  • In new research, mathematicians have narrowed down one of the biggest outstanding problems in math.
  • Huge breakthroughs in math and science are usually the work of many people over many years.
  • Seven math problems were given a $1 million bounty each in 2000, and just one has been solved so far.

The “Millennium Problems” are seven infamously intractable math problems laid out in the year 2000 by the prestigious Clay Institute, each with $1 million attached as payment for a solution. They span all areas of math , as the Clay Institute was founded in 1998 to push the entire field forward with financial support for researchers and important breakthroughs.

But the only solved Millennium Problem so far, the Poincare conjecture, illustrates one of the funny pitfalls inherent to offering a large cash prize for math. The winner, Grigori Perelman, refused the Clay prize as well as the prestigious Fields Medal. He withdrew from mathematics and public life in 2006, and even in 2010, he still insisted his contribution was the same as the mathematician whose work laid the foundation on which he built his proof, Richard Hamilton.

Math, all sciences, and arguably all human inquiries are filled with pairs or groups that circle the same finding at the same time until one officially makes the breakthrough. Think about Sir Isaac Newton and Gottfried Leibniz, whose back-and-forth about calculus led to the combined version of the field we still study today. Rosalind Franklin is now mentioned in the same breath as her fellow discoverers of DNA, James Watson and Francis Crick. Even the Bechdel Test for women in media is sometimes called the Bechdel-Wallace Test, because humans are almost always in collaboration.

That’s what makes this new paper so important. Two mathematicians—Larry Guth of the Massachusetts Institute of Technology (MIT) and James Maynard of the University of Oxford—collaborated on the new finding about how certain polynomials are formed and how they reach out into the number line. Maynard is just 37, and won the Fields Medal himself in 2022. Guth, a decade older, has won a number of important prizes with a little less name recognition.

The Riemann hypothesis is not directly related to prime numbers , but it has implications that ripple through number theory in different ways (including with prime numbers). Basically, it deals with where and how the graph of a certain function of complex numbers crosses back and forth across axes. The points where the function crosses an axis is called a “zero,” and the frequency with which those zeroes appear is called the zero density.

In the far reaches of the number line, prime numbers become less and less predictable (in the proverbial sense). They are not, so far, predictable in the literal sense—a fact that is an underpinning of modern encryption , where data is protected by enormous strings of integers made by multiplying enormous prime numbers together. The idea of a periodic table of primes, of any kind of template that could help mathematicians better understand where and how large primes cluster together or not, is a holy grail.

In the new paper, Maynard and Guth focus on a new limitation of Dirichlet polynomials. These are special series of complex numbers that many believe are of the same type as the function involved in the Riemann hypothesis involves. In the paper, they claim they’ve proven that these polynomials have a certain number of large values, or solutions , within a tighter range than before.

In other words, if we knew there might be an estimated three Dirichlet values between 50 and 100 before, now we may know that range to be between 60 and 90 instead. The eye exam just switched a blurry plate for a slightly less blurry one, but we still haven’t found the perfect prescription. “If one knows some more structure about the set of large values of a Dirichlet polynomial, then one can hope to have improved bound,” Maynard and Guth conclude.

No, this is not a final proof of the Riemann hypothesis. But no one is suggesting it is. In advanced math, narrowing things down is also vital. Indeed, even finding out that a promising idea turns out to be wrong can have a lot of value—as it has a number of times in the related Twin Primes Conjecture that still eludes mathematicians.

In a collaboration that has lasted 160 years and counting, mathematicians continue to take each step together and then, hopefully, compare notes.

Headshot of Caroline Delbert

Caroline Delbert is a writer, avid reader, and contributing editor at Pop Mech. She's also an enthusiast of just about everything. Her favorite topics include nuclear energy, cosmology, math of everyday things, and the philosophy of it all. 

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He Turned His High School Science Fair Project Into a Product That Solves a $390 Billion Problem: 'This Has Not Been Done Before' Vasya Tremsin was just 18 years old when he came up with the idea for outdoor fire sensor company Torch Sensors.

By Amanda Breen Edited by Jessica Thomas Jul 11, 2024

Key Takeaways

  • Torch Sensors' innovative network of sensors can detect fires at great distances, providing comprehensive protection.
  • Tremsin says adaptability and continuous learning are essential for young entrepreneurs pursuing their big ideas.

In 2018, Vasya Tremsin, now COO of outdoor fire sensor company Torch Sensors , was a senior in high school when he saw a familiar but troubling sight on a drive back from Lake Tahoe : a "really big" California wildfire . "I thought to myself, Why does this happen over and over and over? " Tremsin recalls.

problem solving a noun

Growing up in the state, Tremsin often saw large wildfires alongside the highway and on the news, but something clicked that day, and after further research, he realized that "the problem was actually way worse" than he'd believed. Some experts estimate that wildfires account for 20% of total greenhouse gas emissions , and a 2023 congressional report found that they cost the U.S. economy hundreds of billions of dollars annually .

When Tremsin began exploring the issue, "there was basically no technology" that could detect wildfires early enough to stop them before they grew larger, he says. So Tremsin decided to work on the idea for a science fair project — and his invention went on to win the best-of-category award at the International Science and Engineering Fair.

Related: 8 Tips for Entrepreneurial High School Students Ready to Start Their First Businesses

A judge at the fair encouraged Tremsin to turn his idea into a real product . "I was just a high school student," he says, "so I wasn't aware of how startups or funding works or how to build a company — because I was 18 years old." However, one of the judges introduced Tremsin to Michael Buckwald, the co-founder and then-CEO of Leap Motion, a hand-tracking sensor technology company. Buckwald would become Tremsin's co-founder, along with his father, Anton Tremsin, and now serves as Torch Sensors' CEO.

"We quickly realized that at scale, this technology would be much more powerful."

Tremsin says the first prototype for the sensor took a while to build, as they had to make it "very robust" with reliable detection capabilities. To that end, they outfitted the product with infrared and spectral analysis cameras and gas, temperature and humidity sensors, all of which work in tandem "to give you a confident measurement" confirmed by multiple variables, Tremsin explains.

problem solving a noun

"We quickly realized that at scale , this technology would be much more powerful," Tremsin says. "The sensors can actually create this network aspect, and they can cover and protect an entire area — an entire property or community. We went from just one sensor spotting a fire to building a network of sensors covering a whole terrain."

Additionally, Torch Sensors uses its data and other wildfire data sources to help spread the "safety net."

"We [went] to different types of burns all around California to test and calibrate the sensors ourselves," Tremsin says. "After that, we were ready to demo to the big customers. We've been doing a lot of demos within the past year and a half, and we have good feedback , especially about the distance that we are able to see the fire from — we were able to see a fire that's just a few feet in size from the distance of a football field. Sometimes, you couldn't even see it with your eyes, but our sensors were still able to spot it that far away."

Related: The Economic Toll of Maui Wildfires Could Reach a Staggering $6 Billion, Governor Encourages Tourists to 'Help Speed the Recovery'

problem solving a noun

Image Credit: Courtesy of Torch Sensors

Torch Sensors' product generated considerable interest from large enterprises and communities with substantial assets that needed protection.

"They're constantly in a state of pain and worry because of wildfires that can come to them and destroy a lot of the things that they've built or own," Tremsin explains. "So we're alleviating that pain as much as possible with this all-in-one solution that includes a deep-tech hardware product and all of the data we collect."

Related: 21 Success Tips for Young and Aspiring Entrepreneurs

We were literally not able to ramp up and scale the production as fast as we needed for the thousands of acres of coverage that we had demand for."

The high demand has proven challenging from a supply-chain standpoint, Tremsin says.

"We were literally not able to ramp up and scale the production as fast as we needed for the thousands of acres of coverage that we had demand for," he explains, "which is a great problem to have, but it also creates a lot of pressure. We've had utility companies, parks, government entities, private landowners, asking us, 'When can I have this product? When is it going to be ready? We really need this.'"

Fortunately, the company found at least two suppliers for each key sensitive component to help streamline the process as it moves forward. Tremsin says the company is conducting its first batch of enterprise pilot tests this summer.

Related: Jeff Bezos Gets Slammed for Meager 690,000 Donation to Australian Wildfire Crisis

problem solving a noun

Being a young entrepreneur hasn't been without its challenges, Tremsin admits, especially when it comes to establishing credibility and trust . "As a very young person, I've had to prove that our technology does what we claim it does," he says. "Because it's so novel and has not been done before, there's a lot of initial skepticism about what our product can do."

As Torch Sensors continues to prove its technology and scale, Tremsin looks forward to expanding to areas outside the U.S. and doing further research and development on product capabilities, whether it's increasing the sensors' range, decreasing their power usage or making them even better at detecting. He hopes to develop some of those capabilities with government agencies to garner more widespread support and "help all of us fight the problem of wildfires at scale."

Related: 15 Young Founders Rethinking Everything From Artificial Intelligence to Carbon Removal, Sustainable Fashion to...Pizza!

"I had to become more open-minded and willing to accept any and all feedback."

Tremsin also has some advice for young entrepreneurs who want to see their big idea make a real impact on the world.

"Be as adaptable as you can, and treat everything as a learning experience," Tremsin says. "Step one is destroying your ego and being willing to accept that your opinion and way of doing something might be wrong, and it might be best for you to change it. Everything, no matter how difficult or uncomfortable it is in the moment, is a learning experience [that] will 100% come in handy in the future. While building Torch, I had to become more open-minded and willing to accept any and all feedback, whether it's from my customers, my co-founders or even from the people who work for me. And I've gained a terrific base of knowledge."

This article is part of our ongoing Young Entrepreneur® series highlighting the stories, challenges and triumphs of being a young business owner.

Entrepreneur Staff

Senior Features Writer

Want to be an Entrepreneur Leadership Network contributor? Apply now to join.

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problem solving a noun

About Words – Cambridge Dictionary blog

Commenting on developments in the English language

problem solving a noun

Committing, tackling, and solving: Talking about crime

Listen to the author reading this blog post.

A car with a smashed side window

by  Liz Walter

Today’s post is the first in a short series on the topic of crime and it looks at some general vocabulary. Once again, I will be focusing on collocations , or words that go together.

The most important verb you need to talk about crime is commit . We use this both with the word ‘crime’ itself, and with the names of specific crime such as murder or theft . Remember not to use the verb ‘do’ – although people would understand you, it would be considered an error in an exam:

They were committing a crime by flying their drone in the area.

What led her to commit murder?

Someone who commits a crime is a criminal . A nice collocation for a person who has committed a lot of crimes and doesn’t care much about them is hardened criminal :

By the time he was thirty, he was already a hardened criminal.

In more formal contexts, a crime can be called an offence (UK)/ offense (US). The related noun is  offender :

It’s an offence to smoke in this building.

He works with young offenders.

Serious crimes are very bad, whereas the adjectives minor or the slightly more formal petty are used for less serious crimes. Another common collocation is violent , for crimes where people are hurt. In US English, the terms felony and misdemeanor are used to distinguish between serious and less serious crimes. ‘Felony’ is often used before the name of a specific crime:

She was accused of committing a serious crime.

Many of these youngsters are involved in petty crime.

He was held on a charge of felony assault.

The assault was classed as a misdemeanor.

There are several nice collocations connected with stopping crime or making it less common. We try to prevent or reduce crime, or slightly more emphatically to fight , tackle , or combat it:

Improved street lighting can reduce crime.

The government has set out new measures to tackle crime.

If you report a crime, you tell the police about it. The police investigate crimes, and with luck, solve them:

We reported the break-in immediately.

Officers are investigating a shooting in the area.

Her evidence helped police solve the crime.

A common way of describing types of crime is to put another noun in front of the word ‘crime’, for example, gun crime , knife crime , hate crime (committed because of prejudice such as racism), and sex crime :

There has been an increase in knife crime.

Damage to the mosque is being treated as a hate crime.

If someone commits a lot of crimes, we might say they go on a crime spree , while a crime wave occurs when lots of crimes are committed in a particular period:

The gang went on a crime spree, stealing several cars.

Drug addiction has led to a crime wave in the area.

My next post will continue the theme of crime, looking particularly at ways of taking about stealing.

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6 thoughts on “ Committing, tackling, and solving: Talking about crime ”

I’m so happy you’re back with your posts 🙂 (Btw has there ever been a post on this blog on problems with neighbours?)

Thanks, we’ll be able to speak accurately considering these comments.

Thank you for bringing us a useful lesson.

Thank you for your efforts it is more useful words. We wish audio lesson in future

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What cognitive tests can show — and what they can’t

Image

FILE - President Joe Biden, speaks during a presidential debate hosted by CNN with Republican presidential candidate former President Donald Trump, June 27, 2024, in Atlanta. Political opponents, armchair pundits and even nervous supporters are demanding that President Joe Biden undergo cognitive testing after his dismal debate performance – even though his physician says he gets, and passes, an annual neurologic exam. (AP Photo/Gerald Herbert, File)

The memorandum released by the White House from President Joe Biden’s physician Kevin C. O’Connor to White House press secretary Karine Jean-Pierre is photographed Monday, July 8, 2024, in Washington. Political opponents, armchair pundits and even nervous supporters are demanding that President Joe Biden undergo cognitive testing after his dismal debate performance – even though his physician says he gets, and passes, an annual neurologic exam. (AP Photo/Jon Elswick)

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WASHINGTON (AP) — It’s the new chant in Washington politics: “Get a cognitive test!”

Political opponents, armchair pundits and even nervous supporters are demanding that President Joe Biden undergo such testing after his dismal debate performance – even though his physician says he gets, and passes, an annual neurologic exam.

Former President Donald Trump, who’s only a few years younger, makes his own gaffes . He recently bragged about passing a 2018 cognitive test – while calling the doctor who administered it by the wrong name .

With all the concern, what can cognitive testing actually tell about a person’s brain health – and what can’t they answer? And presidents aside, does the average older adult need one?

What are cognitive tests?

They’re brief screening tools, a 10-minute series of questions to assess different brain functions. Two of the most common are called the MMSE, Mini-Mental State Exam, and the MoCA, Montreal Cognitive Assessment.

Recalling a list of five unrelated nouns or seeing how many words beginning with F you can say in a minute can assess short-term memory and language. Counting backward by 7s tests attention and concentration. Drawing a clock with the correct time is a clue to spatial awareness.

Image

How reliable are cognitive screenings?

They don’t diagnose health problems. A bad score is just a red flag that indicates a need for further testing to see if there is a health problem and uncover what kind, said Dr. James Galvin, a neurologist at the University of Miami.

This article is part of AP’s Be Well coverage, focusing on wellness, fitness, diet and mental health. Read more Be Well.

A good score usually is good news. But the highly educated especially tend to be good test-takers even if cognitive trouble is starting to brew. So if someone scores OK yet they, a family member or the doctor sees some day-to-day concern, more testing still could be warranted.

“We simply use it as a benchmark to determine our suspicion level,” Galvin said.

When and how often should cognitive screenings be done?

“A screening test is exactly a snapshot in time. So it tells you in that moment how someone does on that test,” Galvin stressed. “It doesn’t tell you how a person is functioning in their everyday life.”

Simply reporting a concern is reason enough for a primary care doctor to perform one. But it’s also supposed to be part of the annual Medicare wellness visit for those 65 and older.

Galvin wouldn’t discuss Biden or Trump because he hasn’t examined them — but said that generally it’s a good idea for seniors to get checked yearly to spot changes. It’s much like how doctors don’t assume your blood pressure’s still fine, they measure it.

How is a cognitive test different from a neurologic exam?

Cognitive screenings are “pencil and paper tests” usually handled by primary care doctors, while neurologic exams generally are performed by a specialist, Galvin said.

It’s a very detailed physical exam. Doctors watch the patient’s speech patterns and behavior, test how key nerves are functioning, check reflexes that can signal brain diseases and assess muscle tone and function.

If either kind of test signals real cognitive concerns, the next step may be more intensive neuropsychological testing — an exam that often lasts up to three hours.

After an exhaustive interview of the patient and any accompanying family members, the neuropsychologist goes through tests and tasks designed to check specific brain functions – intelligence, memory, verbal ability, problem-solving and reasoning skills, visual and auditory responses, emotion and mood. They may use puzzles, objects to rearrange, or drawing and writing tests.

Blood tests and brain scans also may be ordered. Special types of PET scans can detect Alzheimer’s hallmark amyloid plaques and tau tangles in the brain. An MRI can detect past strokes, helpful in diagnosing vascular dementia.

How can you tell if cognitive concerns are a disease or just getting older?

“Age makes us do things a lot slower,” Galvin said. “We move slower. We think slower. But we’re still moving correctly and we’re still thinking correctly – it just takes us longer.”

Examples of slower cognitive “processing” might be difficulty remembering a name, numbers or specific details under pressure – but they come back to you later.

Galvin noted that sometimes, reversible health problems mimic cognitive trouble. For example, urinary tract infections are notorious for causing sudden confusion in older people. Certain medications affect memory, as can thyroid problems, depression, even poorly controlled diabetes.

Anyone who’s worried about their memory should talk to their doctor, or seek a specialist, “who can reassure you that everything’s OK or develop a treatment plan that’s specific for you,” he said.

The Associated Press Health and Science Department receives support from the Howard Hughes Medical Institute’s Science and Educational Media Group. The AP is solely responsible for all content.

problem solving a noun

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COMMENTS

  1. Problem-solving Definition & Meaning

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  2. "Problem-Solving" Or "Problem Solving"? Learn If It Is Hyphenated

    When discussing the problem-solving hyphen rule, we learn that problem-solving is hyphenated when used to modify a noun or object.

  3. problem-solving noun

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  4. Problem Solving or Problem-Solving?

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  5. PROBLEM-SOLVING definition

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  6. PROBLEM-SOLVING

    PROBLEM-SOLVING definition: the process of finding solutions to problems: . Learn more.

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    problem-solving, n. & adj. meanings, etymology, pronunciation and more in the Oxford English Dictionary

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    This article discusses "Problem Solving or Problem-Solving" exploring its forms as a noun, adjective, and verb with examples for each usage and spelling.

  9. Definition of 'problem-solving'

    The act or process of finding solutions to problems, esp by using a scientific or analytical.... Click for English pronunciations, examples sentences, video.

  10. Problem solving

    problem solving: 1 n the thought processes involved in solving a problem Types: show 14 types... hide 14 types... enquiry , inquiry , research a search for knowledge calculation , computation , figuring , reckoning problem solving that involves numbers or quantities nature study the study of animals and plants in the natural world (usually at ...

  11. Problem-Solving or Problem Solving? Hyphenation Best Practices

    Discover the correct usage of "Problem-Solving" or "Problem Solving" in our comprehensive guide. Learn about hyphenation rules, when to use it, and improve your writing skills for clear communication.

  12. 80 Synonyms & Antonyms for PROBLEM-SOLVING

    Find 80 different ways to say PROBLEM-SOLVING, along with antonyms, related words, and example sentences at Thesaurus.com.

  13. Problem-solving Definition & Meaning

    Britannica Dictionary definition of PROBLEM-SOLVING. [noncount] : the process or act of finding a solution to a problem. Let's do some problem-solving and see if we can't figure out what to do. mathematical problem-solving. problem-solving skills. ASK THE EDITOR.

  14. What is another word for problem-solving

    Synonyms for problem-solving include analytic, analytical, diagnostic, logical, methodical, scientific, systematic, investigative, pinpointing and rational. Find more ...

  15. Which noun express the action of solving a problem?

    0 When I want to express the action or process of solving a (mathematical) problem, I always doubt among using "the problem resolution", "the problem solving" or "the problem solution". Which is the most suitable one?

  16. What are the Differences in Meaning Between "Problem Solving" and

    1 Well, "problem solving" is a noun (or, when hyphenated, an adjective); but "solving problems" is a present-progressive tense verb with an object.

  17. problem solving (noun), problem-solving (adjective)

    problem solving (noun), problem-solving (adjective) open when used as a noun; hyphenated when used as an adjective.

  18. 59 Synonyms & Antonyms for PROBLEM

    Find 59 different ways to say PROBLEM, along with antonyms, related words, and example sentences at Thesaurus.com.

  19. Stumped? Five Ways To Hone Your Problem-Solving Skills

    Problems often arise in organizational life. From understanding the root cause of a problem to using the power of empathy, here are five strategies for solving problems.

  20. 22 Noun Synonyms for Problem-solving

    Another way to say Problem-solving? Synonyms for Problem-solving (nouns).

  21. problem noun

    Definition of problem noun in Oxford Advanced American Dictionary. Meaning, pronunciation, picture, example sentences, grammar, usage notes, synonyms and more.

  22. Definition of 'problem-solving'

    noun. the act or process of finding solutions to problems, esp by using a scientific or analytical approach. Problem-solving is often carried on by processes of visualization. an approach to problem-solving. Collins English Dictionary.

  23. problem-solver noun

    problem-solver, n. meanings, etymology, pronunciation and more in the Oxford English Dictionary

  24. Best Games That Reward Creative Problem-Solving

    Scribblenauts Unlimited builds on its predecessors with an expansive list of nouns, adjectives, and adverbs that players can use and provides multiple ways to solve each puzzle. The game doesn't ...

  25. Explained: Importance of critical thinking, problem-solving skills in

    Here is why it is important to include skills like problem-solving and critical thinking in the curriculum.

  26. Are Mathematicians Close to Solving This Notorious Math Problem?

    Mathematicians Are Edging Close to Solving One of the World's 7 Hardest Math Problems. ... But the only solved Millennium Problem so far, the Poincare conjecture, illustrates one of the funny ...

  27. His High School Project Would Solve a Problem Worth Billions

    He Turned His High School Science Fair Project Into a Product That Solves a $390 Billion Problem: 'This Has Not Been Done Before' Vasya Tremsin was just 18 years old when he came up with the idea ...

  28. Committing, tackling, and solving: Talking about crime

    Expand your vocabulary with this collection of words and collocations for talking about crime and criminal behaviour.

  29. What cognitive tests can show

    After an exhaustive interview of the patient and any accompanying family members, the neuropsychologist goes through tests and tasks designed to check specific brain functions - intelligence, memory, verbal ability, problem-solving and reasoning skills, visual and auditory responses, emotion and mood.

  30. What cognitive tests can show -- and what they can't

    Recalling a list of five unrelated nouns or seeing how many words beginning with F you can say in a minute can assess short-term memory and language. ... problem-solving and reasoning skills ...