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problem
/ˈpɹɒbləm/
In everyday conversation, "problem" can be used as a casual way to say "you're welcome" (e.g., "No problem!"). When talking about math or logic, we usually use the verb "solve" with this word. In formal writing, you might use words like "issue" or "challenge" instead of "problem" to sound more professional.
💬Casual Conversation
KAREN THE SCREEN IS BLACK. I THINK I HAVE A PROBLEM.
Just reboot it, Eleanor. I can't deal with this right now.
Meanings
Examples
I just can't find the problem in this code!
Look, we have a huge problem with the rent, okay?
I've got a small problem with my order, actually.
Is there a problem with the payment method?
That math problem is way too hard for me.
We need to solve this problem before the deadline.
I'm sorry, but that is not my problem now.
Wait, is this a problem we can actually fix?
Collocations & Compounds
solve a problem
To find a solution to a difficult situation or mathematical question.
serious problem
A matter that is very unwelcome, harmful, or dangerous.
problem-solving skills
The ability to find solutions to complex issues or challenges.
tackle a problem
To make determined efforts to deal with a difficult situation.
math problem
A mathematical question proposed for solution via calculation.
Idioms & Sayings
no problem
A phrase used to indicate that a request is easy to fulfill or as a polite response to "thank you".
part of the problem
A contributing factor to a larger difficulty or unwelcome situation.
a problem of [something]
Used to describe a specific type of difficulty, such as "a problem of timing".
Cultural Context
In the world of mathematics, a "problem" is not merely an obstacle or a mistake; it is a mountain to be climbed, a riddle that defines the boundaries of human knowledge. Perhaps the most legendary examples are the Millennium Prize Problems, seven of the most difficult mathematical challenges announced by the Clay Mathematics Institute in 2000. Each problem carries a staggering one-million-dollar prize, but for the mathematicians who pursue them, the money is secondary to the prestige of solving a mystery that has baffled geniuses for decades.
The most famous of these is the Riemann Hypothesis, which concerns the distribution of prime numbers. For over a century, it has remained an unsolved problem, acting as a gateway to understanding the very architecture of arithmetic. To solve it would be to unlock a secret pattern in the chaos of numbers, fundamentally altering our approach to cryptography and number theory.
The narrative of these problems reached a fever pitch with the resolution of the Poincaré Conjecture. For nearly a hundred years, this problem regarding the nature of three-dimensional spheres was considered impenetrable. Then came Grigori Perelman, a reclusive Russian mathematician who solved it in 2002 by posting his proofs on an online archive rather than through traditional academic channels. In a move that shocked the global community, Perelman refused both the Fields Medal and the million-dollar prize, stating that his contribution was no greater than that of the mathematicians who had previously worked on the problem.
This intersection of obsession, intellect, and humility highlights a profound psychological truth: the human mind is biologically wired to seek closure. The "problem" acts as a catalyst for evolution; by attempting to solve an impossible question, we develop new tools, new languages, and new ways of thinking. Whether it is the P versus NP problem or the Navier-Stokes equations, these challenges remind us that the beauty of mathematics lies not in the answer, but in the relentless, agonizing, and exhilarating pursuit of a solution.