Fermat’s Last Theorem, the Collatz Conjecture, and the Riemann Hypothesis are some famous math problems that have stumped people for centuries.
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Mathematics is a field that has challenged some of the most brilliant minds throughout history. There are several math problems that have stumped people for centuries, even millennia, and continue to be studied by mathematicians today. Among the most famous ones are Fermat’s Last Theorem, the Collatz Conjecture, and the Riemann Hypothesis.
Fermat’s Last Theorem, proposed by mathematician Pierre de Fermat in 1637, was finally proved in 1994 by Andrew Wiles, after over 350 years of attempts by several mathematicians. The theorem states that there are no whole-number solutions to the equation xⁿ + yⁿ = zⁿ when n is greater than 2. This is an important theorem in the study of number theory and is considered a triumph for modern mathematics.
The Collatz Conjecture, also known as the 3n + 1 problem, states that if you start with any positive integer, if it’s even, divide it by 2, and if it’s odd, multiply it by 3 and add 1. Repeat this process, and the conjecture claims that you will always end up at the number 1. While this may seem simple, it has yet to be proven and has puzzled mathematicians for over 80 years.
The Riemann Hypothesis, proposed by mathematician Bernhard Riemann in 1859, is a conjecture that deals with the distribution of prime numbers. The hypothesis states that the nontrivial zeros of the Riemann zeta function all lie on the critical line of 1/2. While this has been verified for the first 10 trillion zeros, it has yet to be proven rigorously, leading mathematician Charles Hermite to say, “To affirm the hypothesis would be to give a complete solution of the problem of prime numbers.”
There are many other math problems that continue to challenge mathematicians, from the P vs. NP problem to the Hodge conjecture. As mathematician and Fields Medalist Terence Tao says, “Mathematics is not a spectator sport, but a participatory endeavor. Mathematics is not a collection of independent problems, but an interconnected web of ideas. Mathematics is not a finished product, but an ongoing dialogue.” It is this ongoing dialogue that drives mathematicians to continue working on these problems and to try to gain a deeper understanding of the universe we live in.
Here is a table summarizing some of the most famous math problems and their status:
| Problem | Status |
|---|---|
| Fermat’s Last Theorem | Proven in 1994 by Andrew Wiles |
| Collatz Conjecture | Unsolved |
| Riemann Hypothesis | Unsolved, widely believed to be true |
| P vs. NP problem | Unsolved, considered one of the most important open problems in computer science |
| Hodge conjecture | Solved for certain classes of manifolds, but remains unsolved in general |
| Birch and Swinnerton-Dyer | Unsolved, one of the most famous and important problems in number theory |
In summary, mathematics is a field that continues to fascinate and challenge. As mathematician Paul Erdős famously said, “Mathematics is not about numbers, equations, computations, or algorithms: it is about understanding.” The ongoing pursuit of these math problems, even if they remain unsolved, allows us to deepen our understanding of the world around us and push the boundaries of human knowledge.
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17 Hard Math Problems That’ll Make Your Head Spin
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It took me quite a while to understand how it is that [math] 0.999… = 1[/math]. ALMOST [math]1[/math] sure, but it just seemed like they couldn’t possibly be exactly the same. I’d seen the simple algebraic proof, but it just felt wrong somehow, like the “proofs” that [math]1=2[/math].
What finally made it click for me was realizing that the definition of infinite decimal expansions (the numbers themselves aren’t infinite, only the decimal expansions) is based on the idea of the limit of an infinite sequence. [math]0.999…[/math] is defined as being the LIMIT of the infinite sequence [math][0.9, 0.99, 0.999, 0.9999…][/math] and hence, [math]0.999… = 1[/math] because of how we define things in math.
Does that feel arbitrary? It wasn’t until recently that I really understood the importance of defining things in mathematics. Unlike the physical sciences, mathematics takes place primarily in the mind — it’s about logic and what we do with it. What’s cool about math is that we can just defi…
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In this way, What are the 7 unsolved math problems?
Answer: The seven problems are the Birch and Swinnerton-Dyer Conjecture, the Hodge Conjecture, the Navier-Stokes Equations, P versus NP, the Poincaré Conjecture, the Riemann Hypothesis, and the Yang-Mills Theory. In 2003, the Poincaré Conjecture was proven by Russian mathematician Grigori Perelman.
Besides, What math question tried to stump the Internet? 8÷2(2+2)=?
If you’re like most, your answer was 16 and are flabbergasted someone else can find a different answer. Unless, that is, you’re like most others and your answer was 1 and you’re equally confused about seeing it another way.
What is the hardest known math problem?
Response: Today’s mathematicians would probably agree that the Riemann Hypothesis is the most significant open problem in all of math. It’s one of the seven Millennium Prize Problems, with $1 million reward for its solution.
In this regard, What are the math problems that haven’t been solved? The answer is: The problems consist of the Riemann hypothesis, Poincaré conjecture, Hodge conjecture, Swinnerton-Dyer Conjecture, solution of the Navier-Stokes equations, formulation of Yang-Mills theory, and determination of whether NP-problems are actually P-problems.