How Many Mathematicians Are Secretly Trying to Solve the Riemann Hypothesis?

In summary: A mathematician says that although they might not admit it, most mathematicians try to solve the Riemann hypothesis in their spare time.
  • #1
nonequilibrium
1,439
2
I once had a math professor who said that although they might not admit it, most mathematicians try to solve the Riemann hypothesis in their spare time.

How true is this? Who is trying to solve the Riemann hypothesis? I don't just mean "are you?" (although feel free to speak up if you are) but more generally: how big is the group that is trying to solve this? I suppose this strongly depends on how you define "trying"; I can imagine a lot of different levels of "trying it seriously".
 
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  • #2
Define "trying to solve". There are entire fields of mathematics who's developments shed light on the zeta function, do the people working in those field qualify?
 
  • #3
You can define it yourselves; I welcome answers from different perspectives.

I'd personally be more curious about people that are directly tackeling the problem, without "just" proving results about the zeta function in the hope it might be helpful for other people; on the other that might be the only way to go about it :)

And what about regular mathematicians; do they ever try? Even in their spare time (as claimed by my professor)? Does perhaps most, say, complex analysis mathematicians try to tackle it in their spare time (now and then)?
 
  • #4
I think the statement might be a little too general IMO ;)
 
  • #5
I'm willing to bet there are far more cranky amateurs trying to prove RH than there are professional mathematicians. Less cranks than was previously the case for the superficially far more accessible FLT, but still many.

Lots of these guys are even convinced they've succeeded, but "The Man" (the mathematical establishment) wants to keep them down and suppress their marvellous discovery for its own sinister reasons.
 
  • #6
Right now I am deep in the Belly of the Beast... again. Count me in.
 
  • #7
I've solved it, it was pretty easy.
 
  • #8

What is the Riemann Hypothesis?

The Riemann Hypothesis is a mathematical conjecture proposed by mathematician Bernhard Riemann in 1859. It states that all non-trivial zeros of the Riemann zeta function lie on the critical line with the real part of 1/2. This hypothesis is considered one of the most important unsolved problems in mathematics.

Why is solving the Riemann Hypothesis important?

The Riemann Hypothesis has connections to several important areas of mathematics, including number theory, complex analysis, and probability theory. Its solution would also have implications for prime number theory, which is crucial in fields such as cryptography and data encryption. Additionally, solving the Riemann Hypothesis would provide a better understanding of the distribution of prime numbers, which has practical applications in various fields.

What progress has been made towards solving the Riemann Hypothesis?

Since its proposal, the Riemann Hypothesis has been extensively studied by mathematicians, but no one has been able to prove or disprove it. Several related theorems and conjectures have been proven, but the Riemann Hypothesis itself remains unsolved. The Clay Mathematics Institute has even named it as one of the seven Millennium Prize Problems, offering a prize of $1 million for its solution.

How do mathematicians approach the Riemann Hypothesis?

There is no one definitive approach to solving the Riemann Hypothesis. Some mathematicians use analytical methods, while others use algebraic or geometric techniques. Many have also tried to connect the hypothesis to other mathematical concepts and problems in the hope of finding a solution. Overall, it requires a deep understanding of complex analysis and number theory, as well as creativity and persistence.

What would the impact of solving the Riemann Hypothesis be on mathematics?

The solution to the Riemann Hypothesis would have a profound impact on mathematics. It would resolve one of the most important unsolved problems and potentially lead to new insights and developments in various areas of mathematics. It would also have practical applications in fields such as data encryption and cryptography. Additionally, it would contribute to our understanding of the fundamental properties of numbers and their distribution, which has been a subject of fascination for mathematicians for centuries.

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