Fermi estimate of the week: Riemann hypothesis

In summary, the conversation discusses the concept of Fermi estimate/problem/question and its application in solving mathematical problems. The question posed is how many hours have been spent on the problem since it was first introduced by Riemann in 1859, and how many hours will be spent by the time it is solved. An estimate of 5.1 million hours has been made for the time spent on the problem so far, with an additional 5.3 million hours estimated for the future. The average prize-winnings per hour is calculated to be $0.189.
  • #1
CRGreathouse
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For those not familiar with the term Fermi estimate/problem/question see here:
http://www.vendian.org/envelope/dir0/fermi_questions.html
http://en.wikipedia.org/wiki/Fermi_problem

My question: Between the time that Riemann posed his famous question (in 1859) and now, how many hours have been expended on the problem?

Extra credit: How many hours will have been expended on the problem by the time it is solved? Assuming the Clay institute pays out its million-dollar prize at that point, what is the average prize-winnings per hour? :biggrin:
 
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  • #2
I know pretty much nothing about it, but I like Fermi problems.

I estimate 600K hours between 1859-1900, 1.7M hours between 1901-1950, and 2.8M hours between 1950-present, making 5.1M hours

It needs another few years until I solve it (SARCASM, I PROBABLY WON'T SOLVE IT), so roughly 5.3M hours.

$1M/5.3Mhours = $0.189 per hour
 

1. What is the Riemann hypothesis and why is it significant?

The Riemann hypothesis is a conjecture in mathematics proposed by German mathematician Bernhard Riemann in 1859. It states that all non-trivial zeros of the Riemann zeta function have a real part of 1/2. This has significant implications for the distribution of prime numbers and has been called the "holy grail" of number theory.

2. How does Fermi estimation relate to the Riemann hypothesis?

Fermi estimation is a method of making rough estimates based on a series of assumptions and approximations. In the case of the Riemann hypothesis, Fermi estimation can be used to estimate the number of zeroes of the Riemann zeta function that lie on the critical line, which is a key component of the hypothesis.

3. What is the current status of the Riemann hypothesis?

The Riemann hypothesis remains unsolved and is considered one of the most important unsolved problems in mathematics. Many mathematicians have attempted to prove or disprove the hypothesis, but it remains unproven despite the efforts of some of the greatest minds in mathematics.

4. Why is it so difficult to prove the Riemann hypothesis?

The difficulty in proving the Riemann hypothesis lies in the fact that it touches on many different areas of mathematics, including analysis, number theory, and complex analysis. Additionally, the hypothesis has been shown to be equivalent to other difficult problems in mathematics, making it a challenging and complex task to solve.

5. What are some potential implications if the Riemann hypothesis is proven?

If the Riemann hypothesis is proven, it could lead to a better understanding of the distribution of prime numbers and potentially unlock new mathematical discoveries. It could also have practical applications in fields such as cryptography and data encryption, as the distribution of primes is crucial in these areas.

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