The Riemann Hypothesis and Its Claimed Relevance to Finance

# Implications of the Riemann hypothesis in finance?


# Implications of the Riemann hypothesis in finance?












I was recently at a seminar by a top hedge fund manager at a top university for finance students, when one of the finance professors asked him what do you think are important areas of research for my PhD students. The hedge fund manager responded solve the Riemann hypothesis. My question is, what would be the implications if this were proved true?

## Answer by Matt Wolf (score 15, accepted)

https://quant.stackexchange.com/a/3902

I think he was jokingly suggesting to breed top PhD candidates in pure mathematics. I often heard complaints that a lot of PhDs in Mathematical disciplines lack a rigorous base in pure Mathematics. Obviously the hedge fund manager was not suggesting that the proof of the hypothesis will be in any way relevant to trading or financial pricing applications. On the other side the Riemann Integral is a basic building block of discrete time stochastic calculus which is very much relevant to financial mathematics and pricing derivatives products. But I doubt he was at all thinking about the integral when he explicitly mentioned the hypothesis.

Thus, I would chalk it up as a joke and invitation to send top level candidates his way. Its funny but hard core mathematicians learn to go all the way to the basics (or are supposed to) in order to devote their time to the studies and research of entirely abstract concepts. What they UN-learn is the ability to spot the underlying currents and humor.

My friend, I suggest you are reading way too much into his comments. I would take it as a suggestion to have the professor's students focus on the core of pure Math and that he is interested in top candidates. Not more not less. Thats my take of it.

## Answer by Akavall (score 1)

https://quant.stackexchange.com/a/7201

Riemann Hypothesis is a very import conjecture in mathematics, but it also an extremely hard problem, top mathematicians have worked on it for over 100 years and could not solve it. Moreover, one cannot start to really think about it without proper understanding of the problem; it might take years to understand what is going on even for people with strong math background. Therefore, if someone is telling you to solve Riemann Hypothesis they can't be seriously suggesting you to work on it.

As Freddy and user2303 suggested, it could've been a hint to work on math skills. Or maybe he was hinting at that the research is really not that important, "It doesn't matter what you work on".

I wasn't there and I did not feel the mood of the seminar, but I am sure the manager did not suggest students to go after the Riemann Hypothesis!

## Answer by ReeeeeeeeeMann (score 1)

https://quant.stackexchange.com/a/75443

A number of economic theorems relevant for large financial institutions depend on the truth of the Riemann Hypothesis. They include things like uniqueness results of mixed-strategy game theory equilibria, demonstration that various policies converge and are therefore (eventually) equivalent along some axes, and limiting the potential downside of classes of investment or policy.

The practical policies that depend on RH being true are obviously not going to be massively affected (unless it's proven false), but the policy-choosers will gain substantial peace of mind from upgrading their assumption to a certainty.

## Answer by user35980 (score 1)

https://quant.stackexchange.com/a/75448

The humor aspect alluded to by Matt Wolf and user2303 certainly makes sense: in that vein, since the Riemann hypothesis is one of the unsolved "Millennium" math problems for which there's a monetary award (apparently of USD 1mm) I can certainly see a HF manager's angle on it. Though why he chose that particular problem rather than, say, the Hodge Conjecture, is elusive - perhaps he has an affinity for number theory over geometry!