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Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis

viterbischool.usc.edu

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Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis

#21

Post by VMG »

logicallee wrote: post #20
impendia wrote: post #10

Speaking as an analytic number theorist, the branch of math of which the Lindelof Hypothesis is part: This is a huge deal, if true. But USC's PR machine seems to have jumped the gun. The paper in question, found here https://arxiv.org/pdf/1708.06607.pdf has so far only been posted to the arXiv (and only eight days ago). It has presumably not been subjected to any sort of peer review yet. No third party other than USC…

[EDIT: edited this comment substantially.] Speaking as an analytic number theorist, the branch of math of which the Lindelof Hypothesis is part, could you tell us what you personally think of the paper? (Let's try to avoid just gratuitous negativity: https://blog.ycombinator.com/new-hacker-news-guideline/ ) I read the paper after you linked it and it seems serious. Fokas is the guy who invented the Fokas Method - htt…

Thanks for giving us an example of a stereotypical HN comment!

Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis

#22

Post by [deleted] »

dang wrote: post #19
impendia wrote: post #10

Speaking as an analytic number theorist, the branch of math of which the Lindelof Hypothesis is part: This is a huge deal, if true. But USC's PR machine seems to have jumped the gun. The paper in question, found here https://arxiv.org/pdf/1708.06607.pdf has so far only been posted to the arXiv (and only eight days ago). It has presumably not been subjected to any sort of peer review yet. No third party other than USC…

Sure. We've put that title above.

[deleted]

Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis

#23

Post by yxhuvud »

logicallee wrote: post #20
impendia wrote: post #10

Speaking as an analytic number theorist, the branch of math of which the Lindelof Hypothesis is part: This is a huge deal, if true. But USC's PR machine seems to have jumped the gun. The paper in question, found here https://arxiv.org/pdf/1708.06607.pdf has so far only been posted to the arXiv (and only eight days ago). It has presumably not been subjected to any sort of peer review yet. No third party other than USC…

[EDIT: edited this comment substantially.] Speaking as an analytic number theorist, the branch of math of which the Lindelof Hypothesis is part, could you tell us what you personally think of the paper? (Let's try to avoid just gratuitous negativity: https://blog.ycombinator.com/new-hacker-news-guideline/ ) I read the paper after you linked it and it seems serious. Fokas is the guy who invented the Fokas Method - htt…

No, it is the proper response to unverified claims of scientific breakthrough.

Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis

#24

Post by throwaway0255 »

impendia wrote: post #10

Speaking as an analytic number theorist, the branch of math of which the Lindelof Hypothesis is part: This is a huge deal, if true. But USC's PR machine seems to have jumped the gun. The paper in question, found here https://arxiv.org/pdf/1708.06607.pdf has so far only been posted to the arXiv (and only eight days ago). It has presumably not been subjected to any sort of peer review yet. No third party other than USC…

> This is a huge deal, if true.

What's the potential benefit to humanity that could come about if this is true, without any other dependencies, over the next 30 years?

Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis

#25

Post by Cyph0n »

throwaway0255 wrote: post #24
impendia wrote: post #10

Speaking as an analytic number theorist, the branch of math of which the Lindelof Hypothesis is part: This is a huge deal, if true. But USC's PR machine seems to have jumped the gun. The paper in question, found here https://arxiv.org/pdf/1708.06607.pdf has so far only been posted to the arXiv (and only eight days ago). It has presumably not been subjected to any sort of peer review yet. No third party other than USC…

> This is a huge deal, if true. What's the potential benefit to humanity that could come about if this is true, without any other dependencies, over the next 30 years?

That's just not how pure mathematics works.

For instance, imagine asking that same question about Euler's totient function 50 years before RSA was developed.

I am sure that there are countless other examples where a seemingly useless theorem aided in a practical problem decades or centuries later.

Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis

#26

Post by adrianN »

throwaway0255 wrote: post #24
impendia wrote: post #10

Speaking as an analytic number theorist, the branch of math of which the Lindelof Hypothesis is part: This is a huge deal, if true. But USC's PR machine seems to have jumped the gun. The paper in question, found here https://arxiv.org/pdf/1708.06607.pdf has so far only been posted to the arXiv (and only eight days ago). It has presumably not been subjected to any sort of peer review yet. No third party other than USC…

> This is a huge deal, if true. What's the potential benefit to humanity that could come about if this is true, without any other dependencies, over the next 30 years?

A deeper understanding of pure mathematics? That's like asking what benefits Michelangelo's works had for humanity.

Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis

#27

Post by rfurmani »

impendia wrote: post #10

Speaking as an analytic number theorist, the branch of math of which the Lindelof Hypothesis is part: This is a huge deal, if true. But USC's PR machine seems to have jumped the gun. The paper in question, found here https://arxiv.org/pdf/1708.06607.pdf has so far only been posted to the arXiv (and only eight days ago). It has presumably not been subjected to any sort of peer review yet. No third party other than USC…

I just skimmed through it so maybe I'm missing something, but it also appears to be incomplete. It even says "the completion of the rigorous derivation of the above results will be presented in a companion paper". He brings up equation 1.6 but I don't see a rigorous handling of its asymptotics, nor any precise statement of what the growth rate of zeta on or near the critical line is expected to be. The conclusions section also says about as much. I hope it works out and we will see the conclusion, but I'd really like to see some precise growth rates so we can at least compare it to known bounds and example.

Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis

#28

Post by taneq »

impendia wrote: post #11
cbames89 wrote: post #2

Can someone eli5 the lindelof hypothesis?

The Riemann zeta function is the function zeta(s) = 1 + 1/2^s + 1/3^s + 1/4^s + 1/5^s + 1/6^s + .... For example, zeta(2) = 1 + 1/4 + 1/9 + 1/16 + 1/25 + 1/36 + ... = pi^2/6. As a partially tongue-in-cheek example, zeta(-1) = 1 + 2 + 3 + 4 + 5 + 6 + ... = -1/12. Obviously it doesn't make sense to add all the positive integers (the series doesn't converge ), but if you squint and ignore this, and just do the arithmeti…

> Obviously it doesn't make sense to add all the positive integers (the series doesn't converge), but if you squint and ignore this, and just do the arithmetic a certain way, you get -1/12.

I'm not a pure-maths type person but in my experience, if you get one answer by following simple, well understood maths (like "the sum of two positive integers is a positive integer") and another answer by "squinting and ignoring it", this doesn't mean the simple answer is wrong, it means you did something else wrong (like the hidden divide-by-zero present in your typical "proof that 1 = 2"). Paradoxes point to an error in the formulation of the question.

Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis

#29

Post by QML »

robertelder wrote: post #5
hsienmaneja wrote: post #3

What exactly is the application for cyber security? How does this affect cryptography?

I think it's because any information we gain about the Riemann Hypothesis (Lindelöf hypothesis is implied by RH) gives us information about the distribution of prime numbers. Any time you gain information about the distribution of prime numbers you immediately gain information that can be applied to any form of cryptography that makes use of prime numbers. You could use this information either to break existing forms…

We already have polynomial-time algorithm for primality testing [1]; not sure if a proof of the Riemann Hypothesis will affect cryptography by that much.

[1] https://en.wikipedia.org/wiki/AKS_primality_test

Re: Mathematician-M.D. claims to have solved the 110-year-old Lindelöf hypothesis

#30

Post by throwaway0255 »

Cyph0n wrote: post #25
throwaway0255 wrote: post #24

Earlier quoted context omitted.

> This is a huge deal, if true. What's the potential benefit to humanity that could come about if this is true, without any other dependencies, over the next 30 years?

That's just not how pure mathematics works. For instance, imagine asking that same question about Euler's totient function 50 years before RSA was developed. I am sure that there are countless other examples where a seemingly useless theorem aided in a practical problem decades or centuries later.

Now I and other non-mathematicians can look into Euler's totient function and RSA, and learn more. Thanks for answering.

So is there really never a proof in pure mathematics with more obvious or immediate near-term applications?

Are there any historical examples of that? A major breakthrough in mathematics that once understood, it was immediately obvious that it was going to make X work better, and then it did?

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