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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

#51

Post by algorithm314 »

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…

In my university,my professor told us about the existance of this proof in December,and that he gave a presentation that time.So i guess it has been reviewed thoroughly.

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

#52

Post by fifnir »

naturalgradient wrote: post #50

Just pointing out that interestingly Cambridge, where Fokas is a professor, has not released anything. He is merely visiting USC so it strikes me as weird that they would claim this PR so quickly. Also Mathematician-MD somehow makes it sound like the MD means he is a lesser mathematician or not a full mathematician. Fokas is a well respected Professor at one of the top applied Maths departments in the world. A better…

Isn't MD for..like.. medical doctors ?

If he's an MD but without a medical degree (which I guess is the case), then what's the difference betweeen MD, PHD or 'professor' ??

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

#53

Post by naturalgradient »

fifnir wrote: post #52
naturalgradient wrote: post #50

Just pointing out that interestingly Cambridge, where Fokas is a professor, has not released anything. He is merely visiting USC so it strikes me as weird that they would claim this PR so quickly. Also Mathematician-MD somehow makes it sound like the MD means he is a lesser mathematician or not a full mathematician. Fokas is a well respected Professor at one of the top applied Maths departments in the world. A better…

Isn't MD for..like.. medical doctors ? If he's an MD but without a medical degree (which I guess is the case), then what's the difference betweeen MD, PHD or 'professor' ??

So this goes off on a tangent but I feel it relates to noncentrality [0]. Fokas has a PhD in maths. Being an MD or having gotten an MD 40 years ago is clearly entirely non-central to his career. Calling him Mathematician-MD seems like it is meant to make him seem a lesser mathematician, e.g. by insinuating that this is just something he does part time, and that he can hence be taken less seriously.

I don't know what the poster meant by suggesting 'Mathematician-MD', but it reads weirdly to me for that reason. It's highlighting an attribute of a person that is entirely unrelated to his career or this article. Why if not to denigrate him? The title should be changed to neutrally reflect his position.

https://www.lesswrong.com/posts/yCWPkLi8wJvewPbEp/the-noncen...

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

#54

Post by stochastic_monk »

fifnir wrote: post #52
naturalgradient wrote: post #50

Just pointing out that interestingly Cambridge, where Fokas is a professor, has not released anything. He is merely visiting USC so it strikes me as weird that they would claim this PR so quickly. Also Mathematician-MD somehow makes it sound like the MD means he is a lesser mathematician or not a full mathematician. Fokas is a well respected Professor at one of the top applied Maths departments in the world. A better…

Isn't MD for..like.. medical doctors ? If he's an MD but without a medical degree (which I guess is the case), then what's the difference betweeen MD, PHD or 'professor' ??

If you inspect [0], you'll find that his MD was, in fact, in medicine. What came before that, though, was a PhD in applied math from Caltech, and that immediately after receiving his MD he became chair of Clarkson University's Math and Computer Science department.

Mentioning his MD is a distraction and, as the previous poster commented, suggests that he's something of an amateur. This is very far from the case.

[0] http://www.damtp.cam.ac.uk/user/tf227/

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

#55

Post by hypeibole »

naturalgradient wrote: post #53
fifnir wrote: post #52

Earlier quoted context omitted.

Isn't MD for..like.. medical doctors ? If he's an MD but without a medical degree (which I guess is the case), then what's the difference betweeen MD, PHD or 'professor' ??

So this goes off on a tangent but I feel it relates to noncentrality [0]. Fokas has a PhD in maths. Being an MD or having gotten an MD 40 years ago is clearly entirely non-central to his career. Calling him Mathematician-MD seems like it is meant to make him seem a lesser mathematician, e.g. by insinuating that this is just something he does part time, and that he can hence be taken less seriously. I don't know what…

I actually believe the intent is the opposite.

I think the PR people are just trying to sell Fokas as a polymath genius. "Look, he is not only a mathematician but also an MD, wow!"

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

#56

Post by hardlianotion »

taneq wrote: post #28
impendia wrote: post #11

Earlier quoted context omitted.

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…

In this case, it's worth pointing out that the zeta function admits a functional definition in which you can define some points of the function about their "reflection" in the line Re(z) = 1/2. This allows a perfectly rigorous definition of the function for values like -1. One might call the functional form more fundamental and note that the series form only holds true for Re(z) > 1.

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

#57

Post by naturalgradient »

hypeibole wrote: post #55
naturalgradient wrote: post #53

Earlier quoted context omitted.

So this goes off on a tangent but I feel it relates to noncentrality [0]. Fokas has a PhD in maths. Being an MD or having gotten an MD 40 years ago is clearly entirely non-central to his career. Calling him Mathematician-MD seems like it is meant to make him seem a lesser mathematician, e.g. by insinuating that this is just something he does part time, and that he can hence be taken less seriously. I don't know what…

I actually believe the intent is the opposite. I think the PR people are just trying to sell Fokas as a polymath genius. "Look, he is not only a mathematician but also an MD, wow!"

Thank you, I had not considered that. I think researchers or a HN audience may perceive this differently than the average reader.

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

#58

Post by Koshkin »

Doxin wrote: post #44
taneq wrote: post #43

Earlier quoted context omitted.

> So classically 1-1+1-1+1... doesn't converge, but if you "squint" and take the running averages of the partial sums (1,0,1,0,...) you would get 1/2 Why would you take the running average and how is that relevant to the sum?

He's taking the running average of the partial sums: 1-1 = 0 0+1 = 1 1-1 = 0 0+1 = etc etc The partial sum would end up being equal to the final sum by definition when you're done summing all items. Since we're talking about infinite sequences you're never done summing all items so you'll have to do something else to end up with an answer. for example seeing which way the partial sum trends. In this case it trends so…

> In this case it trends solidly in the direction of 1/2

...except that it doesn't; to me, it even looks more like it trends in the opposite direction, i.e. it is trying to stay away from 1/2.

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

#59

Post by hammock »

Doxin wrote: post #44
taneq wrote: post #43

Earlier quoted context omitted.

> So classically 1-1+1-1+1... doesn't converge, but if you "squint" and take the running averages of the partial sums (1,0,1,0,...) you would get 1/2 Why would you take the running average and how is that relevant to the sum?

He's taking the running average of the partial sums: 1-1 = 0 0+1 = 1 1-1 = 0 0+1 = etc etc The partial sum would end up being equal to the final sum by definition when you're done summing all items. Since we're talking about infinite sequences you're never done summing all items so you'll have to do something else to end up with an answer. for example seeing which way the partial sum trends. In this case it trends so…

>...except that it doesn't; to me, it even looks more like it trends in the opposite direction, i.e. it is trying to stay away from 1/2.

Like two magnets repelling each other: if you were to hold them together and we call that 1/2 - but they are always trying to push away from each other!

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

#60

Post by pure-awesome »

throwaway0255 wrote: post #30
Cyph0n wrote: post #25

Earlier quoted context omitted.

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?

The maths that has an immediate near-term application usually falls, almost by definition, under applied mathematics (or possibly a related field, such as physics, engineering, computer science etc.).

Pure mathematics essentially concerns itself with the mathematics of mathematics. It's basically the process of trying to either prove certain "empirically discovered" mathematical facts, or understand deeply what those facts mean in a more general way. Understanding this type of mathematics in this deep way allows further mathematics to bud off of that specific

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