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The Biggest Problem in Mathematics Is Finally a Step Closer to Being Solved (scientificamerican.com)
38 points by gballan 3 months ago | hide | past | favorite | 25 comments



I didn't know problems in mathematics were subject to some lattice giving a definition of "biggest".

Hilbert posed several nifty problems over 100 years ago, including pithy cool ones not unlike Riemann's zeroes.

https://en.wikipedia.org/wiki/Hilbert%27s_problems

[ edited for my own typos ]


On the scale of clickbait headlines this is pretty minor.

Riemann hypothesis is an important problem that has gathered a lot of attention over an extended period of time. Is it the biggest? Whose to say. It is at least up there in the list of major open problems. Its not like its an obscure problem by any means.


In my mind, the justification for referring to RH as the “biggest” open problem in mathematics is its importance in numerous fields of mathematics. It’s hard to take three steps in analytic number theory without running into Riemann. Zeta functions — and with them RH — have transcended number theory and are fundamental objects of study in other mathematical fields, most prominently representation theory and the Langlands Program.


That Wiki page even has a section about the RH:

> The Riemann hypothesis is noteworthy for its appearance on the list of Hilbert problems, Smale's list, the list of Millennium Prize Problems, and even the Weil conjectures, in its geometric guise. Although it has been attacked by major mathematicians of our day, many experts believe that it will still be part of unsolved problems lists for many centuries. Hilbert himself declared: "If I were to awaken after having slept for a thousand years, my first question would be: Has the Riemann hypothesis been proved?"


Your complaint here is that vernacular English ("biggest") isn't as precise as mathematics?


it was a joke. i get english just fine, am a native speaker, with a pure math degree.


I'm not criticizing your skill with English. I'm criticizing your surprise that English isn't as precise as mathematics.


It was a joke. We'll have to agree to disagree. Take care now.


Oh great. The crazy guy from the street corner is now following me. I'm so surprised.

Stop harassing me you creepy fuck.


If people are interested, this is probably the best explanation of the Riemann Hypothesis I’ve seen: https://youtu.be/zlm1aajH6gY?si=d3dbimf2Y7wTe8GP


Eduard Frenkel does a pretty good job at it: https://m.youtube.com/watch?v=d6c6uIyieoo


Isn't P=NP more interesting?


Isn't this a Physics problem?




What about this?

Accurate and Infinite Prime Prediction from Novel Quasi-Prime Analytical Methodology

https://arxiv.org/abs/1903.08570


Based on the title I had hoped someone made progress in the Collatz conjecture.


Where do people look for non paywall links


Here, but as the other person commented: TFA's link is not paywalled for me neither...

https://archive.is/9AT4O


It is for me.


I was scrolling down and encountered a grey block of links, and thought I hit a paywall. But I kept scrolling and the article continued below.


FWIW, it's not paywalled for me (even in incognito mode).


Maybe it is just Firefox (128.0.2 Windows 10). I tried it with Chrome and it worked fine.


The exponent was reduced from 0.60 to 0.52. The bar for getting excited has dropped so much ...


First major improvement to the bound since 1940. Many other things can now be improved as a result, that depended on the earlier bound.




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