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A Solver of the Hardest Easy Problems About Prime Numbers
- irjustin 4y agoMaynard is absolutely incredible. He's up there with Terence Tao[0]. [0] https://www.quantamagazine.org/james-maynard-solves-the-hardest-easy-math-problems-20200701/ https://www.quantamagazine.org/james-maynard-solves-the-hard...
- macintux 4y agoIdly curious, did this HN post originally reference a different article? Your link is the same as the post.
- bdn_ 4y agoThe HN articles still links to this for me: https://www.quantamagazine.org/number-theorist-james-maynard-wins-the-fields-medal-20220705/ https://www.quantamagazine.org/number-theorist-james-maynard... It's possible that Quantum Magazine changed the title and is redirecting this old URL to the new one.
- irjustin 4y agoYeah I had the same problem initially. It LOOKS really similar because they both use the same picture and are by the same author. But the HNews one is 2022 and mine is back from 2020.
- macintux 4y agoAha, I see. The new article is the old one, augmented.
- wanderingmind 4y agoNot to take away anything from Maynard, but Tao is in a different league. He is the last of the generalist among mathematicians having made significant contributions to multiple streams on number theory, harmonic analysis, differential equations among others. In the age of hyper specialisation, we might never be able to see another Tao in any foreseeable future.
- meltyness 4y agoI fell under a collective (and also formally published) delusion that one might use prime factorization and run-length encoding to achieve data compression, but repeated experiments suggests this fails, when actually constructed. I've come to suspect the primes in this way are just a base, like any other. Unfortunately, I don't know how to argue one way or another very well.
- jumi99 4y agoDo you have a reference of that publication? Lossless compression should be impossible unless there's a specific probability distribution that makes some of the messages more probable than others.
- meltyness 4y agoI cede that I could be misunderstanding "Efficient Data Compression Using Prime Numbers" Authors: Kalyan Guchait Debasish Chakraborty, Snehasish Kar Conference: Emerging Research in Computing, Information, Communication and Applications Here's some code too, but it's scrapped and non-functioning mostly: https://github.com/meltyness/eggschmidt https://github.com/meltyness/eggschmidt
- FartyMcFarter 4y agoThis is a case where the general problem is easier to reason about than a specific problem. Forget about prime numbers for a moment: it is impossible to achieve lossless compression that always succeeds in compressing N bits into fewer than N bits. This is because 2^M is smaller than 2^N when M<N. You can't map X objects into fewer than X objects without losing information. So the issue is not that prime factorisation fails to reliably compress things. It's that every possible method you can try would fail to do so, no matter how advanced or fancy it is. Sometimes you'll manage to make the data smaller, sometimes you won't. Relatedly, there's an interesting proof that there exist infinite prime numbers that uses the idea of data compression in it: https://en.m.wikipedia.org/wiki/Euclid%27s_theorem#Proof_using_the_incompressibility_method https://en.m.wikipedia.org/wiki/Euclid%27s_theorem#Proof_usi...
- sneakerblack 4y agoQuanta magazine always seems to have a very approachable way of writing about complex topics that I really appreciate. I wish more organizations did what they do.