Riemann Hypothesis ...

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M

MartinQ

Guru
Ok, apologies for the limited audience for this post, but there is a(nother) claim to have proven the Riemann Hypothesis, one of the great unsolved problems in maths. The guy has form (Fields medal, Abel prize), although there have been a few other false claims in the past.
https://www.newscientist.com/articl...ims-proof-of-160-year-old-riemann-hypothesis/

Stay tuned on Monday (well I will be) ... For info, the Riemann hypothesis is about how frequently prime numbers occur and was kicked off by Gauss. Quite of a bit of the basic maths is relatively straightforward, but its proven a really tough nut to crack (150 years).
 
mjr

mjr

Comfy armchair to one person & a plank to the next
Location
mostly Norfolk, sometimes Somerset
I have discovered a truly remarkable proof of this theorem which this forum is too small to contain.
 
srw

srw

It's a bit more complicated than that...
Hmmmmmm.

Two things make me sceptical. First, as Atiyah acknowledges, most mathematicians do their best work before they're 40. He's 90. And second, he claims that the proof is "simple". History has shown that unsolved problems are generally unsolved because they're incredibly difficult. A simple "proof" is likely to be wrong, especially for such a famous question, otherwise someone would have found it.

When I was trying to be a graduate mathematician the story used to go round that every well-known number theorist had a stock of preprinted cards saying "Thank you for your proposed proof of Fermat's last theorem. The first error is on page _____."
 
C R

C R

Guru
Location
Worcester
Going slightly further off topic, the interesting thing about Fermat's theorem is that Fermat claimed to have found a simple proof, but the modern proof is anything but.

On the other hand, I don't think Riemann claimed such for his hypothesis. Also, if the proof is correct, it now becomes a theorem, doesn't it?
 
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marinyork

marinyork

Resting in suspended Animation
Location
Logopolis
There are some recent examples of some big work published later in life. **Cough** Yitang Zhang. **Cough** Number theory.

Although Zhang was a spring chicken compared to Atiyah. I didn't realise Atiyah was still alive.

I think there is a perception again thanks to Hardy (a lot of things can get blamed on Hardy's quotable bits) based on history and modern academia.
 
marinyork

marinyork

Resting in suspended Animation
Location
Logopolis
If anyone is interested there's a popular science book by Keith Devlin on the millenium prize problems. Plenty of others on just the Riemann hypothesis and many related areas.

Cheers for heads up, seen a few P v NP claims in recent years and when I was at undergraduate the Poincaré conjecture was verified as proven.
 
OP
OP
M

MartinQ

Guru
C R said:
Going slightly further off topic, the interesting thing about Fermat's theorem is that Fermat claimed to have found a simple proof, but the modern proof is anything but.

On the other hand, I don't think Riemann claimed such for his hypothesis. Also, if the proof is correct, it now becomes a theorem, doesn't it?
Click to expand...

I liked the Simpson's episode (Singh's book) which flashed up a counter example to Fermat
http://digital.vpr.net/post/did-homer-simpson-actually-solve-fermats-last-theorem-take-look#stream/0
and the Dr Who (Christmas?) episode where he talks about giving a proof of Fermat's Last Theorem, not the Wiles one, the real one ...

I think Riemann was fully aware that he'd not proven it, but the link between summing natural numbers and multiplying primes is neat. Whether it becomes a theorem is interesting, although I think it would cause shock waves if it wasn't right.
 
nickyboy

nickyboy

Norven Mankey
Location
You want hills? We got hills
Well I think the chances of Atiyah having a cast iron proof of the Riemann hypothesis are slim but Monday will be an interesting day one way or another

I went back to looking at the maths, inspired by this thread. But I found I had drunk more bourbon than was probably wise
 
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