Mathematics news

[Evariste Euler Gauss]

Tomorrow (i.e. Monday 24th), at the Heidelberg Laureate Forum, retired Professor Michael Atiyah will deliver a lecture, in which, according to his abstract, he will deliver a proof of the Riemann Hypothesis, which is generally regarded as the greatest, most important unsolved problem in mathematics.

It's fair to say that the general buzz in the mathematical community by those who have openly speculated is very sceptical. Atiyah, whilst undoubtedly being one of the greatest mathematicians of the 20th century, is now aged 89, and there's a widepsread view that his claim will turn out to be a mistake due to old age catching up with him, a bit sad really. On the other hand, not all who have relevant expertise are sceptical.

G H Hardy once asserted that no important original result in maths had ever been achieved by anyone over 50 (due to the waning of one's mathematical powers as the brain, errm, develops with age - undoubtedly the raw logic processing power does decay substantially already by middle age, and the balance between the accumulation of relevant knowledge and the ability to use whatever knowledge one has to prove new things starts tipping downwards probably already by the age of around 40). If the Riemann Hypothesis, the greatest of all mathematical challenges, is proved tomorrow by a man aged 89, that will be nothing short of miraculous.

[I see from OTF's spellchecker, presumably based on North American software, that "sceptical" starts "sk.." west of the Atlantic.]

[ursus arctos]

Very interesting

Is there no pre-presentation review of his paper?

[Evariste Euler Gauss]

Apparently not.

[ursus arctos]

Laureate status has its advantages

[Evariste Euler Gauss]

I believe it's common in the world of mathematical research for papers to be presented without prior review (in contrast of course to publication in an academic journal where - at least in the case of any journal with a serious reputation - a full peer review process prior to publication is mandatory).

To give one famous example, Andrew Wiles announced a "proof" of Fermat's Last Theorem in 1993 in a series of lectures. His work was then examined and found to have one error, which took him (with help from Richard Taylor) around a year to fix before delivering a correct proof in 1994.

[Edit: these days maths papers sent to journals for publication tend to be simultaneously placed on some publicly accessible website called something like Arxiv, so the curious can examine them simultaneously with the referees. The privilege of delivering a high profile lecture rather than just posting something to Arxiv is one that comes with rank I guess.]

[ursus arctos]

Didn’t know that, though it makes sense in retrospect

[Wouter D]

It wouldn't be the first time someone claims to have solved a problem of this magnitude, only to be proven wrong later. However, why would an 89-year-old who is generally held in high respect risk their reputation like this, if they weren't absolutely certain about their work?

Looking forward to hearing the fallout.

[Duncan Gardner]

Doesnt ability to process complex mathematical operations tend to peak at 8 or 9 rather than 89?

At my South Belfast school we had a special prize for abstract proofs which I was fortunate to win.

In Finaghy?

No, imaginary numbers

[Bizarre Löw Triangle]

It wouldn't be the first time someone claims to have solved a problem of this magnitude, only to be proven wrong later. However, why would an 89-year-old who is generally held in high respect risk their reputation like this, if they weren't absolutely certain about their work?

Looking forward to hearing the fallout.

He's not really risking his reputation. Considering what some academics approaching senility in other fields have come out with (looking firmly at James Watson here), unveiling a proof with an error in it is hardly going to cause anyone to reassess Atiyah's earlier career.

Much of this is sort of how mathematics works. People submit their work, other people pull it apart. Sometimes, that work will stand up, sometimes it'll need patching up, sometimes it'll be unsavable. Sometimes demonstrating a new approach will lead others to use that approach to solve the problem or other problems. Sometimes it'll be fatally flawed.

[Sporting]

There's a nice maths puzzle in today's Grauniad which may interest some of the experts (not me!) here:


https://www.theguardian.com/science/...he-puzzle-king

[Evariste Euler Gauss]

Thanks Sporting, might try that one.

I'd forgotten about this thread. The story just seemed to kind of fizzle out. Clearly Atiyah provided nothing remotely close to a proof, but nobody was bold enough to dismiss it definitively, so it just seems to have been politely forgotten. Atiyah has died in the meantime.