"I always want to try to understand why things work. I’m not interested
in getting a formula without knowing what it means. I always try to
dig behind the scenes, so if I have a formula, I understand why it’s
there. And understanding is a very difficult notion. People think
mathematics begins when you write down a theorem followed by a
proof. That’s not the beginning, that’s the end. For me the creative
place in mathematics comes before you start to put things down on
paper, before you try to write a formula. You picture various things,
you turn them over in your mind. You’re trying to create, just as a
musician is trying to create music, or a poet. There are no rules laid
down. You have to do it your own way. But at the end, just as a
composer has to put it down on paper, you have to write things
down. But the most important stage is understanding. A proof by itself
doesn’t give you understanding. You can have a long proof and no idea
at the end of why it works. But to understand why it works, you have
to have a kind of gut reaction to the thing. You’ve got to feel it."
– Sir Michael Francis Atiyah
Sad to hear that Michael Atiyah has died. I studied many of his papers, and I enjoyed his classical "Introduction to commutative algebra" (which is by no means an introduction to the field). Also I had the honor to meet him several years ago in person. He had a kind and humble character, and by no means I felt I was discussing mathematics with one of the best mathematicians of the previous century. He was always lowering his level to match mine. He explained everything clear and he gave good advice that helped my career in many ways. Thank you, and requiescat in pace.
An amazing mathematician, to put it lightly. I remember learning the Atiyah-Singer index theorem  and how it relates to anomalies in quantum theories, it absolutely blew my mind. And then every time I came back to anomalies I would rediscover this fact and be floored again, one of my favorite physics/theory/math connections.
 e.g. https://en.wikipedia.org/wiki/Atiyah%E2%80%93Singer_index_th... (though not the best for the more physics minded)
For anyone with an interest in maths, do give https://youtu.be/uMN5t3tzchI a watch
Thanks, we've changed to that first link from https://en.wikipedia.org/wiki/Michael_Atiyah.
That makes me sad. He came across as such a gentle and down to earth mathematician. He truly was math nobility.
quantamagazine did a nice write up on Michael Atiyah back in 2016. They rightly brought it back to the font page. Here is a link:
This is a sad story, mostly about everyone deciding what the most kind way is to treat broken work by someone whose best days are well behind them.
Interesting discussion at:
And mathematicians taking him seriously:
You don’t have to be a follower of a famous mathematician to find sadness in the intellectual decline of someone.
Our ability to preserve bodies far longer than mind is a major problem for everyone.
Mainstream consensus is that his 'proof' didn't do anything besides introducing an analytic function called the Todd function that doesn't appear to satisfy his claims.
Can you please add any link(s) for further reading?
Unfortunately, his proof is broken and didn't help community make progress on the problem.
Wow. Sir Michael Atiyah claimed he solved Riemann hypothesis just short four months ago.
I followed this reasonably closely, and I didn't see anyone in the Math community criticize Atiyah. And Math is certainly pretty pro-speculation.
People were mostly just sad that journalists were hyping up an obvious case of age-related cognitive decline from a brilliant Mathematician.
And to be clear, Atiyah's last work wasn't speculation – it was completely off, in the "not even wrong" category. Unfortunately, that's pretty common as people get older, but there's no reason to publicize it.
>Unfortunately, that's pretty common as people get older
Are there other examples of this in Mathematicians? Nash and Godel come to mind, but both of them had non-math-related issues.
i think it is relatively common in creatively brilliant people who become older. some people solve problems in ways that are counterintuitive and against the grain. it takes a lot of courage to do this, especially social courage. so for the few people that have success with this way of thinking, as they get older, they are trying to resummon the processes they've used before. much of that includes not listening to those who tell you you're wrong. but some declination of mental faculties makes this a bit dangerous as the mind isn't as sharp as it once was. although some of it may be even as simple as they miss the attention.
this is my theory anyway.
Note to self: Keep a pet-puzzle(s) that is difficult but solvable. As I grow old, keep solving the puzzles to determine how senile I am. No need to believe others assertions at face value.
Try these? https://artofproblemsolving.com/wiki/index.php/AIME_Problems...
I seem to recall that another mathematician, John Conway, did something a bit like that: perhaps he had set up his computer to force him to do his "Doomsday" algorithm in his head whenever he logged on, or something like that. I can't remember exactly (perhaps I'm going a bit senile).
That's interesting ideas. Only caveat is after awhile brain will learn the pattern and you might solve on autopilot.
It seems to me people were more upset with the conference organizers allowing him to submit the talk knowing he was going senile, though I don't know the full story or whether or not he was going senile.
It is not hard to say that something is wrong. It is not hard to hope that someone so intelligent is allowed to show publicly how his intelligence has gone astray.
It's sad to me that people were so hard on him for his last works. I wish mathematics had a positive space for speculation.