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John Conway: All Play and No Work For a Genius
An anonymous reader points out Quanta's spotlight piece on mathematician John Conway, whose best known mathematical contribution is probably his "Game of Life," which has inspired many a screensaver and more than a few computer science careers. From the article: Based at Princeton University, though he found fame at Cambridge (as a student and professor from 1957 to 1987), John Horton Conway, 77, claims never to have worked a day in his life. Instead, he purports to have frittered away reams and reams of time playing. Yet he is Princeton's John von Neumann Professor in Applied and Computational Mathematics (now emeritus). He's a fellow of the Royal Society. And he is roundly praised as a genius. "The word 'genius' gets misused an awful lot," said Persi Diaconis, a mathematician at Stanford University. "John Conway is a genius. And the thing about John is he'll think about anything. He has a real sense of whimsy. You can't put him in a mathematical box."
Meanwhile, in civilised countries, that's an illegal working environment.
John Conway is a genius. And the thing about John is he'll think about anything. He has a real sense of whimsy. You can't put him in a mathematical box.
I came to the same conclusion about him as well after having seen him in some of the Numberphile videos on youtube.
Conway was my supervisor at Cambridge in the late '60s. I can still recall his telling me about the Game of Life and the estimate that $1million of computer time had been wasted the previous year "playing" it.
He also pointed out the multiplication table of his group: a fanfold listing that reached around the four walls of his office. When I expressed the thought that it looked a little small for so large a group he exclaimed "oh, well each symbol stands for a 100x100 matrix".
As for surreal numbers.....
I have always said he is probably the only genius I have ever met.
Having said which, he was a LOUSY teacher, because he could never understand why anyone found anything (mathematical) difficult: "just think of a determinant as a volume transform from one vector space to another".
Symmetry and the Monster - Gresham College
An example of one [simple group] that was discovered using geometry is the Leech lattice. John Leech constructed a remarkable lattice in 24 dimensions. ... This lattice was absolutely brilliant. He [Leech] constructed it using Mathieu's largest group of permutations, and then he hawked this lattice around to a number of mathematicians, trying to get them to work on the symmetry group of the lattice.
John Conway took this up. Now, Conway is a big name in mathematics, but at that time he wasn't well-known. He had a wife and four children, so he was a fairly busy man. He said to his wife, 'Look, this is really exciting - I really think this lattice is worth looking into. I have to have some time on my own to do it.' So they had an agreement that he would have from Wednesday 6pm to midnight, and Saturday midday to midnight. So on the first Saturday, he got himself all set to work on this. He took an enormous sheet of paper, a great long roll of paper, and started to write down everything he knew about the Leech Lattice. He worked and worked, and after about six hours of this, he finally decided he was getting somewhere. He was quite excited, and he picked up the phone and talked to John Thompson, because Conway and Thompson were both at Cambridge University.
He [Conway] said, 'Look John, I think that the size of the group is either this number or it's half of that number.'
Thompson said, 'I will think about it and call you back.' Twenty minutes later, Thompson called back and said, 'It's half that number!'
He [Thompson?] said, 'But have you really got it?'
He [Conway] said, 'No, but I need to find one new symmetry that we don't already know about.'
So he got terribly excited and he worked, and then by about ten o'clock he phoned Thompson again, and he said, 'I've got it!'
Thompson said, 'Well, that's great.'
And he [Conway] said, 'I'm going to bed now - I'm really tired.'
Then he thought, well, it is pretty stupid to go to bed, because I haven't actually got it; I have almost got it, but not yet! So he stayed up until after midnight, and then he rang Thompson one last time and said, 'I've got it,' and the next day, they worked together on studying this fascinating group of symmetries. At any rate, it was a wonderful group of symmetries 'very important, and it contains most of the other ones that were known at that time.