More Geometry Whilst Re-visiting John Conway

 A little John Conway courtesy of Futility Closet:

https://www.futilitycloset.com/2021/08/15/the-conway-circle-theorem/

Siobhan Roberts Returns With More...

You probably think you've read enough about him by now, but yet another fantastic Siobhan Roberts' piece on John Conway in today's NY Times (ought not be missed):

https://www.nytimes.com/2020/05/16/science/john-conway-math.html

ADDENDUM:  ...and a day later, Jim Propp adds his own personal memories/experience to the mix:
https://mathenchant.wordpress.com/2020/05/16/confessions-of-a-conway-groupie/

Playing Games

From the inimitable John Conway:

“You get surreal numbers by playing games. I used to feel guilty in Cambridge that I spent all day playing games, while I was supposed to be doing mathematics. Then, when I discovered surreal numbers, I realized that playing games IS mathematics.”

Numbers are Very Real

Sunday reflection: 

"It’s quite astonishing and I still don’t understand it, having been a mathematician all my life. How can things be there without actually being there? There’s no doubt that 2 is there or 3 or the square root of omega. They’re very real things. I still don’t know the sense in which mathematical objects exist, but they do. Of course, it’s hard to say in what sense a cat is there, too, but we know it is, very definitely. Cats have a stubborn reality but maybe numbers are stubborner still. You can’t push a cat in a direction it doesn’t want to go. You can’t do it with a number either. I’m only using the word number because you’ll have a vague idea in your head as to what I mean. The objects that a mathematician studies are more abstract than numbers but very real.
"I often think of cats. I think of trees. I think of dogs occasionally but I don’t think of them all that much because dogs are agreeable. They do what you want them to do to some extent. Some people believe that mathematics is what we think it is and it’s created by our thoughts. I don’t. I’m a Platonist at heart, although I know there are very great difficulties in that view."

           -- John Conway

For Now Just a Note

All my life my tastes/interests have been rather mis-aligned from the American masses. So it wasn't altogether surprising that this morning I found myself in line at Barnes & Noble with about a half-dozen folks in front of me clutching their new, just-released Harper Lee sequel, and a half-dozen folks in back of me doing the same... and me in the middle clutching Siobhan Roberts' newly-released "Genius At Play" (which a manager had to dig out of the backroom for me, because they had forgotten to put it out on display!).
By the time I reached the cashier he gave me this look as if to say, 'What's THIS? are you sure this is what you meant to pick up?' To which I was responding silently in my head with, 'WHAT is WR-R-RONG with YOU people! you're reading a pack of lies and made-up fiction when you could be reading about the true life of a fascinating, actual human being; grrrrummmpffff.' ...But I stayed silent.

Anyway, I'm only a few dozen pages into this volume and feel safe in saying every mathematician out there (perhaps even most scientists) will want to read this wonderful account. Likely, most biography-lovers (which entails a lot of people) will also enjoy it immensely. Outside of those two categories, I'm not sure who will be drawn to this book, but I hope that somehow it falls into the hands of a great many, including math-phobes.

In some ways, Richard Feynman was the crown prince of modern physics, who much of the public only learned about in books, writings, and video clips after his death. Similarly, John Conway is a sort of crown prince of modern-day mathematics, who the larger public is unfortunately little aware of. I hope this book brings him into greater public consciousness while he is still among us. He deserves it.

I'll probably eventually have a full review of the volume over at MathTango, though I can't do any better than the splendid one Colm Mulcahy put up today:
http://www.huffingtonpost.com/colm-mulcahy/john-h-conway-genius-at-p_b_7749796.html

For now, this is my idea of Christmas in July!

[My full review is now up HERE.]

 

"Sensual and Exciting"

In honor of Siobhan Roberts' newly-released biography of the man, a little reflection on mathematics from John Conway:

"I'm not so much a mathematician as a teacher. In America, kids aren't supposed to like mathematics. It's so sad... Most people think that mathematics is cold. But it's not at all! For me, the whole damn thing is sensual and exciting. I like what it looks like, and I get a hell of a lot more pleasure out of math than most people do out of art!... I feel like an artist. I like beautiful things -- they're there already; man doesn't have to create it. I don't believe in God, but I believe that nature is unbelievably subtle and clever. In physics, for instance, the real answer to a problem is usually so subtle and surprising that it wasn't even considered in the first place. That the speed of light is a constant -- impossible! Nobody even thought about it. And quantum mechanics is even worse, but it's so beautiful, and it works!... I really do enjoy the beauty of nature -- and math is natural. Nobody could have invented the mathematical universe. It was there, waiting to be discovered, and it's crazy, it's bizarre."

 (as quoted in an old Charles Seife piece)

Incomparable Conway

Fa-a-a-antastic post yesterday from Colm Mulcahy on John Conway, about whom, it turns out, there is a biography, "Genius At Play," coming out in July!... Wooo-hooo, 400+ delicious pages on one of the most interesting maths guys around. Anyway, short videos, lotsa good links, and 'tales' to be had below:

http://tinyurl.com/lgtexw6

Also, a much older, longer (and very interesting) Charles Seife piece on Conway here:

http://www.users.cloud9.net/~cgseife/conway.html

Quoting Conway from the Seife piece:

"I'm not so much a mathematician as a teacher. In America, kids aren't supposed to like mathematics. It's so sad... Most people think that mathematics is cold. But it's not at all! For me, the whole damn thing is sensual and exciting. I like what it looks like, and I get a hell of a lot more pleasure out of math than most people do out of art!... I feel like an artist. I like beautiful things -- they're there already; man doesn't have to create it. I don't believe in God, but I believe that nature is unbelievably subtle and clever. In physics, for instance, the real answer to a problem is usually so subtle and surprising that it wasn't even considered in the first place. That the speed of light is a constant -- impossible! Nobody even thought about it. And quantum mechanics is even worse, but it's so beautiful, and it works!... I really do enjoy the beauty of nature -- and math is natural. Nobody could have invented the mathematical universe. It was there, waiting to be discovered, and it's crazy, it's bizarre."

John Conway, A Mathematician's Mathematician

I'm not even sure what that phrase means ("a mathematician's mathematician"), but it just sounds right for John Conway!....

John Horton Conway

Over at companion blog MathTango I now have up a review of "The New York Times Book of Mathematics," an anthology of superb past NY Times columns that relate to mathematics. I love the volume, and recommend it. And because it's a compendium of past newspaper columns, many can be found online, so the book is a rich source for future posts/links here as well!
I'll start with this wonderful 1993 profile by Gina Kolata of Princeton's fascinating John Conway (renowned for his math creativity, and inventing the "Game of Life") which comes near the end of the anthology:

http://tinyurl.com/nxon8zw

A few endearing lines about Dr. Conway from the piece:

 "But Dr. Conway has so many peculiar interests and quirks, and he can so easily be made to sound eccentric, that his deep love of mathematics and the natural world can be lost in the fluff. In a way, he is oblivious to the routines and customs of ordinary life...
"Yet though indifferent to fashion or fads, Dr. Conway is intensely aware of nature, and wants to know it deeply and intimately. He is infinitely curious and observant, seeing nature not only in a spider web or the details of a daffodil but in mathematics."

There are probably some more recent, up-to-date profiles of Conway available, but likely none any more splendidly composed. Give it a read; you'll be glad you did!