I went to math camp as a kid in middle school. John Conway was one of the lecturers. He was clearly a brilliant man, slightly eccentric in the way that most great mathematicians are. But he was humble enough to devote several days of his time to hangout with a bunch of nerdy kids and teach us about ordinals, knot theory, and I believe Ramsey numbers. Really nice of him to do that for what I'm sure was pennies if it paid at all.
John Conway has died
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Re: John Conway has died
#52There's thin black banner at the top of HN at the moment. Is that in honor of John Conway?
Re: John Conway has died
#53I've spent the last year or two obsessed with Conway operators ( https://en.wikipedia.org/wiki/Conway_polyhedron_notation ): https://github.com/IxxyXR/Polyhydra/
and I was planning to get in touch just to say hello and ask him a few geometry questions. If you ever have a thought like that about someone in their 80s then just do go ahead and do it.
The Game of Life came with the example cassette of software for my first computer so he's been with me from the beginning of my journey into algorithms and software.
Re: John Conway has died
#54As a teen, I was obsessed with knot theory, and Conway's knot notation always felt like magic to me. The notation works by counting the number of twists in a segment, and then looking for another twist directly connected to the previous twist, and so on. This gives you a sequence of integers, one counting the number (and direction) of twists. If the entire knot is made of twists connected this way, then the continued…
Can two different knots have the same integer sequence?
No, they can't, since they are just representations of the knot diagram.
As for uniqueness, even "rational knots," the ones from the simplest of the fundamental polyhedra, have multiple fractions representing them.
Re: John Conway has died
#55Re: John Conway has died
#56RIP professor Conway.
Thanks for kicking our butts in Linear Algebra and for all your strange but endearing quirks, like "if you see a John Conway without a bike around his neck, that is not the real John Conway" or throwing your shoe at the window to wake us up in class.
Re: John Conway has died
#57People here might know him best for the "Game of Life"[0], but he did so much more. The book about Conway by Siobhan Roberts is an interesting read about the man and his work. There's a review here.[1] Some will know Conway via is work on the Classification of Finite Simple Groups (with many others), some via his "Look and Say" sequence, while still others will know his book "Winning Ways"[2], written with Richard Gu…
Oh, I absolutely love the surreal numbers! The surreals are a superset of the reals, but that's not why I think they are interesting.
In mainstream pure mathematics, you first create the naturals (whole numbers). Then from there you create the rationals, as fractions of naturals. Then from there you can create the reals as infinite sequences of rationals.
This works, but it is arguably inelegant. We like to say naturals are a subset of rationals, and rationals are a subset of reals. But by this construction they're not ontologically the same. (We can of course find a subset of the reals that look like the rationals, etc., but they aren't identical, only equivalent.)
In contrast, the surreal numbers are all constructed in one go. Very elegant.
Re: John Conway has died
#58There's thin black banner at the top of HN at the moment. Is that in honor of John Conway?
Yes.
Re: John Conway has died
#59[deleted]
Re: John Conway has died
#60Game of Life was the first computer program I wrote exactly 50 years while in high school. It was in Dartmouth BASIC on a teletype to PDP 8(?) at some local college.