cinelli wrote:This is not a puzzle, but this board seems the most appropriate place for an obituary.
Who was the most famous mathematician of the twentieth century? Arguably it was the eccentric John Horton Conway, who has recently died. Siobhan Roberts wrote a long appreciation of him in the Guardian and she has also written a book about him:
https://www.theguardian.com/science/201 ... -the-worldHe was remembered too in Radio 4’s obituary programme “Last Word”:
https://www.bbc.co.uk/sounds/play/m000j2vm
Another good obituary is this one in Scientific American:
https://blogs.scientificamerican.com/ob ... hn-conway/Like UncleEbenezer, I knew him at Cambridge, first as a lecturer as an undergraduate, and later more socially as a postgraduate. I played many games of backgammon (probably rather too many!) either against him or with him looking on and probably kibitzing... (This was not ill-mannered, by the way: kibitzing was an
expected accompaniment to playing backgammon in the maths department common room!)
I think there's a more arguable case that he was the most famous
pure mathematician of the 20th century; as UncleEbenezer says, Einstein and Hawking were surely more famous, but they were primarily applied mathematicians / theoretical physicists (I won't try to commit myself as to which - the distinction between them is decidedly hard to pin down!).
GoSeigen wrote:Ha! Had no idea Game of Life came out of Go, but makes perfect sense now that I know it. Was he any good as a player?
I suspect it only came out of Go in the sense that a Go set is a convenient tool to investigate Life patterns if you have to do that without a computer: the board is a big enough square grid to hold a good variety of interesting Life patterns, and the black and white stones can help keep track of the states of the individual cells (though having three colours rather than just two would make it easier). There's no similarity of rules between them, so I don't think the Game of Life was derived from Go.
I never saw him play Go, so have no idea how good he was as a player. I'd be very surprised though if he wasn't a player at least at some stage in his life - it would be totally out of character for him not to have investigated the game! Also, he invented a decidedly challenging game called "Philosopher's Football" or "
Phutball" for short that can be played using a Go board and stones (though properly speaking one should block off four columns to reduce it to a 19x15 board). Again, it has very different rules - from both Go and the Game of Life.
His 'surreal numbers' are a very rich number system - one in which infinity, infinity+1, infinity-1, infinity squared, the square root of infinity, etc all exist, are all infinite
and are all different from each other, 1/infinity, 1/(infinity+1), 1/(infinity-1), etc, all exist, are all infinitesimal and are all different from each other, etc, etc, etc. This doesn't contradict the mathematical rule infinity+1 = infinity that people tend to learn, because that rule applies to the cardinal numbers - which are useful for counting how many there are of something. The surreal numbers are instead useful for measuring how far ahead you are in a class of games, and can be used in the analysis of how far ahead you are in a larger class of games. They are for instance useful in analysing Go endgames.
He did an amazing variety of things in a very wide range of mathematical areas, from very deep stuff that I won't try to describe because I don't really understand it myself to ingenious 'tricks'. An example of the latter is his '
Doomsday rule' for quickly mentally calculating the day of the week for any calendar date. I won't try to describe it fully - see the link for that - but a very simple version of it for any date in the current year is:
* Memorise once and for all the following collection of 'Doomsdays':
Duplicated even numbers from 4 upwards: 4/4, 6/6, 8/8, 10/10, 12/12
The 5-9 pair: 9/5, 5/9
The 7-11 pair: 11/7, 7/11
The last day of February - i.e. the 28th in non-leap years, the 29th in leap years
The 3rd of January in non-leap years, the 4th of January in leap years (mnemonic "3 non-leap years, the 4th is a leap year")
Note that in the first three categories, it doesn't matter whether you use English or American date numbering, as you end up memorising the same collection of Doomsdays either way.
* At the start of each year, look up the day of the week of one of those 'Doomsdays' and memorise it for the year. For example, this year's Doomsdays are Saturdays.
* When given a date in the current year, find the Doomsday in the month it specifies, which always exists except when the month is March: in that case, use the last day of February and think of it as the 0th of March. Then do a subtraction to work out how many days it is ahead of or behind the Doomsday. Divide by 7 to work out how many full weeks and odd days that is, and use the odd days to work out the day of the week from the Doomsday.
For example, Christmas Day this year is a Friday, because the December Doomsday is 12/12, 25-12 = 13 days ahead, which is a full week and 6 odd days ahead; 6 days ahead from Saturday is Friday.
With a bit of practice and a little facility at mental arithmetic, it's not difficult to get one's time for doing that calculation down to a second or two, and one can expand the range of years covered a bit by remembering e.g. that last year's Doomsdays were Thursdays and next year's will be Sundays. Covering a lot of years involves learning another calculation to get a year's Doomsday day of the week, and if one wants to do the job really well, two versions of that calculation, one for the Julian calendar and one for the Gregorian calendar, plus memorising a whole lot of dates when different countries switched from the former to the latter - much more challenging!
No deep mathematics in the Doomsday rule, of course - just imagining that there might be an easily memorable collection of dates that all fall on the same day of the week in each year and cover all the calendar months, and then actually looking for them and finding them. But quite an impressive trick to those who don't know how it's done, and even to those who do for doing all years as opposed to just the current year and maybe a small range of years around it!
Gengulphus