John F. Nash Jr. was 86.
He invented a game, known as Nash, that became an obsession in the Fine Hall common room... [M]ost real world interactions are... complicated, where players’ interests are not directly opposed, and there are opportunities for mutual gain. Dr. Nash’s solution, contained in a 27-page doctoral thesis he wrote when he was 21, provided a way of analyzing how each player could maximize his benefits, assuming that the other players would also act to maximize their self-interest.
This deceptively simple extension of game theory paved the way for economic theory to be applied to a wide variety of other situations besides the marketplace.
ADDED: Nash and his wife were passengers in a taxi on the New Jersey Turnpike:
[T]he driver lost control while trying to pass another car and hit a guard rail and another vehicle.... The couple were ejected from the cab and pronounced dead at the scene.
The cab driver survived.
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22 comments:
Wait. He proved Fermat's Last Theorem in the 50s? I know it's been proven -- finally -- but fairly recently, and basically by brute force.
Why have we never heard of this? My guess is that it's because it's, er, not actually true.
I guess I'm not the only one that ignores the seat belts in the taxi cab.....I might have to change my thinking.
"Wait. He proved Fermat's Last Theorem in the 50s?"
Yeah, he was all I have discovered a truly marvellous proof but I don't have enough paper to write it down.
tl;dw
Not surprisingly, the New York Times was sloppy about Nash proving "Fermat’s classic theorem". It wasn't Fermat's Last Theorem that Nash proved as a teen. It's a different result called Fermat's Little Theorem: If n is a whole number and p any prime, then n multiplied by itself p times minus n is divisible by p.
A tragedy, condolences, and all the rest, but how many of us had heard of John Nash before the movie A Beautiful Mind? (I'll admit: Not me.)
He was on the way home from a trip to Norway where he had just received the Abel Prize in mathematics.
He had an amazing life.
- Krumhorn
gsgodfrey,
Thanks. I knew that couldn't be right.
"Fermat's Little Theorem" is damned interesting all by itself.
So (n^p - n)/p = whole number?
Wear seat belts in cabs, people don't for some reason. I was laughed at by a boss years ago for wearing one, but I started after a co-worker broke her jaw and lost most of her teeth (among other injuries) hitting her face on the back seat. Then there was the woman who had her back broken in a slow speed crash. Both had extremely long and painful recoveries.
Wear your seatbelt, even in the backseat of a cab, even if the ride is short.
"Wear seat belts in cabs, people don't for some reason."
1. Seatbelts in cabs sometimes don't work, and few people are willing to say "stop, let me out, I want a safer cab."
2. Seatbelts are often stuffed down between the cushions and covered with crud.
3. People don't think.
As for the cabdriver losing control, I have seen a lot of reckless driving by cabbies so this is no surprise.
"Wear your seatbelt, even in the backseat of a cab, even if the ride is short."
And good luck finding and buckling the seatbelt buckled before the cabbie darts into traffic like Mad Max.
His long life was not lived in vain. If we can learn anything from the study of his life and work it's that it is important to wear seat belts, even--perhaps especially--in cabs.
Fermat's last theorem was solved in the last 15 years. I have the NYT cut out somewhere.
So tragic about Nash but they died together. The book Beautiful Mind is very good and the movie was ok too. His wife fought to not subject him to shock therapy and lose his precious memory.
There is a useful corrective piece today at that points out the movie was wrong in a number of respects. I did not see it as I suspected that Hollywood would do its usual job.
The bar scene in “A Beautiful Mind” likewise gets it 180 degrees wrong—going for the non-beautiful girl is NOT a Nash equilibrium. The setup cannot produce a Nash equilibrium at all. (3) Nash almost certainly did NOT have “paranoid schizophrenia” as he remained productive until the end. He almost certainly had bipolar disorder, a condition that may yield transient psychotic episodes. I know many brilliant scientists with this condition. He may have been diagnosed with schizophrenia upon his initial admission to Maclean Hospital, but that would have been before Harrison and Pope, at Maclean, in 1984, later reviewed all the previous records and discovered that 50% of such “schizophrenia” diagnoses were in error and were actually manic-depression (bipolar). (3) During his manic/psychotic episodes, Nash would become paranoid (this happens in mania) and would then begin spouting crazed LEFTWING fantasies. When he was normal, he was politically conservative. The movie “A Beautiful Mind” deliberately reversed this because of its obvious implications.
There is more at the link.
The couple were ejected from the cab and pronounced dead at the scene.
The wife and I routinely buckle up in a cab. We might not be as smart as Nash, pre- and post-schizophrenia, but perhaps we are wiser.
@Michael K, the book claims paranoid schizophrenia, including hearing voices. In the movie he sees and talks to invisible "friends," but Nash himself famously said that when he had his psychotic episodes it was similar to when he got his mathematical insights.
I'm an economist. I didn't know John Nash but I know people who knew him.
John Nash truly had a beautiful mind. He was really remarkable.
I have no doubt the movie had inaccuracies but it was a great portrayal of mental illness. I've always wondered if it was true that he figured out he was having delusions by recognizing that his friend's sister didn't age.
http://math.stackexchange.com/questions/1268791/fermats-last-theorem-generalization , at this link, you may deduce a very simple solution, also note the other post by the same author (sequence & convergent series) before few heros of maths remove them permenetly
You may have a look here before they delete it. http://math.stackexchange.com/questions/1268791/fermats-last-theorem-generalization
Fermat's last theorem and Andrew Wiles
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