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thatsmaths.com
| | njwildberger.com

There are several approaches to the modern theory of "real numbers". Unfortunately, none of them makes complete sense. One hundred years ago, there was vigorous discussion about the ambiguities with them and Cantor's theory of "infinite sets". As time went by, the debate subsided but the difficulties didn't really go away. A largely unquestioning uniformity...
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| | rjlipton.com

Connections in mathematics: games and graphs John Nash is famous for his creation of what has become one of the central notions of modern game theory---his concept of what is a ``solution" for a non-zero sum game. For this work he was awarded the Nobel Prize in Economic Sciences in 1994, along with John Harsanyi...
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| | terrytao.wordpress.com

Don't just read it; fight it! Ask your own questions, look for your own examples, discover your own proofs. Is the hypothesis necessary? Is the converse true? What happens in the classical sp...
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| | geohot.github.io

I wrote a tweet about this but deleted it, since it's a much more nuanced topic than can be discussed there. Nuclear weapons are the Chekhov's gun on the world stage.
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