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 Alef Corner: ICM2022
 The probabilistic proof that 2^400593 is a prime: a revolutionary new type of mathematical proof, or not a proof at all?
 With Avi at Suzanna
 Meeting Michael H. at Rio
 What is mathematics (or at least, how it feels)
 Alef’s Corner
 To cheer you up in difficult times 22: some mathematical news! (Part 1)
 Cheerful News in Difficult Times: The Abel Prize is Awarded to László Lovász and Avi Wigderson
 Amazing: Feng Pan and Pan Zhang Announced a Way to “Spoof” (Classically Simulate) the Google’s Quantum Supremacy Circuit!
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 Alef Corner: ICM2022
 The probabilistic proof that 2^400593 is a prime: a revolutionary new type of mathematical proof, or not a proof at all?
 To Cheer You Up in Difficult Times 15: Yuansi Chen Achieved a Major Breakthrough on Bourgain's Slicing Problem and the Kannan, Lovász and Simonovits Conjecture
 Alef's Corner
 With Avi at Suzanna
 TYI 30: Expected number of Dice throws
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 Possible future Polymath projects (2009, 2021)
 R(5,5) ≤ 48
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Monthly Archives: November 2008
Sarkaria’s Proof of Tverberg’s Theorem 2
Karanbir Sarkaria 4. Sarkaria’s proof: Tverberg’s theorem (1965): Let be points in , . Then there is a partition of such that . Proof: We can assume that . First suppose that the points belong to the dimensional affine space in … Continue reading
Sarkaria’s Proof of Tverberg’s Theorem 1
Helge Tverberg Ladies and gentlemen, this is an excellent time to tell you about the beautiful theorem of Tverberg and the startling proof of Sarkaria to Tverberg’s theorem (two parts). A good place to start is Radon’s theorem. 1. The theorems of Radon, … Continue reading
Bad Advice; An Answer to an Old Trivia Question
A transparency and a lecture using transparencies. (No relation to the advice.) Our bad, worse and worst advice corner Bad – When you give a talk with transparencies or computer presentations, don’t go over the content of the transparencies but rather assume … Continue reading
Thomas Bayes and Probability
How can we assign probabilities in cases of uncertainty? And what is the nature of probabilities, to start with? And what is the rational mechanism for making a choice under uncertainty? Thomas Bayes lived in the eighteenth century. Bayes’ famous … Continue reading
About Conjectures: Shmuel Weinberger
The following paragraph is taken from the original “too personal for publication draft” of an article entitled ” ‘Final values’ of functors” by Shmuel Weinberger for a volume in honor of Guido Mislin’s retirement from ETH. (L’enseignement Mathematique 54(2008), 180182.) Shmuel’s remarks … Continue reading
Would you decide the election if you could?
One mental experiment I am fond of asking people (usually before elections) is this: Suppose that just a minute before the votes are counted you can change the outcome of the election (say, the identity of the winner, or even … Continue reading
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Impagliazzo’s Multiverse
Update (July 2009): Here are links to a related post on Lipton’s blog, and a conference announcement on Russell’s possible worlds. On the occasion of Luca’s post on his FOCS 2008 tutorial on averagecase complexity here is a reminder of Russell … Continue reading
Detrimental Noise
“Imagine there’s no heaven, it’s easy(?) if you try,” John Lennon Disclaimer: It is a reasonable belief (look here, and here), and an extremely reasonable working assumption (look here) that computationally superior quantum computers can be built. (This post and the draft … Continue reading