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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!
Top Posts & Pages
 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
 Possible future Polymath projects (2009, 2021)
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 R(5,5) ≤ 48
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Category Archives: Games
Test Your Intuition (21): Auctions
You run a singleitem sealed bid auction where you sell an old camera. There are three bidders and the value of the camera for each of them is described by a certain (known) random variable: With probability 0.9 the value … Continue reading
Posted in Economics, Games, Test your intuition
Tagged Auctions, Roger Myerson, Test your intuition
4 Comments
Itai Ashlagi, Yashodhan Kanoria, and Jacob Leshno: What a Difference an Additional Man makes?
We are considering the stable marriage theorem. Suppose that there are n men and n women. If the preferences are random and men are proposing, what is the likely average women’s rank of their husbands, and what is the likely average … Continue reading
Test Your Intuition (19): The Advantage of the Proposers in the Stable Matching Algorithm
Stable mariage The GaleShapley stable matching theorem and the algorithm. GALESHAPLEY THEOREM Consider a society of n men and n women and suppose that every man [and every woman] have a preference (linear) relation on the women [men] he [she] knows. Then … Continue reading
Test Your Intuition (17): What does it Take to Win TicTacToe
(A few more quantum posts are coming. But let’s have a quick break for games.) Tic Tac Toe is played since anciant times. For the common version, where the two players X and O take turns in marking the empty squares … Continue reading
Ann Lehman’s Sculpture Based on Herb Scarf’s Maximal Lattice Free Convex Bodies
Maximal latticefree convex bodies introduced by Herb Scarf and the related complex of maximal lattice free simplices (also known as the Scarf complex) are remarkable geometric constructions with deep connections to combinatorics, convex geometry, integer programming, game theory, fixed point computations, … Continue reading
Posted in Art, Computer Science and Optimization, Economics, Games
Tagged Ann Lehman, Herb Scarf
5 Comments
Angry Bird Skepticism
Lenore Holditch is a freelance writer. Here is what she wrote to me: “I love learning about new topics, so I am confident that I can provide valuable content for your blog on any topic you wish, else I can … Continue reading
The Privacy Paradox of Rann Smorodinsky
The following paradox was raised by Rann Smorodinsky: Rann Smorodinsky’s Privacy Paradox Suppose that you have the following onetime scenario. You want to buy a sandwich where the options are a roast beef sandwich or an avocado sandwich. Choosing … Continue reading
Eyal Sulganik: Towards a Theory of “Mathematical Accounting”
The following post was kindly contributed by Eyal Sulganik from IDC (Interdiciplinary Center) Herzliya. Eyal was motivated by our poll on certainty “beyond a reasonable doubt,” which is related to several issues in accounting. Mathematicians, I believe, are always looking … Continue reading
Galvin’s Proof of Dinitz’s Conjecture
Dinitz’ conjecture The following theorem was conjectured by Jeff Dinitz in 1979 and proved by Fred Galvin in 1994: Theorem: Consider an n by n square table such that in each cell (i,j) you have a set with n or more elements. … Continue reading
Posted in Combinatorics, Games
6 Comments
Another way to Revolutionize Football
The angle of Victoria Beckham’s hat (here in a picture from a recent wedding) is closely related to our previous post on football One of the highlights of the recent Newton Institute conference on discrete harmonic analysis was a football … Continue reading