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 Mathematical Gymnastics
 Media Item from “Haaretz” Today: “For the first time ever…”
 Jim Geelen, Bert Gerards, and Geoﬀ Whittle Solved Rota’s Conjecture on Matroids
 Media items on David, Amnon, and Nathan
 Next Week in Jerusalem: Special Day on Quantum PCP, Quantum Codes, Simplicial Complexes and Locally Testable Codes
 Happy Birthday Ervin, János, Péter, and Zoli!
 My Mathematical Dialogue with Jürgen Eckhoff
 Test Your Intuition (23): How Many Women?
 Happy Birthday Richard Stanley!
Top Posts & Pages
 Believing that the Earth is Round When it Matters
 Exciting News on Three Dimensional Manifolds
 The Ultimate Riddle
 The KadisonSinger Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava
 Why Quantum Computers Cannot Work: The Movie!
 Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
 Two Math Riddles
 Mathematical Gymnastics
 New Ramanujan Graphs!
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Category Archives: Probability
Buffon’s Needle and the Perimeter of Planar Sets of Constant Width
Here is an answer to “Test your intuition (8)”. (Essentially the answer posed by David Eppstein.) (From Wolfram Mathworld) Buffon’s needle problem asks to find the probability that a needle of length will land on a line, given a floor … Continue reading
Test Your Intuition (7)
Consider the following game: you have a box that contains one white ball and one black ball. You choose a ball at random and then return it to the box. If you chose a white ball then a white ball is added to … Continue reading
Chess can be a Game of Luck
Can chess be a game of luck? Let us consider the following two scenarios: A) We have a chess tournament where each of forty chess players pay 50 dollars entrance fee and the winner takes the prize which is 80% … Continue reading
Posted in Controversies and debates, Economics, Games, Law, Probability, Rationality
Tagged Chess, Gambling, Games of luck, Games of skill, Poker, Robert Aumann
38 Comments
Answer To Test Your Intuition (4)
Let G be a graph and u and v two vertices. (1) Let H be a random graph where every edge of G is chosen with probability ½. Let p be the probability that there is a path between u … Continue reading
Test Your Intuition (4)
Let G be a graph and u and v two vertices. (1) Let H be a random graph where every edge of G is chosen with probability ½. Let p be the probability that there is a path between u … Continue reading
Posted in Probability
18 Comments
Some Philosophy of Science
The Bayesian approach to the philosophy of science was developed in the first half of the twentieth century. Karl Popper and Thomas Kuhn are twentiethcentury philosophers of science who later proposed alternative approaches. It will be convenient to start with … Continue reading
Posted in Philosophy, Probability
14 Comments
A Problem on Planar Percolation
Conjecture (Gady Kozma): Prove that the critical probability for planar percolation on a Cayley graph of the group is always an algebraic number. Gady mentioned this conjecture in his talk here about percolation on infinite Cayley graphs. (Update April 30: Today Gady mentioned … Continue reading
A Conference and a School on Oded Schramm’s Mathematics
There will be a conference this summer in Redmond and a school in December in Jerusalem devoted to Oded Schramm’s mathematics. Oded Schramm Memorial Conference Probability and Geometry Redmond WA, August 3031, 2009 To be held at Microsoft … Continue reading
Noise Sensitivity Lecture and Tales
A lecture about Noise sensitivity Several of my recent research projects are related to noise, and noise was also a topic of a recent somewhat philosophical post. My oldest and perhaps most respectable noiserelated project was the work with Itai Benjamini and Oded … Continue reading
Test Your Intuition (1)
Question: Suppose that we sequentially place balls into boxes by putting each ball into a randomly chosen box. It is well known that when we are done, the fullest box has with high probability balls in it. Suppose instead that … Continue reading
Posted in Computer Science and Optimization, Probability, Test your intuition
Tagged Test
11 Comments