- 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
- Why is mathematics possible?
- Polymath 8 - a Success!
- The Kadison-Singer Conjecture has beed Proved by Adam Marcus, Dan Spielman, and Nikhil Srivastava
- Two Math Riddles
- The Ultimate Riddle
- Emmanuel Abbe: Erdal Arıkan's Polar Codes
- Believing that the Earth is Round When it Matters
- Why Quantum Computers Cannot Work: The Movie!
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
Author Archives: Gil Kalai
…while we keep discussing why mathematics is possible… The news Adam Marcus, Dan Spielman, and Nikhil Srivastava posted a paper entitled “Interlacing Families II: Mixed Characteristic Polynomials and the Kadison-Singer Problem,” where they prove the 1959 Kadison-Singer conjecture. (We discussed part … Continue reading
In a previous post I mentioned the question of why is mathematics possible. Among the interesting comments to the post, here is a comment by Tim Gowers: “Maybe the following would be a way of rephrasing your question. We know … Continue reading
Yitang Zhang’s very recent shocking paper demonstrated that bounded gaps between primes occur infinitely often, with the explicit upper bound of 70,000,000 given for this gap. Polymath8 was launched for the dual purpose of learning Zhang’s proof and improving the upper bound … Continue reading
Joram Lindenstrauss 1936-2012 This week our local Institute of Advanced Study holds a memorial conference for Joram Lindenstrauss. Joram was an immensely powerful mathematician, in terms of originality and conceptual vision, in terms of technical power, in terms of courage to confront … Continue reading
The news in brief Andriy V. Bondarenko proved in his remarkable paper The Borsuk Conjecture for two-distance sets that the Borsuk’s conjecture is false for all dimensions greater than 65. This is a substantial improvement of the earlier record (all dimensions … Continue reading
Spectacular advances in number theory Last weeks we heard about two spectacular results in number theory. As announced in Nature, Yitang Zhang proved that there are infinitely many pairs of consecutive primes which are at most 70 million apart! This is a sensational achievement. … Continue reading
Enlightenment at a red traffic light Wolf Prize laureate Prof. George Daniel Mostow made his greatest scientific breakthrough while driving. Haaretz tells the story of how Dan Mostow reached his breakthrough known as Mostow’s rigidity theorem. Congratulations, Dan! French-Isreali Meeting … Continue reading
You run a single-item 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
A commentator named Oz proposed the following question: You have a box with n red balls and n blue balls. You take out each time a ball at random but, if the ball was red, you put it back in the box and take out … Continue reading
Yeshu Kolodni and Lord Kelvin The question In 1862, the physicist William Thomson (who later became Lord Kelvin) of Glasgow published calculations that fixed the age of Earth at between 20 million and 400 … Continue reading