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- A Breakthrough by Maryna Viazovska Leading to the Long Awaited Solutions for the Densest Packing Problem in Dimensions 8 and 24
- Answer: Lord Kelvin, The Age of the Earth, and the Age of the Sun
- Three Conferences: Joel Spencer, April 29-30, Courant; Joel Hass May 20-22, Berkeley, Jean Bourgain May 21-24, IAS, Princeton
- The Quantum Computer Puzzle @ Notices of the AMS
- Polymath10: The Erdos Rado Delta System Conjecture
- Can Category Theory Serve as the Foundation of Mathematics?
- Seven Problems Around Tverberg's Theorem
- János Pach: Guth and Katz's Solution of Erdős's Distinct Distances Problem
- Believing that the Earth is Round When it Matters

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# Monthly Archives: December 2008

## Fundamental Impossibilities

An Understanding of our fundamental limitations is among the most important contributions of science and of mathematics. There are quite a few cases where things that seemed possible and had been pursued for centuries in fact turned out to be … Continue reading

## Debates

Debates are fascinating human activities that are a mixture of logic, strategy, and show. Not everybody shares this fascination. The German author Emil Ludwig considered debates to be the death of conversation. Jonathan Swift regarded debates as the worst … Continue reading

## Controversies In and Near Science

Controversies and debates in and around science – between researchers within the same discipline, between competing theories, between competing fields, and between accepted scientific viewpoints and viewpoints rooted outside science – are common. Is there global warming and is it … Continue reading

## Lior, Aryeh, and Michael

Three dear friends, colleagues, and teachers Lior Tzafriri, Aryeh Dvoretzky and Michael Maschler passed away last year. I want to tell you a little about their mathematics. Lior Tzafriri ( 1936-2008 ) Lior Tzafriri worked in functional analysis.

## Lovasz’s Two Families Theorem

Laci and Kati This is the first of a few posts which are spin-offs of the extremal combinatorics series, especially of part III. Here we talk about Lovasz’s geometric two families theorem. 1. Lovasz’s two families theorem Here … Continue reading

Posted in Combinatorics, Convexity, Open problems
Tagged exterior algebras, Extremal combinatorics, shellability
5 Comments

## Seven Problems Around Tverberg’s Theorem

Imre Barany, Rade Zivaljevic, Helge Tverberg, and Sinisa Vrecica Recall the beautiful theorem of Tverberg: (We devoted two posts (I, II) to its background and proof.) Tverberg Theorem (1965): Let be points in , . Then there is a partition of … Continue reading

## Test Your Intuition (2)

Question: Let be the cube in centered at the origin and having -dimensional volume equal to one. What is the maximum -dimensional volume of when is a hyperplane? Can you guess the behavior of when ? Can you guess the plane which … 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
12 Comments