# Monthly Archives: May 2009

## 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 twentieth-century philosophers of science who later proposed alternative approaches. It will be convenient to start with … Continue reading

Posted in Philosophy, Probability | 14 Comments

סדנא לתלמידי בוגר מצטיינים במתמטיקה מכון איינשטיין למתמטיקה, האוניברסיטה העברית בירושלים   יום א’ י”ז אלול – יום ה’ כ”ח אלול תשס”ט   6-17/9/09   המכון למתמטיקה של האוניברסיטה העברית מזמין תלמידי מתמטיקה מצטיינים המסיימים שנה ב’ או ג’ של … Continue reading

Posted in Uncategorized | 1 Comment

Question: Let be the -dimensional cube. Turn into a torus by identifying opposite facets. What is the minumum -dimensional volume of a subset of which intersects every non-trivial cycle in . Answer: Taking to be all points in the solid … Continue reading

## Ulam and The Future of Mathematics

Ulam was scheduled to give a talk at the University of Chicago titled “The future of mathematics.” Stanislaw Ulam was a rather famous mathematician and a major player in building the H-bomb, so a large audience gathered.

## How Large can a Spherical Set Without Two Orthogonal Vectors Be?

The problem Problem: Let be a measurable subset of the -dimensional sphere . Suppose that does not contain two orthogonal vectors. How large can the -dimensional volume of be?   A Conjecture Conjecture: The maximum volume is attained by two … Continue reading

Posted in Open problems | 4 Comments

## Extremal Combinatorics VI: The Frankl-Wilson Theorem

Rick Wilson The Frankl-Wilson theorem is a remarkable theorem with many amazing applications. It has several proofs, all based on linear algebra methods (also referred to as dimension arguments). The original proof is based on a careful study of incidence … Continue reading

Posted in Combinatorics | Tagged , | 6 Comments

## Recent and Future Excitements

It is very hectic around here and on top of the eight or so regular research seminars at math (and quite a few more at CS) we have many visitors as school terms at the US are over. A week … Continue reading

## The Cap-Set Problem and Frankl-Rodl Theorem (C)

Update: This is a third of three posts (part I, part II) proposing some extensions of the cap set problem and some connections with the Frankl Rodl theorem. Here is a post presenting the problem on Terry Tao’s blog (March 2007). Here … Continue reading