In 2007, Zeev Dvir shocked experts by giving a one-page proof of
the finite field Kakeya problem. The new idea in the proof was to
introduce high degree polynomials into a problem about points and
lines. This idea has led to progress on several...
olynomials are a special class of functions. They are useful in
many branches of mathematics, often in problems which don't mention
polynomials. We discuss two examples: polynomials in
error-correcting codes and polynomials in geometric
Incidence geometry is a part of combinatorics that studies the
intersection patterns of geometric objects. For example, suppose
that we have a set of L lines in the plane. A point is called
r-rich if it lies in r different lines from the set. For a...