**Prime Numbers: Progress and Pitfalls **

**Daniel Goldston**

**Tuesday, November 11, 2014**

**6:30-7:30 pm**

**Carriage House**** **

**Abstract:** Thanks to work of Zhang, Maynard, and Tao in the last two years, we now know that there are infinitely often primes that are within a bounded distance of each other. The current record on that bound is 246. These results were truly shocking to most experts who believed they were far beyond what could be proved at our current state of knowledge. And most experts still think the twin prime conjecture (that there are infinitely many pairs of primes differing by 2) is out of reach, although they are a little less vocal than before. At the same time amateurs have been churning out hopelessly wrong proofs of the twin prime conjecture for years, and continue to do so. This talk will describe some of the ideas behind the recent work on primes and why both amateurs and experts are always getting fooled by primes.

**Biography: **Daniel Goldston was born on January 4, 1954, in Oakland, California. He attended the University of California Berkeley starting in 1972, receiving his Ph.D. in 1981 under the supervision of R. Sherman Lehman. He worked at the University of Minnesota Duluth for a year before spending the 1982–1983 academic year at the Institute for Advanced Study in Princeton. Since 1983 he has worked at San Jose State University except for semesters spent at the Institute for Advanced Study in 1990, the University of Toronto in 1994, and the Mathematical Sciences Research Institute in 1999. He was awarded a 2014 Cole Prize in Number Theory as were János Pintz, Cem Y. Yildirim, and Yitang Zhang.

Mathematical Association of America