# 2011-2012 Baylor Lecture Series in Mathematics

## Ron Graham

Professor Graham is the Irwin and Joan Jacobs Professor in Computer Science and Engineering at the University of California, San Diego and the Chief Scientist at the California Institute for Telecommunications and Information Technology. He is a mathematician credited by the American Mathematical Society as being *"one of the principal architects of the rapid development worldwide of discrete mathematics in recent years"*. For his important and fundamental contributions to mathematics and computer science, in particular to graph theory, combinatorial number theory, scheduling theory, Ramsey theory, and approximation algorithms, Ron was elected as a member of the National Academy of Sciences in 1985.

At the age of 15, Ron started his university studies at the University of Chicago. Dr. Graham received his Ph.D. in mathematics from the University of California, Berkeley in 1962. For the next 37 years, Dr. Graham worked at AT&T Bell Laboratories in New Jersey working on several problems in pure and applied mathematics. His work at Bell Labs gave rise to worst-case analysis theory in scheduling, and helped lay the groundwork for the now-popular field of computational geometry. It also ignited interest in an obscure branch of discrete mathematics called Ramsey theory, which deals with the underlying order in apparently disordered situations. For his contributions to these fields, the American Mathematical Society awarded Graham the Steele Prize for Lifetime Achievement in 2003. In 1999, Ron returned home to California when he accepted a position at UC-San Diego.

An important 1977 paper by Dr. Graham considered a problem in Ramsey theory, and gave a "large number" as an upper bound for its solution. This number has since become well known as the largest number ever used in a mathematical proof (is listed as such in the Guinness Book of Records), and is now known as Graham's number.

Graham popularized the concept of the Erd';s number, named after the highly prolific Hungarian mathematician Paul Erd';s (1913-1996). He co-authored almost 30 papers with Erd';s, and was also a good friend.

Between 1993 and 1994 Graham served as President of the American Mathematical Society. He also served as President of the Mathematical Association of America in 2003-2004. Graham was featured in Ripley's Believe It or Not for being not only "one of the world's foremost mathematicians", but also "a highly skilled trampolinist and juggler", and past president of the International Jugglers' Association.

In 2003, Graham won the American Mathematical Society's annual Steele Prize for Lifetime Achievement. In 1999 he was inducted as a Fellow of the Association for Computing Machinery. Graham was also one of the laureates of the prestigious Pólya Prize the first year it was ever awarded, and among the first to win the Euler Medal. The Mathematical Association of America has also awarded him both the Lester R. Ford prize which was "...established in 1964 to recognize authors of articles of expository excellence published in The American Mathematical Monthly...", and the Carl Allendoerfer prize which was established in 1976 for the same reasons, however for a different magazine, the Mathematics Magazine.

Professor Graham has published more than 320 papers and five books, including *Concrete Mathematics* with Donald Knuth and Oren Patashnik.

The titles, and abstracts, for his two lectures were:

*Thursday, April 12, 2012 at 4:00 pm - D109 (Baylor Sciences Building)*

### Computers and Mathematics: Problems and Prospects

**Abstract**: There is no question that the recent advent of the modern computer has had a dramatic impact on what mathematicians do and how they do it. However, there is increasing evidence that many apparently simple problems may in fact be forever beyond any conceivable computer attack. In this talk, I will describe a variety of mathematical problems in which computers have had, may have or will probably never have a significant role in their solutions.

*Friday, April 13, 2012 at 3:30 pm - SR 344*

### The Combinatorics of Solving Linear Equations

**Abstract**: A major branch of modern combinatorics, usually called Ramsey theory, studies properties which are preserved under partitions. Its guiding philosophy can be neatly summarized by the statement "Complete disorder is impossible". In this talk I will survey what is known and what is still unknown from this perspective for solution sets of linear equations over the integers.