Jan Mycielski Explained

Jan Mycielski (Polish: ; born February 7, 1932)^[1] is a Polish-American mathematician, logician and philosopher, a professor emeritus of mathematics at the University of Colorado at Boulder.^[2] He is known for contributions to graph theory, combinatorics, set theory, topology and the philosophy of mathematics.

Life and career

Mycielski received his Ph.D. in mathematics from the University of Wrocław in 1957 under the supervision of . His dissertation was entitled "Applications of Free Groups to Geometrical Constructions". Following positions at the Centre National de la Recherche Scientifique in Paris, the Institute of Mathematics of the Polish Academy of Sciences, the University of California, Berkeley, and Case Western Reserve University, he took a permanent faculty position at Colorado in 1969.^[1]

Among the mathematical concepts named after Mycielski are:

The Ehrenfeucht–Mycielski sequence, a sequence of binary digits with pseudorandom properties
The Mycielskian, a construction for embedding any undirected graph into a larger graph with strictly higher chromatic number without creating any additional triangles.
The Mycielski–Grötzsch graph, the Mycielskian of the 5-cycle, an 11-vertex triangle-free graph that is the smallest possible triangle-free graph requiring four colors.
Mycielski's theorem that there exist triangle-free graphs with arbitrarily large chromatic number.

In 1965, he received the Stefan Banach Prize of the Polish Mathematical Society.

In 1990, he was awarded the Wacław Sierpiński Medal and Lecture by the Polish Mathematical Society.^[3]

In 2012, he became a fellow of the American Mathematical Society.^[4]

A note in Adventures of a Mathematician. Stanislaw Ulam. University of California Press, 1991.