Jan Mycielski (Polish: ; February 7, 1932 – January 18, 2025) was a Polish-American mathematician, logician and philosopher, who was a professor of mathematics at the

University of Colorado at Boulder The University of Colorado Boulder (CU Boulder, CU, or Colorado) is a Public university, public research university in Boulder, Colorado, United States. Founded in 1876, five months before Colorado became a Federated state, state, it is the fla ...

. He is known for contributions to

graph theory In mathematics and computer science, graph theory is the study of ''graph (discrete mathematics), graphs'', which are mathematical structures used to model pairwise relations between objects. A graph in this context is made up of ''Vertex (graph ...

combinatorics Combinatorics is an area of mathematics primarily concerned with counting, both as a means and as an end to obtaining results, and certain properties of finite structures. It is closely related to many other areas of mathematics and has many ...

set theory Set theory is the branch of mathematical logic that studies Set (mathematics), sets, which can be informally described as collections of objects. Although objects of any kind can be collected into a set, set theory – as a branch of mathema ...

topology Topology (from the Greek language, Greek words , and ) is the branch of mathematics concerned with the properties of a Mathematical object, geometric object that are preserved under Continuous function, continuous Deformation theory, deformat ...

and the

philosophy of mathematics Philosophy of mathematics is the branch of philosophy that deals with the nature of mathematics and its relationship to other areas of philosophy, particularly epistemology and metaphysics. Central questions posed include whether or not mathem ...

Life and career

Mycielski was born in Wiśniowa, Podkarpackie Voivodeship, Poland on February 2, 1932.Curriculum vitae
from Mycielski's web site, retrieved 2010-03-10. Mycielski received his Ph.D. in mathematics from the

University of Wrocław The University of Wrocław (, UWr; ) is a public research university in Wrocław, Poland. It is the largest institution of higher learning in the Lower Silesian Voivodeship, with over 100,000 graduates since 1945, including some 1,900 researcher ...

in 1957 under the supervision of . His dissertation was entitled "Applications of

Free Group In mathematics, the free group ''F'S'' over a given set ''S'' consists of all words that can be built from members of ''S'', considering two words to be different unless their equality follows from the group axioms (e.g. ''st'' = ''suu''− ...

s to Geometrical Constructions". Following positions at the

Centre National de la Recherche Scientifique The French National Centre for Scientific Research (, , CNRS) is the French state research organisation and is the largest fundamental science agency in Europe. In 2016, it employed 31,637 staff, including 11,137 tenured researchers, 13,415 eng ...

in Paris, the Institute of Mathematics of the

Polish Academy of Sciences The Polish Academy of Sciences (, PAN) is a Polish state-sponsored institution of higher learning. Headquartered in Warsaw, it is responsible for spearheading the development of science across the country by a society of distinguished scholars a ...

, the

University of California, Berkeley The University of California, Berkeley (UC Berkeley, Berkeley, Cal, or California), is a Public university, public Land-grant university, land-grant research university in Berkeley, California, United States. Founded in 1868 and named after t ...

, and

Case Western Reserve University Case Western Reserve University (CWRU) is a Private university, private research university in Cleveland, Ohio, United States. It was established in 1967 by a merger between Western Reserve University and the Case Institute of Technology. Case ...

, he took a permanent faculty position at Colorado in 1969. Mycielski died in January 2025, at the age of 92.

Contributions

Among the mathematical concepts named after Mycielski are: *The

Ehrenfeucht–Mycielski sequence The Ehrenfeucht–Mycielski sequence is a recursively defined sequence of binary digits with pseudorandom properties, defined by . Definition The sequence starts with the single bit 0; each successive digit is formed by finding the longest suffix ...

, a sequence of binary digits with

pseudorandom A pseudorandom sequence of numbers is one that appears to be statistically random, despite having been produced by a completely deterministic and repeatable process. Pseudorandom number generators are often used in computer programming, as tradi ...

properties *The Mycielskian, a construction for embedding any

undirected graph In discrete mathematics, particularly in graph theory, a graph is a structure consisting of a set of objects where some pairs of the objects are in some sense "related". The objects are represented by abstractions called '' vertices'' (also call ...

into a larger graph with strictly higher chromatic number without creating any additional

triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...

s. *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.

Awards and honors

In 1965, he received the Stefan Banach Prize of the Polish Mathematical Society. In 1990, he was awarded the

Wacław Sierpiński Wacław Franciszek Sierpiński (; 14 March 1882 – 21 October 1969) was a Polish mathematician. He was known for contributions to set theory (research on the axiom of choice and the continuum hypothesis), number theory, theory of functions ...

Medal and Lecture by the Polish Mathematical Society. In 2012, he became a fellow of the

American Mathematical Society The American Mathematical Society (AMS) is an association of professional mathematicians dedicated to the interests of mathematical research and scholarship, and serves the national and international community through its publications, meetings, ...

.List of Fellows of the American Mathematical Society
retrieved 2013-02-10.

Selected works

* 1991. ''A Note on S. M. Ulam's Mathematics''. : A note in ''Adventures of a Mathematician''. Stanislaw Ulam. University of California Press, 1991.

References

External links