Thomas Craig Brown (born 1938) is an American-Canadian mathematician, Ramsey Theorist, and Professor Emeritus at Simon Fraser University.
[1] As a mathematician, Brown’s primary focus in his research is in the field of Ramsey Theory.
When completing his Ph.D., his thesis was 'On Semigroups which are Unions of Periodic Groups'[2] In 1963 as a graduate student, he showed that if the positive integers are finitely colored, then some color class is piece-wise syndetic.
[3] In A Density Version of a Geometric Ramsey Theorem,[4] he and Joe P. Buhler showed that “for every
ε > 0
elements must contain 3 collinear points” where
-dimensional affine space over the field with
In Descriptions of the characteristic sequence of an irrational,[5] Brown discusses the following idea: Let
be a positive irrational real number.
The characteristic sequence of
.” From here he discusses “the various descriptions of the characteristic sequence of α which have appeared in the literature” and refines this description to “obtain a very simple derivation of an arithmetic expression for
.” He then gives some conclusions regarding the conditions for
He has collaborated with Paul Erdős, including Quasi-Progressions and Descending Waves[6] and Quantitative Forms of a Theorem of Hilbert.