Editing Hugo Steinhaus (section)

==Mathematical contributions==
{{See also|Banach–Steinhaus theorem|Steinhaus chessboard theorem}}

Steinhaus wrote over 170 works.<ref name=mac/> Unlike his student, Stefan Banach, who tended to specialize narrowly in the field of [[functional analysis]], Steinhaus made contributions to a wide range of mathematical sub-disciplines, including [[geometry]], [[probability theory]], functional analysis, theory of [[Trigonometric series|trigonometric]] and [[Fourier series]] as well as [[mathematical logic]].<ref name=kac/><ref name=mac/> He also wrote in the area of [[applied mathematics]] and enthusiastically collaborated with [[engineers]], [[geologists]], [[economists]], [[physicians]], [[biologists]] and, in Kac's words, "even [[lawyers]]".<ref name=kac2/>

Probably his most notable contribution to [[functional analysis]] was the 1927 proof of the [[Banach–Steinhaus theorem]], given along with Stefan Banach, which is now one of the fundamental tools in this branch of mathematics.

His interest in [[game]]s led him to propose an early formal definition of a [[Strategy (game theory)|strategy]], anticipating [[John von Neumann]]'s more complete treatment of a few years later. Consequently, he is considered an early founder of modern [[game theory]].<ref name=uniw/> As a result of his work on infinite games Steinhaus, together with another of his students, [[Jan Mycielski]], proposed the [[axiom of determinacy]].<ref name=kac2/>

Steinhaus was also an early contributor to, and co-founder of, probability theory, which at the time was in its infancy and not even considered an actual part of mathematics.<ref name=kac2/> He provided the first [[axiom (disambiguation)|axiom]]atic [[measure theory|measure-theoretic]] description of [[coin toss|coin-tossing]], which was to influence the full axiomatization of probability by the Russian mathematician [[Andrey Kolmogorov]] a decade later.<ref name=kac2/> Steinhaus was also the first to offer precise definitions of what it means for two events to be "[[Independence (probability theory)|independent]]", as well as for what it means for a [[random variable]] to be "[[Uniform distribution (continuous)|uniformly distributed]]".<ref name=mac/>

While in hiding during World War II, Steinhaus worked on the fair cake-cutting problem: how to divide a heterogeneous resource among several people with different preferences such that every person believes he received a [[Proportional division|proportional]] share. Steinhaus' work has initiated the modern research of the [[fair cake-cutting]] problem.{{Cref2|B}}

Steinhaus was also the first person to conjecture the [[ham-sandwich theorem]],<ref name=kac2/><ref name= beyer/> and one of the first to propose the method of [[k-means clustering|''k''-means clustering]].<ref name=cluster/>