Sir William Timothy Gowers, FRS (/ˈɡaʊ.ərz/; born 20 November 1963) is a British mathematician. He is the holder of the Combinatorics chair at the Collège de France, a Research Professor at the University of Cambridge and a Fellow of Trinity College, Cambridge. In 1998, he received the Fields Medal for research connecting the fields of functional analysis and combinatorics.

Gowers attended King's College School, Cambridge, as a choirboy in the King's College choir, and then Eton College as a King's Scholar, where he was taught mathematics by Norman Routledge. In 1981, Gowers won a gold medal at the International Mathematical Olympiad with a perfect score. He completed his PhD, with a dissertation on Symmetric Structures in Banach Spaces at Trinity College, Cambridge in 1990, supervised by Béla Bollobás.

After his PhD, Gowers was elected to a Junior Research Fellowship at Trinity College. From 1991 until his return to Cambridge in 1995 he was lecturer at University College London. He was elected to the Rouse Ball Professorship at Cambridge in 1998. During 2000–2 he was visiting professor at Princeton University. In May 2020 it was announced that he would be taking up the Chaire de Combinatoire at the College de France beginning in October 2020, though he continues to reside in Cambridge and maintain a part-time affiliation at the university, as well as enjoy the privileges of his life fellowship of Trinity College.

Gowers initially worked on Banach spaces. He used combinatorial tools in proving several of Stefan Banach's conjectures in the subject, in particular constructing a Banach space with almost no symmetry, serving as a counterexample to several other conjectures. With Bernard Maurey he resolved the "unconditional basic sequence problem" in 1992, showing that not every infinite-dimensional Banach space has an infinite-dimensional subspace that admits an unconditional Schauder basis.

After this, Gowers turned to combinatorics and combinatorial number theory. In 1997 he proved that the Szemerédi regularity lemma necessarily comes with tower-type bounds.

In 1998, Gowers proved the first effective bounds for Szemerédi's theorem, showing that any subset ${\displaystyle A\subset \{1,\dots ,N\}}$ free of k-term arithmetic progressions has cardinality ${\displaystyle O(N(\log \log N)^{-c_{k}})}$ for an appropriate ${\displaystyle c_{k}>0}$. One of the ingredients in Gowers's argument is a tool now known as the Balog–Szemerédi–Gowers theorem, which has found many further applications. He also introduced the Gowers norms, a tool in arithmetic combinatorics, and provided the basic techniques for analysing them. This work was further developed by Ben Green and Terence Tao, leading to the Green–Tao theorem.

In 2003, Gowers established a regularity lemma for hypergraphs, analogous to the Szemerédi regularity lemma for graphs.

In 2005, he introduced the notion of a quasirandom group.