In a famous essay, Tim Gowers (see page 14), professor of mathematics at the University of Cambridge, distinguishes between two mathematical cultures. Drawing in particular on Paul Erdös (1913–1996) and Sir Michael Francis Atiyah (1929–2019), he observes that professional mathematicians broadly fall into two categories, depending on whether their aim is to solve problems or to build and understand theories.
Of course, no mathematician entirely neglects either of these two aspects—the two perspectives seem complementary and indispensable—but they do not all assign them the same priority. Gowers illustrates his point with combinatorial problems that enabled him to gain a deeper understanding of the theory of Banach spaces of arbitrary dimension, including infinite dimension, and to answer longstanding open questions in this area. It was his work forging an initially difficult-to-imagine link between functional analysis and combinatorics that earned him the Fields Medal in 1998.
Beyond his original and profound mathematical results, Tim Gowers stands out for several initiatives that are epistemologically important and fairly characteristic of our time. These initiatives place particular emphasis on sharing and collaboration, both in research—as shown by his efforts to establish massively collaborative structures (see page 14) and his advocacy of open access to scientific publications—and in bringing mathematics to the general public.
