I present snapshots of my seventy-year journey through the world of science, first as a would-be engineer, then as a physicist and later as a mathematician and a mathematical physicist.

In many encounters with colleagues in different areas of research I learned that mathematics and a mathematical perspective can be pivotal in developing our thinking about physics. This fundamental connection between mathematics and physics was not always accepted at the beginning of my career, and it was even vigorously denied by some mathematicians and physicists. I mention some of my work to illustrate the value of mathematical physics for theoretical physics and to pure mathematics, the first being the Polaron bound found with K. Yamazaki in Kyoto in 1957. Another is the “ice problem”, where I calculated the number of ways to colour a chess board with only three colours so that neighbouring squares never have the same colour.

Professor Elliott H Lieb is introduced by Professor Shivaji Sondhi, Wykeham Professor of Physics, University of Oxford. The lecture is followed by a Q&A.