Imagine you are walking along and you see a piece of string wound loosely round a lamp post. You’re curious and want to know how many times it has gone around the post — one, two times, or maybe a hundred? If you pull away the string, will it come off or get stuck?

British mathematician Sir Michael Atiyah, together with Isadore Singer, devised an answer to the conundrum in the early 1960s. The Index Theorem is what Prof Atiyah describes as “a good way to count.” In addition to tallying loops on a string, the theorem can help determine how many solutions an equation has, the number of particles in a physical system, among other things.

Heralded as one of the landmarks of 20th century mathematics, the Index Theorem has had far-reaching impacts in the fields of both mathematics and physics. It led to important new links between analysis, topology and differential geometry, and later played a role in the development of string theory.

For establishing the Index Theorem, Prof Atiyah was awarded the Fields Medal — often called the “Nobel prize for mathematics” — in 1966. He is also well known for developing K-theory, together with Friedrich Hirzebruch. K-theory is the study of flat space and how it moves around, and is applied in the study of topology and geometry.

Prof Atiyah was born in London, but spent his early years in Sudan where his father worked and at a boarding school in Egypt. After World War Two, 16-year-old Atiyah returned to England together with his family. Prof Atiyah went on to study at Trinity College at the University of Cambridge, where he obtained his BA and PhD degrees.

According to a story frequently told by his father, Prof Atiyah displayed an aptitude for mathematics from an early age. The family travelled frequently and whenever they crossed borders, the young Prof Atiyah would trade in his pocket money for the new currency — always making a profit.

While at college, Prof Atiyah became very interested in chemistry. However, he eventually chose to specialise in mathematics, because the latter didn’t require one to have a good memory or “be burdened with vast amounts of facts.”

In addition to the Fields Medal, Prof Atiyah has been awarded the Abel Prize — the two highest accolades a mathematician can receive. Currently an honorary professor at the University of Edinburgh, Prof Atiyah previously served as president of the Royal Society of London, was knighted in 1983 and awarded the Order of Merit in 1992.

# Speakers

Sir Michael Atiyah

Fields Medal

1966