Paul Halmos and Tom Blyth

Tom Blyth, a long-term member of the Mathematics department in St Andrews, died in May this year at the age of 85.

Last week, I spotted the Head of Department talking to a woman carrying a big heavy bag. We learned later that it was Abigail, Tom’s daughter, who had brought his mathematics books to the department; we were invited to help ourselves, so I took a couple.

One of them was I want to be a mathematician: an automathography, by the Hungarian-American mathematician Paul Halmos.

Halmos was a wide-ranging mathematician. He was once introduced by Frank Bonsall with the words “Professor Halmos may look like one mathematician, but in reality he is an equivalence class, and has worked in several fields, including algebraic logic and ergodic theory; this afternoon his representative from Hilbert space will address us.”

So what does he have in common with Tom Blyth?

For one thing, both wrote linear algebra textbooks. Halmos published Finite-Dimensional Vector Spaces in 1942. It is very difficult now, when linear algebra is part of the bedrock of mathematics, applicable in many fields (including statistics, dynamics, quantum mechanics and economics), to realise how non-standard and innovative it was back then. Blyth’s book Basic Linear Algebra (with Edmund Robertson) came out in 1998 in the SUMS series and was one of their best sellers.

But there must be more. Blyth’s copy of Halmos’s automathography bears the handwritten inscription “To Tom Blyth, with all best wishes, Paul Halmos”. On reading it, I discovered that Halmos was very fond of Scotland and visited a number of times. On looking up St Andrews in the index, I found that he had been an invited lecturer at the St Andrews Mathematical Colloquium in 1972. He writes, “I made some new friends at that colloquium and met several old ones. Tom Blyth was the junior faculty member at St Andrews and was charged with local arrangements, and he discharged his duties very well.” After that, he came to the Colloquium whenever he could.

So this was no doubt a thank-you present.

Incidentally, Halmos calls his book an “automathography”, explaining that it is the story of his mathematics, not of his life. This is true: many mathematicians appear and are named in its pages, but as far as I can tell he does not tell us the name of his wife, though she accompanied him on a number of trips. He also tells of non-mathematical adventures in places like Montevideo, Moscow, and Washington (the last of these on an attempt to challenge the authorities’ refusal to give him a passport to attend the ICM in 1952).