Ian Macdonald

More sad news: Ian Macdonald has died. (To avoid confusion, this is the Ian Macdonald who introduced the Macdonald polynomials, not the one who taught me group theory.)

My first exposure to the ideas of algebraic geometry came at Oxford, from the Mathematical Institute lecture notes called “Notes on Commutative Algebra” by Atiyah and Macdonald, which became the famous book.

Ian Macdonald had a careful and precise style, enlivened by a sense of humour. In the introduction to “Symmetric functions and Hall polynomials”, he explains the difference between two conventions for writing Young tableaux and similar things by saying, “Francophones should read this book upside down in a mirror.” (I remember puzzling over this comment, since I was not familiar with the French convention. The difference between the labelling of elements of a matrix (or words in a left-to-right language) and Cartesian coordinates is a 90 degree rotation and does not require a reflection. I learned about Young tableaux using the matrix convention. I think that a different convention would require more changes than just reading the book upside down in a mirror. For example, the Robinson-Schensted algorithm involves “bumping” an element out of a row, so that it falls down to the row below and tries to find a place there. How would you describe that with a different convention?)

I will tell two anecdotes about Ian Macdonald. The first one he told me himself, and I witnessed the second.

He directed a programme at the Isaac Newton Institute. He arrived and was installed in a big office. A little later, the technician came running round: there was a problem on the network, a computer had crashed. Ian’s response: “That thing was sitting there humming; I found it distracting, so I turned it off.”

He was a plenary speaker at the British Combinatorial Conference at the University of Surrey. At that time, the medium of choice for giving a big lecture was overhead projector slides; but Ian preferred to write on the board in his elegant handwriting. Below the big screen were fixed blackboards running the entire width of the room. He began at the top left and worked his way across. At the point where he had filled all the boards and came back to the top left, he was about to generalise the whole set-up, so only minor changes were needed to what was already there. Given that he presumably had not seen the set-up of boards before arriving at the conference, this achievement would have required careful preparation!

He has left us with some conjectures about characters of finite groups, on which group theorists are making good progress. If I understand correctly, the truth of these conjectures follows from the truth of considerably stronger (and more complicated) conjectures about simple groups, which can probably be proved using the classification of finite simple groups. Whether Macdonald would regard this as a proof from the book, I do not know.