“Er, nothing,” replied Conway.
“There’s a position opening here, why don’t you apply?”
“How do I go about it?”
“You write me a letter.”
“What should I say?”
Cassels took pity. He offered to write the letter for Conway. He sat down at the side of the road on a stone wall in front of King’s College, rummaged through his briefcase, found a pen, pulled out a piece of paper, and began, “Dear Professor Cassels, I wish to apply for …”
For one student, Edward Welbourne, now a software engineer in Oslo, the most memorable was Conway’s linear algebra course – specifically, a session wherein Conway proved that for two symmetric quadratic forms, both can be simultaneously diagonalised (no small feat). “Doing each takes a moderately tricky piece of computation,” said Welbourne. “To do two at the same time is thus doubly tricky, like balancing a broom by its handle on one’s chin while juggling.” This is exactly what Conway did, while concluding the proof.