John Conway explained in an interview that he’s never applied for an academic job.
I am rather proud of the fact that, in some sense, I never applied for an academic position in my life. What happened: I was walking down King’s Parade, the main street in Cambridge, after I received my Ph.D. The chairman of the mathematics department said, “Oh, Conway, what have you done about applying for jobs? And I said, “Nothing.” “I thought that might be the answer,” he said, “Well, we have a position in our department, and I think you should apply.” And I said, “How do I apply?” And he said, “You write a letter to me.” And I said, “What should I put in that letter?” Then he lost his patience, pulled out of his pocket a letter — which had been written on one side — turned it over, and scribbled “Dear Professor Cassels” — that was his name — “I wish to apply for dot-dot-dot.” He handed it to me, and I signed it. It would have been nice if I’d gotten the job. I didn’t that year, but I got the same job the next year with the same letter.