A "Sliding Doors" moment

Gwynneth Paltrow - whether or not she makes the tube train - you remember?

Anyway, I had a retrospective "Sliding Doors" moment on Saturday evening. I was at Alan's 30th birthday bash, and got chatting to a guy called Mike Mark who recently "paused" mid-way through a maths PhD. It turns out that his field is closely related to the area that I found most interesting back in the mid '80s when I was an undergraduate. I loved maths logic and foundations of maths, and particularly enjoyed the course on Gödel's Theorem, which proves that there are undecidable statements in mathematics (statements which can neither be proved or disproved). These undecidable statements are effectively independent of the rest of maths - you can build consistent versions of maths with or without each of them.

But Gödel didn't really find any interesting undecidable propositions. That had to wait for Paul Cohen who, in the '60s, proved in particular that the axiom of choice is independent of the rest of maths. In the mid '80s, this seemed to be where this particular line of study had dried up. I had found out about Paul Cohen by myself, but gave up on the idea of writing an optional paper on his work after my lecturers either said "who?" or "if you write it, I'd be interested to read it so I can find out what it's all about" (to be fair, the fact that it was supposed to be written over the Summer holiday didn't help!). I think this represented the high water mark of my mathematical career, and after cruising along to a 2.1, I threw away all my lecture notes and concentrated on rock-and-roll :)

Fast forward to Saturday night. It turns out, according to Mike Mark, that the whole field got fresh impetus in the early '90s when some important new results were proved using a development of Paul Cohen's "forcing" technique. I suddenly saw a whole other life that I might have led if I'd written that paper, stuck with my gut feeling that this was the most interesting thing happening in maths and stuck with maths. A life as an academic that never was!

I doubt that I ever had the talent to be a career mathematician, and I have no regrets about the choices I made. In fact looking back is not something I ever really do. On Saturday night, though, I had a momentary "wow - I could have gone down that path" sensation. It soon passed - probably aided by beer :)

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