Tuesday, October 4, 2016

The Man Who Knew Infinity: Why are Senior Mathematicians so Calm?

Time for some amateur psychoanalysis. I recently saw The Man Who Knew Infinity, which tells the amazing story of the Indian mathematician Ramanujan and his relationship with the English mathematician Hardy. It's an excellent film, but I won't spoil it for you -- let's just say that if it were fiction instead of a true story, nobody would believe it. The movie does an amazing job of portraying the actual process of doing mathematics. (I wrote earlier about the difficulties of writing math-based science fiction in this post.)

I should admit at this point that I thought seriously about going into mathematics in college.  But I was a good enough mathematician to realize that I was not a good enough mathematician to do mathematics professionally. So I went into theoretical physics instead. I've never regretted my decision, but I do envy the more senior members of the mathematics community for their relative calm, as compared to those of us in theoretical physics. What do I mean by that? You'd think that senior tenured physicists would eventually kick back and relax, instead of continuing to seek awards and other kinds of validation for their work. But it ain't so (and I am as guilty as anyone else). On the other hand, I've found senior mathematicians to be relatively more relaxed about such things. And I have a theory as to why this is the case.

Theoretical physics is always a tentative business. If I produce a theory, there is no guarantee that it is correct -- I have to wait and see if it gets confirmed by experiment.  And even if it eventually becomes accepted as "true", there's always a chance that it could be refuted or completely modified by future data.

Mathematics is a very different game. A mathematician who proves something is certain (modulo actual errors) that his work is correct. Not only that, but once he proves something, it stays proved.  No future work is going to undo his accomplishment. I think that's why senior mathematicians are, on the whole, more relaxed about their accomplishments than theoretical physicists. And now Dr. Freud will see the next patient.


bill e.g. said...

Loved the movie too. I like especially the struggle to get Ramanujan to do the actual proofs after his intuition gave him the answer. By-the-way, as shown in the movie, his intuition was not always right.

I have heard from my mathematician friends, one of whom left physics because you can never really know something is true. Physics "truth" is all "approximation" until the next, more detailed experiment. While if you prove something, at least within the suppositions of the proof, that will always be true (as you say, modulo actual errors). That clause I wrote, "within the suppositions of the proof" also says to me that the proof is an approximation...true and always true within that part of the space of all possible suppositions. Maybe the profession will find your proof useful, maybe not at all. Is that too utilitarian?

Robert Scherrer said...

There's no doubt that mathematicians and theoretical physicists, despite the superficial similarity between their two fields, think and work very differently.

Wolfram Research Communications said...

Thanks for the experience-based response you had to The Man Who Knew Infinity. The level of mathematical insight and intuition Ramanujan possessed is phenomenal. Did you know that physicist and Mathematica inventor Stephen Wolfram helped with some post production for the film? In addition, Wolfram actually shares your interest in the science behind sci-fi. He recently wrote a blog that I believe would interest you. The topic is a consulting project he took on helping the filmmakers behind Arrival. Here's a link: .