Tag Archives: experimental math

What experimental math taught me about my intuition

The project I’m working on with David Brown and Bryden Cais is the first thing I’ve ever done involving computational experiments as a serious part of the development of the ideas.  We’re trying to formulate a reasonable conjecture about the limiting distribution of some arithmetic objects, and I thought we’d arrived at a pretty good heuristic — call it conjecture A — which fit nicely in a context with other conjectures and theorems about similar objects.

But the data we’d collected didn’t fit conjecture A very well.  In fact, when we looked at the data carefully, it appeared to be pointing strongly at conjecture B, which has a similarly clean formulation but for which we didn’t have any theoretical justification.

So I spent much of the weekend thinking about this, and by the end of it, I felt pretty confident that conjecture B was pretty reasonable — even, in a way, more reasonable than conjecture A — though we still didn’t have a strong justification for it.

Today it turned out that there was a mistake in the data collection, and conjecture A looks good after all.   But it’s a sobering reminder that my intuitions about “what ought to be true,” which I think of as rather rigorous and principled, are in fact quite malleable.

 

 

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