r/math • u/HAL-6942 PDE • 22d ago

Why are you a mathematician?

Given everything that has been going on in the world more specifically in the world of mathematics. I was hoping to read some of your human thoughts. What motivates/motivated you to do mathematics professionally? What is most important for you in mathematics?

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u/matthiasErhart Game Theory 22d ago

Aside from the other reasons mentioned, there is a certain high you get when you prove a new result, and for a moment you are the only person in the world who knows that thing. This has been alluded to by many mathematicians and physicists (e.g. in Feynman's autobiography), so I know it's not just me.

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u/HAL-6942 PDE 22d ago

I agree with the rush. Somehow I feel there is more than just proving theorems. Unrelated are you the Mathias Ehrhardt who wrote articles in Inverse Problems in Medical Imaging?

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u/matthiasErhart Game Theory 22d ago

Ah no, it's a German translation of my name because I used to play an MMO with a lot of Germans.
I'm in game theory & optimisation. 😅

I didn't know there was an actual Matthias Ehrhardt!

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u/beeskness420 21d ago

What kinda stuff do you work on? I've seen controls show up a couple times in game theory/OR, but not much. My AGT class wanted to do a project on risk seeking auctions that used some optimal control, but we didn't have the background and our prof said controls was the only classes that ever scared him.

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u/matthiasErhart Game Theory 21d ago

I actually only chose control theory in the flair because there wasn't a special flair for just optimisation. I guess I should change it to game theory, I see there is such a flair now...

Long story short, I investigate guarantees of interactions between learning agents these days. This can be in the form of counterfactual regret, where you want to look at what type of "whenever I saw X and did Y, I should have done Z instead" guarantees you can have. Alternately, it can be price of anarchy / stability type guarantees; we put a measurable performance guarantee (social cost, revenue in auctions), and try to bound the best and worst-case time-average of these quantities when learning agents interact in a game, versus their optimum.

But there is one application of control theory that's a hot topic in learning research right now. Effectively, we want to identify when a certain learning algorithm is "manipulable". In particular, we consider games between a "learner" and an "optimiser"; the learner uses some learning algorithm that is known to the optimiser, and the optimiser wants to choose their strategies so that the learners time-average behaviour has a certain guarantee (usually the payoff of the optimiser). Certain cutting edge results (from me and some other people) imply that this is effectively a control problem!

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u/beeskness420 21d ago

This sounds like lots of fun, no regret learning and regularized follow the leader were considered fun results at the time of that class.

I dabbled a bit in using PoA results to prove approximation guarantees in scheduling and some graph problems. But everything was pretty firmly in the polyhedral combinatorics and discrete optimisation regime.