Terence Tao: evaluation

Transcript context

…But anyway, so you are known for this ability to go both deep and broad in mathematics. So you’re the perfect person to ask. Do you think there are threads that connect all the disparate areas of mathematics? Is there a kind of a deep, underlying structure to all of mathematics? There’s certainly a lot of connecting threads, and a lot of the progress of mathematics can be represented by taking… By stories of two fields of mathematics that were previously not connected, and finding connections. An ancient example is geometry and number theory. So in the times of the ancient Greeks, these were considered different subjects. I mean, mathematicians worked on both. Euclid worked both on geometry, most famously, but also on numbers, but they were not really considered related. I mean, a little bit, like you could say that this length was five times this length because you could take five copies of this length and so forth, but it wasn’t until Descartes, who developed analytical geometry, that you can parameterize the plane, a geometric object, by two real numbers. So geometric problems can be turned into problems about numbers. Today this feels almost trivial. There’s no content to this. Of course, a plane is X and Y, because that’s what we teach and it’s internalized, but it was an important development that these two fields were unified, and this process has just gone on throughout mathematics over and over again. Algebra and geometry were separated, and now we have this fluid, algebraic geometry that connects them, and over and over again, and that’s certainly the type of mathematics that I enjoy the most. I think there’s sort of different styles to being a mathematician. I think hedgehogs and fox… A fox knows many things a little bit, but a hedgehog knows one thing very, very well, and in mathematics, there’s definitely both hedgehogs and foxes, and then there’s people who can play both roles, and I think ideal collaboration, British mathematicians involves very… You need some diversity, like a fox working with many hedgehogs or vice versa, but I identify mostly as a fox, certainly. I like arbitrage, somehow. Learning how one field works, learning the tricks of that wheel, and then going to another field which people don’t think is related, but I can adapt the tricks. So see the connections between the fields.…

Stored transcript either side of the excerpt. The highlighted words are the published quote; the surrounding text is unedited source, never generated.