[grahamannett]

Terence Tao is so incredibly interesting and unpretentious. I've often found that math "geniuses" seem to be the least pretentious of the genius level people in academia/stem and I slightly wonder if that's actually true and if so, why?

[kkylin]

He is also incredibly clear -- I've had the chance to hear a couple of his (technical) talks. He does not oversimplify, but has a way to explaining the heart of the issue in non-technical terms so one could follow without being an expert in the specific area being discussed. (Though I'd imagine experts would get even more out of his talks.)

[btilly]

That is no accident.

A requirement for clear speech is clear thinking. Very clear thinking is required to be a successful polymath in a technically challenging field.

In order to accomplish in a technical field, such as math, you need to think very "efficiently". It is possible to do this by spending so long coming up with a mental model of a specific area that your thoughts are efficient, but cannot necessarily be communicated to people except when their mental understanding is a reasonable match to your own.

However you cannot do this simultaneously in a great many areas. Therefore a polymath must find ways to construct models that are both simple and efficient. The underlying simplicity of their understanding then becomes evident in how clearly they can explain a precise understanding of whatever they are talking about.

[kornish]

Well phrased. It's no coincidence that Feynman, another famous polymath, was also famously clear and concise.

[kkylin]

I agree with all that, though I also want to add that the converse is not true -- clear thinking is not, by itself, enough for clear exposition. The latter requires investing additional effort, which many people are unwilling or unable to make.

[FeteCommuniste]

After they finish their work for the day, they have nothing left to prove. (Sorry).

[z2]

Jokes aside, I think that's exactly it. Mathematicians aren't tempted in the way that others may be in connecting what they do to humanity. Not being in it to cure a disease, build a better mousetrap, or create a triumphant explanation for existence does wonders to keep the ego in check.

[curuinor]

Difficulty of mathematics and the fact that they can be wrong can also keep ego in check.

[dwohnitmok]

In a related vein, the only debates I've heard where all participants will constantly flip back and forth between opposing positions and earnestly argue for each position before converging on a common understanding (all in the same debate) are discussions of math proofs. I don't know if this generalizes to mathematicians as people, but I find those debates much more fruitful and fun than other debates.