> The author of the post is Terence Tao that is the best live mathematician. If he says it's a "breakthrough", it's a breakthrough.
I think it's pretty silly to say that Tao is the best living mathematician, but even if he were I don't think that this would be a useful way to think about things.
> I think it's pretty silly to say that Tao is the best living mathematician
I agree. I was going to write "one of the best" or "probably the best" or something like that. It's like discussing if Messi or Maradona were the best football players. [1]. Anyway, all three of them are quite good.
> but even if he were I don't think that this would be a useful way to think about things.
I also agree. It's just and argument by authority. For a decition that would change the lives of millons of persons and has a lot of subtle tradeoff and unknown unknowns, I'd ask for a better justification and evidence. But deciding if this is a breakthrough or not, may only change the lives of a few graduate students and a few grown up mathematicians, so I'm happy to take the word of Tao.
No matter what you think, best living mathematician is what other mathematicians say about him.
But I'll humor you. How would you prefer we say things?
- Highest IQ on record.
- One of only 3 people to score over 700 on the Math SAT before he was 8. He had the highest score of the three with 760.
- At ages 10, 11, and 12 he set the record for winning Bronze, Silver, and Gold respectively in the International Math Olympiad. After that he lost interest.
- PHD from Princeton at 21.
- Full professor at UCLA at 24. This is a record.
- He is a respected leader in at least a half-dozen areas of mathematics. He regularly publishes in many more. It is unusual for a mathematician to have significant publications in 2 areas.
- Wikipedia lists 28 major prizes for him. Excepting Australian of the Year in 2022, all are major mathematics prizes. No other mathematician comes close.
- Once you exclude junk journals, Tao publishes papers faster than any other mathematician. And his are all good.
- Tao's papers show up in the popular press more often than the next 3 mathematicians combined.
And so on.
At what point is there a better way to think about this than, "best live mathematician"?
(And yeah, until I began noticing Tao, I would have also thought that a silly way to think...)
The idea that Tao has accomplished more than, say, Serre because the latter, who won the Fields medal at 27, only received his PhD at 25 and his bachelor's at 22 while the former received his PhD at 21 and his bachelor's at 16 is so absurd that it can be refuted merely by alluding to it.
Serre is indeed a top mathematician. (I'm actually surprised to find out that he's still alive!)
At this point Tao only has 3/4 his number of publications, similar numbers of textbooks, a similar number of awards (using https://mathshistory.st-andrews.ac.uk/Biographies/Serre/ to count awards), and so on. I'd count Tao as having more of what I see as major breakthroughs, but that is subjective. But then again, Tao is half of Serre's age.
Yeah. I still think it is fair to put Tao in the same tier as Euler, Gauss and Hilbert.
Sorry, I think this style of hagiography is completely goofy, there's nothing else to say about it. And I'm sure it's not even true that he has the "highest IQ on record."
To make a claim like "greatest living mathematician" it would be more appropriate to talk about his actual research accomplishments and how they compare to canonical figures like Gromov, Milnor, Serre, Smale, Yau, among many younger counterparts.
But, personally, I think defending any such claim for any particular person is kind of a juvenile exercise. I am a mathematician and among the slight minority of mathematicians I know who would take the question seriously, a minority of them would select Tao. Which of course isn't to say that he isn't universally considered a top mathematician.
I think it's pretty silly to say that Tao is the best living mathematician, but even if he were I don't think that this would be a useful way to think about things.