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.
This is clever application of existing ideas, not the sort of new idea which is needed. No one can really imagine what sort of machinery will need to be built to prove the RH. A proof is completely outside the realm of speculation at this point.
See my sibling comment - where does the insistence that octopus is third declension come from? The reality is that while most Greek loanwords are third declension, many are not, and Latin authors tended to not be consistent.
No. You seem very confident, but octopi is (grammatically) perfectly acceptable. The English word octopus is taken from the Latin (coined by Linnaeus) word octopus, which is of Greek origin. Greek loanwords in Latin were used very inconsistently, but many people on the internet seem to believe that it MUST be a third declension noun. However, Pliny treats the structurally identical polypus as second declension and uses the plural polypi (see https://www.perseus.tufts.edu/hopper/text?doc=Plin.+Nat.+9&f...).
> Every layman can see that these ideas are exceedingly important. Hence there won't be any money in it. You only make money on ideas which have escaped the general public. If you invent something like artificial rubies for the watch-making industry, you'll make more money than with the Uranium-Engine
After hearing news of the bomb
> That shows at any rate that the Americans are
capable of real cooperation on a tremendous scale. That
would have been impossible in Germany. Each one said
that the other was unimportant.
> I have known a great many intelligent people in my life. I knew Planck, von Laue and Heisenberg. Paul Dirac was my brother in law; Leo Szilard and Edward Teller have been among my closest friends; and Albert Einstein was a good friend, too. But none of them had a mind as quick and acute as Jansci [John] von Neumann. I have often remarked this in the presence of those men and no one ever disputed me.
But Einstein's understanding was deeper even than von Neumann's. His mind was both more penetrating and more original than von Neumann's. And that is a very remarkable statement. Einstein took an extraordinary pleasure in invention. Two of his greatest inventions are the Special and General Theories of Relativity; and for all of Jansci's brilliance, he never produced anything as original.
This quote really goes to the heart of it. I think he was being fairly precise here in the use speed and acuity, contrasted with insight and originality. Our brains just like the rest of our bodies have a lot of different capabilities. I don't think most of us would find it particularly meaningful to compare the strongest lifter with the fastest runner, yet related to intelligence people do this sort of thing all the time. This quote seems a better informed view.
Your other points are similar.