Interestingly, Scott Locklin and Roger Schlafly, both math or physics PhDs, regards quantum computing as pretty much a bullshit field, too out of tough with reality, that almost certainly won’t ever deliver any practical results. They say that the experimental side of it has made marginal progress of the past three decades. That field I also feel like is more (applied) mathematics that proves some stuff that’s a mix of Hilbert spaces and theoretical computer science than physics.
Speaking of applied math, I now want to learn the theory of distributions and Sobolev spaces, which was developed by Laurent Schwartz in 30s and 40s, with Schwartz winning 1950 Fields Medal for that (along with Atle Selberg for his work in analytic number theory).
Here’s a list of a mathematicians who did Fields Medal level work but did not win the prize, compiled by a from China who did math graduate school in Russia and France. https://gmachine1729.wpcomstaging.com/2021/04/06/a-list-of-mathematicians-who-did-fields-medal-level-work-but-did-not-win-the-prize/
Interestingly, the two Chinese mathematicians on this list are Shiing-shen Chern and Feng Kang. Apparently, he regards Feng Kang as higher than Hua Luogeng, who is leagues more famous in China, whose best work was in analytic number theory and several complex variables. I wondered why, and a few days ago, I learned that Feng Kang in 1965 in China was actually the first in the world to rigorously prove convergence and stability of the finite element method that he independently developed in the late 1950s. This paper, https://www.jstor.org/stable/43692901?seq=1, mentions after Feng’s 1965 paper a paper in 1968 by a Czech mathematician who proved the rate of convergence of a similar method. I had known about Feng Kang before, including that he spent the early 50s at Steklov Institute with the genius blind mathematician Lev Pontryagin and that he later independently developed the theory of finite elements, but I had never known before that he had actually arguably gotten there first. I was thoroughly impressed.
Peter Lax is also in that list, and here, he extolled Feng Kang: http://lsec.cc.ac.cn/fengkangprize/article2.pdf. Sadly, pretty much nobody in the general public in China knows about him. He is almost certainly more mathematically significant than Shing-tung Yau and Terence Tao, the two ethnic Chinese Fields Medalists, who happen to both have Hong Kong family background. Given that Fields was a Canadian, it’s not surprising that there is some pro-Anglo bias in the Fields Medal. I only really learned that math is certainly not a strong point of the Anglo world over the past few years. The French, Germans, Russians, and Japanese produce more profound mathematicians than the Anglos. One can also arguably put Shiing-shen Chern, who was German and French educated, above any other 20th century Anglo mathematician. He should’ve gotten the Fields Medal in 1950, which was the second time it was given, the first being in 1936. Most of the best mathematicians in American universities were not American born. Even with all those far tail immigrants, continental Europe and Japan beats America at math. Top American universities tend to pay big salaries to great mathematicians, like Gerd Faltings and Atle Selberg and many of those former Soviet geniuses, after they had already done their best work elsewhere.