The most press he's gotten recently has been from this "eigenvectors from eigenvalues" thing that he solved three ways in two hours, probably because it's the least technical thing he's done.
I'm reminded of education research of the form "We tried to teach topic T to students in grade G. We taught it really, really badly. Surprisingly, that didn't work! We draw the obvious conclusion... students in grade G are developmentally unready to understand topic T."
So yes, it might truly be unsolvable. It's certainly difficult. Non-interactive defusing of misconceptions is dauntingly hard - even harder than remedial filling of foundational gaps. Then you add constraints on article length, and the medium may just not be adequate.
But I would be more comfortable with such an argument, if there was wider recognition of how wretched our current science education content is, and how badly it's failing students. How poor the stories we tell about the physical world. If your five-year old wants to know what finger-paint color to use for the Sun, don't ask first-tier astronomy graduate students - there's a wide-spread misconception, so they'll mostly get it wrong. On HN a few days back, there was something like a 'best 2019 astronomy books for children'... and the books were something vaguely like 0 of 10 on getting it right. We're just not set up to teach misconception-free transferable broad understanding.
Seeing research talks, I frequently think "Oh nifty - that concept/description/graphic/video is awesome: accessible and clarifyingly insightful. It should be part of every introduction to this topic. Down to primary school even." ... and won't be any year soon. The pipeline from researcher conversation, to talk, to paper and professional tome, down and down to education and popular content, is regrettably also a gradient from accessible/insightful/transferable/correct to confused/superficial/unusable/nonsense. There just hasn't been the incentives and infrastructure to do better.
In another comment you mention intro physics and olympiads. So take friction. We now know how friction works, down to nanoscale. But last I saw, we don't even try to teach that. Instead it's the decades-old plug-and-chug on Amontons' Laws of large objects sliding on pig fat. Sure, there's some nice training on system decomposition. But if we cared about actual understanding of the physical world, rather than the educational artifact of "Introductory Physics", our teaching focus would need to be different. Similarly, professors complain about PhD candidates lacking a rough quantitative feel for the field, and the current educational focus is far from fixing that. But, perhaps I'm out of date, and things are more-recently improving? Fermi problems are becoming much more common, for instance.
Ending on an upbeat note. An MIT project to create introductory cell-biology VR, obtained domain expertise by pulling in and interviewing researchers. One challenge was apparently... getting them to leave. Such was their enthusiasm. Suggesting that if infrastructure has the right shape, the massive and scarce expertise needed for better content might actually be plausibly obtained. And personalized education via XR might be sufficient, and sufficiently disruptive, to deliver it. So perhaps there's hope to do transformatively better than we have been.
In practice, high school and even college introductory classes have a hard time making the basics stick -- stuff as simple as just F = ma. Redirecting half the time you spend on that towards an exquisitely detailed model of friction is not going to produce better physicists. On the average, it's going to produce students that understand F = ma even less, but can recite a couple friction-related buzzwords.
There is no magic curriculum fix that will suddenly make mass education easy. Everybody who thinks about education starts by imagining there is, then reality hits.
We treat education like an assembly line that's supposed to turn every kid into a productive member of society, using a one-size-fits-all curriculum. That's a wrong-headed approach. We should treat it like a mix between olympic trials and career fair. Identify the precocious and the enthusiastic in each subject area. Let teens decide what they want to do.
It won't work, however, until we give teens the right to self-determination. Helicopter parents trying to force their kids to be engineers or doctors, ability be damned, is one of the most pernicious factors in the sorry state of education. The other, perhaps equally pernicious, is the parents who can't or won't help their kids with anything despite their eagerness to learn.
A while back, I had a conversation with a biology professor, about a speculative alternative approach to teaching a topic, which might yield deeper understanding. Their reply was roughly, "Nifty, but... My students will soon be taking the MCAT. It will determine whether their years of effort and dreams will succeed or fail. The MCAT doesn't test for that deeper understanding. It asks for <demonstration of superficial memorization of topic>. I would be doing my students a disservice, to spend our limited time together, on anything else."
Which is completely reasonable. One encounters similar constraints down into middle-school.
Similarly, imagine you are talking with a teacher in a country whose educational system prioritizes memorization and superficial understanding even more than our own. India perhaps.
You emphasize the importance of moving beyond rote whole-classroom call-and-response memorize-and-regurgitate. Of developing skills of system modeling, equational reasoning, and problem solving. More like the USA. And the teacher replies to you, similarly to the biology professor above.
Which is completely reasonable.
But surely, that's not all there is. One can step back, and deal with a larger picture. At least within the education research community of that country, there seems value in awareness and discussion, that there might be different, better ways of doing things. And an exploration of what might become possible under unfamiliar sets of deployment constraints. To inform long-term funding and effort. And system-level tweaks. But which might also turn up bits of overlooked opportunities for nearer-term improvement.
I suggest there is value in similar awareness, discussion, and exploration, within our own country/system.
And that there's value, possibly great value, in doing more of it than we have been. Examples of existent efforts might be life-sciences degree curriculum rewrites, and quantitative introductory biology.
For a concrete illustration (illustrative examples is what those "hyper-focus" points earlier were also intended to be ;) of opportunity, somewhat analogous to F=ma, is a second-year college biology top-of-the-wish-list that incoming students have a firmer grasp of central dogma. Which it turns out, with appropriate tooling, is accessible and useful down into middle-school. And so there's now community and institutional support for spreading that tooling and content.
Another is, there's some work on engineering early science education content, to "immunize" against later misconceptions. Early as in K and even pre-K, for primary/middle-school misconceptions. Some of it almost as side effect - content you might use anyway, but tweaked to have nice long-term properties. Rather than struggling to overwrite naive understandings later, you nudge them in the right direction while they're still being formed. I don't recall whether anyone has explored doing this for motion misconceptions, but they seem the kind of thing it might work for.
When people are doing desperate triage in production hell, they understandably have limited attention for someone saying "you know, if we had resources that we don't, and time that we don't, it might be possible to do much better here, and hmm... what might that look like...?" But a healthy tool ecosystem will have some people discussing and exploring that.
Have tried multiple times to follow his work (from the blog). But I'm not math-fluent enough to understand or otherwise appreciate the content. Possibly I could but it requires so much effort.
It's much easier to enjoy Bach's or Messi's genius :)
I've had some success with the following analogy. Music is not math, but the conversation between research mathematicians is a bit like the conversation between composers. In order for them to understand each other well they must understand the notation, but also the instruments/tools, the history, etc. However we non-composers can still listen to what they wrote if someone performs it for us - we may not catch everything another composer does, but we can enjoy it. The tough thing about mathematics is that there is no orchestra or possibility of one; in order to consume it at all you have to learn some of the details.
Think of all the people that might think 'wow this is what you get at Princeton'. Of course logically you know that is not the case and that this is a feature on one very special person. But emotionally (more powerful) that is not what the feeling is.
[1] In reverse if you want proof of this point look at all the people that have entered politics and in particular the Presidential race since Trump was elected. People who in years earlier would have been scared off thinking they were not 'smart' enough. These are people who never realized that a President (regardless of what you think about Trump) does not have to know everything as he relies on others who have expertise (in theory).
I wonder though if such narratives may be necessary (in the world as it is, rather than how it should be) in order to generate fame, specifically the kind of fame that is best able to propagate and reach the eventual endpoints who may be inspired to follow in his footsteps. Annoyances like this may be some sort of social evolutionary adaptation.
I think I saw it linked along with this article about the warped portrayal of genius Hollywood feeds us (especially in the Imitation Game): https://www.huffpost.com/entry/turing-the-myth-of-the-heroic...
So Tao's celebrity status as a genius does have that positive aspect. I think he disproves many stereotypes of genius and helps people believe that it's possible to brilliant, decent, humble, social and likable. I think that's useful.
He talked about this eloquently in his own blog where he argues against the "cult of genius" and says one needn't be a genius to be a mathematician: https://terrytao.wordpress.com/career-advice/does-one-have-t...
So, by lionizing him as a genius I think media actually undermines its own narrative about what genius is. In that sense, maybe the cult of genius is bad but if we have to put a genius on a pedestal, it's great to have it be one who seems so normal.
With respect to his work, I always think of what Richard Feynman said in the start of this book "What do you care what other people think?" (https://www.amazon.com/gp/product/0393355640) He tells a story about an artist who holds up a flower and says "I, as an artist, can see how beautiful a flower is. But you, as a scientist, take it all apart and it becomes dull." Feynman thinks he's nutty. He can see the beauty of the flower and the beauty of the science.
People who don't understand Tao's work probably think it's dull. I can't understand Tao's mathematical work. I'm studying math and I really hope someday I could. But math and science have gone so far now that work at the cutting edge really is incomprehensible to people outside the field. So, I'm inspired by the person who does the work. It's just the surface but it's what I have access to.
Feynman talks about this at the end of the chapter that starts with the flower. His father helped him love science and taught him how to think. Then he sent him to university to learn all the things he hadn't. But when Feynman came home, he couldn't explain quantum mechanics simply. So his father never learned what he didn't know. I hope he still loved his son for understanding it.
Personally I gave up on math as a career once I realized all the people who got into top grad schools for math were like international IMO participants, USAMO or equivalent at least, started taking classes beyond calculus in 10th grade, etc. Even though I love it and even have an undergrad degree in it, and maybe could have performed that well if adults in my life nudged me in that direction, the fact that there were so many people who would always have massive advantages turned me off from it.
However this fixation with his “extraordinary capacity”, scores, medals and accolades; I wish we could skip it.
Let’s talk about the awesome work and why it’s awesome. Let’s play through some of it: I’m relatively sure most people know nothing more about Tao than “he’s a genius”. What’s the point of that?
I think we’d be better off if we took the time to understand great work and let our appreciation of great people live through that.