On Ed Witten and innate talent: a winding digression

“Obviously Witten is a little smarter than the average bear.”

— “mathwonk”, in a physicsforums.com thread


(Warning: today’s post is a bit long.)

Ed Witten is famous for having a great turbine of a mind.

He kick-started the second superstring revolution essentially single-handedly, has the highest h-index of any living physicist (that said, h-index is obviously flawed – see e.g. here and here and here, although see here for an argument that it still has better predictive power of future scientific achievement than other indicators considered), is the only physicist to ever win the Fields Medal, etc. Here are quotes about him I can quasi-procedurally recall (don’t remember them specifically, but I remember how to Google for them) right off the bat – and I haven’t even been reading about him for a while. Regardless of whether or not you agree, they’re definitely entertaining.

They also reinforce the idea of innate intellectual ability, a topic I’ve been interested in for a very long time. See e.g. this very interesting article on the so-called “cult of genius” which exists in academic circles in physics, but is also relevant to math and the more “theoretical” sciences, or the touching essayThe Outsiders by Mega Society member Grady Towers, or Yudkowsky on Conway (although reading this would make you think he “just pulled a Malcolm Gladwell“), or Chris Langan, or Marilyn vos Savant (of Monty Hall fame), etc. I bring this up to contextualize the opinions I’ll quote below, who are by people who seem to adamantly believe that “talent” is an overblown and perhaps even elitist concept: I don’t understand their position intuitively, but I want to.

(Digression: This article begins with the very intriguing premise “That intelligence (g) in healthy people is nearly impossible to improve is clear from the failure of psychology to provide any such method.”)

John Randolph Huffman Professor of Physics at Yale writing of his experience of working with Witten:

[O]ne day Ed Witten said to me, ‘I just learnt a new way to find exact S-matrices in two dimensions invented by Zamolodchikov and I want to extend the ideas to supersymmetric models. You are the S-matrix expert, aren’t you? Why don’t we work together?’ I was delighted. All my years of training in Berkeley gave me a tremendous advantage over Ed—for an entire week.

Peter Baida, a close friend of Witten back in Park School (his high school):

I suppose it’s common that kids in any high school sit around talking about who the smartest person in the class is. But we used to sit around — when Edward wasn’t there — and talk about how he was the smartest person in the world.

Michio Kaku (whose bio is really cool) in an article:

I do believe there really is a category for a genius who is a supernova — a supernova that lights up the entire scientific landscape and that is Ed Witten…. I think he is as close as you are going to get to a living Albert Einstein today.

“Max Raker”, commenting on the admittedly rather inane question “who’s the greater living genius, Terence Tao or Ed Witten?” in a discussion thread; this will provide context for something I’ll talk about near the end of this post:

So unlike most other people at his level, Witten didn’t really have scientific interests as an undergrad. The first time in which he officially had anything related to math/physics on his resume was when he started as a grad student at Princeton. I’m not even sure exactly how he got in, but i think within a few months he was working for David Gross. Gross was at this time likely the best physicist in the world. Just before Witten joined his group, he had just finished some very important work on asymptotic freedom SU(3) and the strong interaction. This was work that he and his student, Frank Wilczek later received a Nobel prize for.

So Gross was at the top of his game and also had good experience will gifted and Nobel prize worthy students. Witten had a BS in History and had worked in politics. There are many stories you hear around Princeton about how frustrating Witten was to mentor. David would come up with a problem that he thought would take anybody a few weeks to solve and require a ton of calculations, which a person sort of needs to go through to be educated as a theoretical physicist. Witten would instead come back in a day or 2 with a one page proof that required no calculations and was based on some deep symmetry or other hidden but mathematically sophisticated technique.

You can talk to some profs who were at Princeton at the time and as a school its produced its share of talent (including Tao) but I don’t think the faculty has ever been blown away like they were with Witten. He must have had one of the quickest journeys from “I want to be a physicist” to “I am the most important person in the field” in history.

Brian Greene (from the same link):

Everything I’ve ever worked on, if I trace its intellectual roots, I find they end at Witten’s feet.

(Sounds kind of like this quote said of Hermann Weyl: “In the Mathematical Intelligencer (1984, vol.6 no.1), Michael Atiyah (Professor, School of Mathematics, 1969-72) noted that whenever he examined a mathematical topic, he found that Weyl had preceded him.”)

Timothy Ferriss, acclaimed science writer, in his bestselling book The Whole Shebang:

In the high carrels of theoretical physics, where intelligence is taken for granted, Witten is regarded as preternaturally, almost forbiddingly, smart. A tall, boyish-looking man, he wears the habitual small smile of the theoretician for whom sustained mathematical thinking has something like the emotional qualities that mystics associate with meditation. He speaks in a soft, high pitched voice, floating short, precise sentences punctuated by witty little silences–the speech pattern of a man who has learned that he thinks too fast to otherwise be understood. Though he is the son of a theoretical physicist, Witten came to science in a roundabout fashion. He graduated from Brandeis College in 1971 as a history major, wrote political journalism for the Nation and the New Republic, and worked in George McGovern’s presidential campaign. Primarily a mathematician, he picked up physics along the way, almost as a hobby.

John H. Schwarz in an article:

Witten is both deep and fast: After thinking through the ideas, he can compose an essentially error-free 100-page manuscript, often describing breakthrough original research, on his computer in a day.

In 1987 Michael Green and I coauthored a monograph entitled “Superstring Theory’’ with Witten. We were thrilled that Witten agreed to join us, since we knew that his contributions would greatly improve the final product. This work, consisting of more than 1,000 pages packed with equations, was completed in nine months. For Green and me this required dedicating 100-hour workweeks to the project. Witten, on the other hand, was able to do his share while completing several major research projects at the same time.

Nathan Seiberg:

I think in perspective of a hundred years or three hundred years, his name will stay…. It will not be forgotten — his contributions are really lasting — contributions which will stay there.

He combines the rigor and precision of a mathematician with intuition of a physicist. But what is really remarkable about him is the clarity of his thinking.

He shows the direction for the rest of us…. His main strength is that he’s powerful in everything. Both in math — the most sophisticated math — and physics … he has remarkable physics intuition as well as complete control over the math that is needed. And, in that respect, I think he’s unique.

(“He shows the direction for the rest of us”? That does trigger my cult-detection heuristics alarms (although see here for interesting commentary on “cultishness-detecting heuristics” etc), which I’m sure people like Lee Smolin will approve of.)

Michael Atiyah, legendary geometer and Fields Medalist, on Witten’s work that led to him being awarded the Fields:

Although he is definitely a physicist (as his list of publications clearly shows) his command of mathematics is rivalled by few mathematicians, and his ability to interpret physical ideas in mathematical form is quite unique. Time and again he has surprised the mathematical community by his brilliant application of physical insight leading to new and deep mathematical theorems.

Keith Devlin on why Witten turning 50 is “worth celebrating”, paraphrased:

Witten’s work in manifold theory brings up yet another comparison with Newton. Neither of them were concerned with finding mathematically correct proofs to support their arguments. Relying on their intuitions and their immense ability to juggle complicated mathematical formulas, they both left mathematicians reeling in their wake. It took over two hundred years for mathematicians to develop a mathematically sound theory to explain and support Newton’s method of the infinitesimal calculus. Similarly, it might take decades — maybe even centuries — before mathematicians can catch up with Witten.

For most mathematicians, myself included, the only way to convince ourselves that something is true in mathematics is to find a proof. A very small number of individuals, however, seem to be blessed with such deep and powerful insight that, guided by little else besides their intuitions and a sense of “what is right”, they can cut through the logical thickets and discover the truth directly — whatever that means. Newton did it with calculus. The great Swiss mathematician Leonhard Euler did much the same thing with infinite sums in the eighteenth century. Arguably the Indian mathematician Srinivasa Ramanujan did something similar with the arithmetical patterns of numbers he discovered. And now Witten is doing the same with infinite dimensional manifolds. On several occasions, Witten has made a discovery — a physicist’s discovery since it is technically not a mathematical discovery — that mathematicians subsequently showed to be “correct” by the traditional means of formulating a rigorous proof. Given the complexity of the “insights” that Newton, Euler, Ramanujan, and Witten have made — and the difficulty of the subsequent proofs — this cannot be a case of making lucky guesses.

Here’s a list of honors and awards Witten’s garnered over the years:

….honorary degrees from Brandeis University (1988), the Hebrew University of Jerusalem (1993), Columbia University, New York (1996), the University of Southern California (2004), Johns Hopkins University (2005), and Harvard University (2005). He has received the Einstein Medal from the Einstein Society of Berne, Switzerland (1985), the Award for Physical and Mathematical Sciences from the New York Academy of Sciences (1985), the Dirac Medal from the International Center for Theoretical Physics (1985), the Alan T Waterman Award from the National Science Foundation (1986), the Madison Medal from Princeton University (1992), the New Jersey Pride Award (1996), the Award of the Golden Plate from the American Academy of Achievement (1997), the Klein Medal from Stockholm University (1998), the Dannie Heineman Prize from the American Institute of Physics (1998), the Nemmers Prize in Mathematics from Northwestern University (2000), the Clay Research Award from the Clay Mathematics Institute (2001), the Shalom Award from Americans for Peace Now (2002), the National Medal of Science (2003), the Pythagoras Award from Crotone, Italy (2005), the Harvey Prize from the Technion, Israel (2006), the Poincaré Prize from the International Association Of Mathematical Physics (2006), and the Crafoord Prize in Mathematics from The Royal Swedish Academy of Sciences (2008). He has been elected a Fellow of numerous academies and societies such as American Academy of Arts and Sciences (1984), the American Physical Society (1984), the National Academy of Sciences (1988), the American Philosophical Society (1994), the Royal Society of London (1998), the Academy of Sciences of Paris (2000), and the Pontifical Academy (2006).

If you think I’m trying to make an argument for Witten being “the greatest theoretical physicist alive”, or something related, hold your horses. I’ll get to my point.

Now I’ve previously written on how independent researcher Ron Maimon, whose interests lie in theoretical physics and biology, tends to speak his mind on things that run contrary to standard opinion without regard for e.g. reputation loss, which I’ve found really valuable in instances when I want to know what people really think, instead of what’s polite or sounds publicly acceptable. (If your mental knee-jerk reaction to that was “crank”, you might find said post interesting. You might also find this Less Wrong post on how we intuitively use the absurdity heuristic in screening out claims interesting.) Quoting his user profile on Quora, where he’s now banned:

I am blocked, excellent! It means I did my duty to the absolute limit of acceptability.

In the following Quora answer he replies to the query “is Ed Witten really the world’s greatest living theoretical physicist?” The way he begins immediately gets my attention, probably because it “sounds contrarian“:

I think the greatest living theoretical physicist is Stanley Mandelstam.

But this is just a stupid opinion, like “what’s your favorite pizza topping”. ….to ask who is greater, it’s a question of whether discovery X plus discovery Z is more important than discovery Y, which is completely inane.

Sounds good. Ron then bashes the h-index along the way:

Witten is a great physicist, and never speak ill of a great physicist. However, his number one position has been granted by a corrupt and wrong political process, similar to the h-index, and this is not an acceptable way to go about doing science. It turns a discovery art into a contact sport where the main activity is citation sowing and reaping. The people who win at contact sports are the ones that trample over the field and hurt others.

The rest of the answer (where he goes on about the h-index) is worth reading for entertainment value alone, as is usually the case with Ron, even if you don’t agree with him.

Now it’s well-known that Ed Witten got his physics doctorate in a rather roundabout manner, as e.g. Max Raker’s quote above indicates; just “for the sake of completeness” I’ll include the following quote by Robert Weisbrot to set the stage:

I liked Ed, but felt sorry for him, too, because, for all his potential, he lacked focus. He had been a history major in college, and a linguistics minor. On graduating, though, he concluded that, as rewarding as these fields had been, he was not really cut out to make a living at them. He decided that what he was really meant to do was study economics. And so, he applied to graduate school, and was accepted at the University of Wisconsin. And, after only a semester, he dropped out of the program. Not for him. So, history was out; linguistics, out; economics, out. What to do? This was a time of widespread political activism, and Ed became an aide to Senator George McGovern, then running for the presidency on an anti-war platform. He also wrote articles for political journals like the Nation and the New Republic. After some months, Ed realized that politics was not for him, because, in his words, it demanded qualities he did not have, foremost among them common sense. All right, then: history, linguistics, economics, politics, were all out as career choices. What to do? Ed suddenly realized that he was really suited to study mathematics. So he applied to graduate school, and was accepted at Princeton. I met him midway through his first year there–just after he had dropped out of the mathematics department. He realized, he said, that what he was really meant to do was study physics; he applied to the physics department, and was accepted.

It’s stuff like this – the impression that Witten had innate preternatural gifts of cognition, because you can’t just apply to a physics doctorate program under a recent Nobel Prize winner with a degree in history and linguistics who even does that? – that makes what I’m about to quote so interesting, because Ron himself doesn’t believe in extraordinary innate intelligence (Spearman’s g, the notion of IQ in general, etc). (So does e.g. Terence Tao in his blog post here.) This is rather counterintuitive when you consider that Ron found Math 55 boring (it’s notorious for being perhaps “the hardest undergrad course in the country”), and that Tao was one of the most famous child prodigies of modern times, etc.

(I recall reading Ron’s explanation of Ramanujan’s case, long the clincher for me for the existence of innate prodigious talent, as something like what he used to do himself amplified. Couldn’t find it though)

Responding to a commenter who references the above narrative as proof positive that innate prodigious talent exists, in particular by asking “how do you explain that?“, what Ron writes again strikes me as basically a reflection of what he himself went through as a child, a situation that mirrored Tao’s; it’s also interesting because (and this was the point I forgot to emphasize) it’s an insider view:

He knew exactly what he was doing, politically and also physics. He was the first physics to understand the political lessons of the 1960s (and also the mathematics). Witten had a physicist father, a General Relativist, and this is where he made his early major, major breakthroughs (the positive mass theorem the bubbles of nothing Schwarzschild instanton, the gravitational compactifications of supergravity), he certainly knew General Relativity and Quantum Mechanics since high school, perhaps earlier, maybe in middle school (once you learn calculus, some differential equations it’s easy enough to learn the rest in high school), he studied on his own (like almost every other decent physicist), especially mathematics, in his college years, so he chose a bullshit major he could do in his sleep, but one he was genuinely interested in, because he GOT the politics of the 1960s, and he knew it was going to replace the staid Soviet/Eisenhower/De-Gaulle bureaucratic politics of the 1950s. He also just studied all the math he could, probably wanting to do pure math.

He did a bunch of politics and linguistics, but McGovern lost, and that meant it was going to be terrible in the US for a while longer (nobody guessed how long). Physics in 1972 was still very politically stagnant— the field was split in two, S-matrix and field theory, everyone was stoned and nobody was calculating anything (in Feynman’s words, from that era). Also, it had an atom-bomb stench, maybe that was a factor, maybe not. It certainly was for others back then, who refused to study physics because of the association with atomic bomb work.

Then in 1974 or so, it becomes clear this young Dutch guy named ‘t Hooft has renormalized gauge theory, and ‘t Hooft is producing monumental results left and right, on anomalies, instantons, new gauges, Feynman diagram summations, 2-d models, everything. When he sees this (and he saw it for sure) Witten immediately switches fields. He applies to a graduate program in applied mathematics where he knows David Gross is active (he has a plan), goes over to David Gross and talks physics to him, at which point Gross arranges for him to switch departments, and Witten is considered a phenom, because he already knows everything (it was a stupid trick in the print era– if you just read the literature, and you look like a genius— he was also a genius though).

Then he gets a PhD under Gross (who is by this time very famous, Gross knows S-matrix theory, he studied under Chew, but he is also a major leader in field theory, after asymptotic freedom, plus he knows condensed matter and does 2d stuff too, all things Witten expertly absorbed). He gets a job on the East Coast, at Harvard, where S-matrix and strings are taboo. Then he collaborates with all the big shots, Venziano, Coleman, and so on. Coleman is impressed to no end, and starts studying gravitational things in this era. (Witten is also doing great solo work at this point, like the nonabelian bosonization), and the endless schmoozing and obvious talent and knowledge pushes his h-index to the roof.

Then he goes to Princeton, where he switches and supports string theory, bringing every other marginalized voice up from the gutter, and now he is ABSOLUTELY UNTOUCHABLE, politically, he is Albert Einstein. One cannot thank him enough for this, it was the most important political move in physics history, and that’s not an exaggeration. He also does amazing work to push string theory forward from this point on, formulating open string field theory, finding realistic compactifications, and finding subtle physical consequences of string theory which would give possible observational signatures. He also does amazing work in all fields of high energy physics, and has pure mathematics breakthroughs.

It’s interesting how he keeps emphasizing that having learned all the material going in is “just a stupid trick”.

I don’t know how to properly conclude this post because I forgot the point I was trying to make, so I’ll just end with another Ron quote:

Witten has contributed extremely significantly to mathematics, but so did Candlin with the Berezin integral, and so did Berezin with the proto-SUSY, and most significantly Pierre Ramond, who created graded algebras. You can’t forget Ramond. And Belavin, Polyakov, Zamolodchikov and Knizhnik, who quadruple-handedly founded one of the most active fields of mathematics. Witten too, and Witten’s contributions are closer to the center of what mathematicians find interesting, but you see how the stupid politics gets in the way— he is praised so much, you can’t praise him as he deserves without feeling you are neglecting other people.

The problem with mathematics is that the evaluation of quality is often by human judgement, not by nature, and that can lead to politics too. That’s also somewhat true in physics, but physicists have ways to get around that, by doing experiments, or by pretending to do certain experiments and then breaking our head to come up with an answer as to what happens. The mathematicians have their own “though experiment” solution benchmarks, these are famous conjectures.

Witten solved many interesting mathematical problems of great depth, and also formulated and solved many physical problems (one of my favorite works of his is the superconducting cosmic string paper from the mid 80s, another is a failed paper to try to solve the cosmological constant problem from the 90s, failed, but he gave it a major creative inspirational shot).

But stop trying to rank people on a line, it’s really stupid.

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