Princeton University Alumni

"[E]very human life... is unique, especially seen from the inside. ...You might look like the boring doldrums and the standard... path to somebody else, but for each individual... that person is living only once, and unique experiences... are not... replaceable by anything else... I'm not sure that my experience is qualitatively different from other people's... [P]eople struggle through various difficulties and have moments of joy and... discovery and sometimes... get fed up and... want to leave... [T]hen sometimes they come back and so on... I don't think that it's that different. ...People should realize that their experience is unique and it's interesting, if you make it interesting. ...[I]f you decide that, "Oh, I'm a boring person..." of course you become, ', a boring person... [O]ther people will not help you out. They'll say you're boring, but... you live only once, and... I'm sure there's lot's going on in your brain that the rest of the world cannot see, naturally... [Y]ou should cherish it..."

"[T]he one lesson that I drew from coming in from... lots and lots of detours. ...[T]he other side of the coin. ...I started doing mathematics seriously quite late ...That had interesting consequences. ...Most people in mathematics came into mathematics early ...typically in your teens ...[T]he phenomenon of exists ...only in music and mathematics. ...[C]hild prodegies exist primarily as performers, and the mathematical equivalent is problem solvers, rather than theory builders, and the music equivalent would be s. It's true that Mozart was a child prodigy in composition, but on the whole... performers and problem solvers are the dominant types of child prodigies... [T]his phenomenon only exists in music and mathematics, and correspondingly, they come in quite early... Innate or not... it involves a lot of ... Well, maybe there is such a thing as talent... but one necessary condition for a child prodigy... is... the... that could bear with long long long hours of enormous amounts of training, and sometimes it becomes an obsession. ...I'm aware that child prodigies exist in chess and in ... and in go and so on, but that's... a small variation on mathematics... I don't know about innateness and... I'm not sure about... talent. ...[T]he human brain is a very complicated machine and it would be very surprising if there is no... innate difference between one brain and another... after all, there are innate differences between one body and another... I have seen lots and lots of mathematics students... who are very talented... by the standard judgement... But ultimately... on the whole, I am simplifying... it's really the effort, and how much you really like the subject that made a difference as to ultimate success."

"The study of languages, some... call it linguistics, but the nuance is quite different. Linguistics, since especially Chomsky and that school, became very... analytical and almost mathematical, and so I'm absolutely not interested in or... an analytical study of languages. ...I'm a mathematician, and if I wanted to that... I'll just do... straight mathematics... [I]nstead, philology in the glory days of the 19th century meant primarily the reconstruction of the Indo-European family. So people knew lots and lots of languages, and their peculiarities, and their accidentals and evolution in Greek, Latin, Sanskrit... [I]t was practiced outside the European family, for notably the Semitic family, especially languages that have a lot of written records that go way back, and you can do science. So that's what philology means and that's what they used to do, but I do emphasize that I'm... absolutely not interested in mathematical aspects of linguistics. I'm interested in the languages themselves."

"So I'm not such a great believer in talent. Maybe I'd rather use the word ... because... I find that the people talk too much about the genius, and... correspondingly to the... in music and... mathematics... That's a dangerous word, and I'm not sure that it's socially beneficial to talk about... whether it exists or not. ...Maybe scientifically you can talk about the concept of genius, but it... does more damage sociologically, than it does good."

"People say... discovering things is difficult and... extracting science from everyday life, and the mundane facts... requires talent and special aptitude and so on. I believe that's wrong for the following reason. The reason presupposes a certain belief and outlook on the universe. My outlook is... people say... "I don't like science." That's fair enough... and "Oh, I like science, but... I get tired after a while and I can't continue for so long"... [T]hat's very very reasonable. Or, "I try very very hard but I can't get through some difficulties." Well, what's more human than that? Sure, but... however fragile and... weak humans are, there's... one... creature (anthropomorphically speaking)... who keeps practicing science very very successfully, in fact with 100% success, 24 hours a day, 7 days a week with no stop... and has been doing it for ages and ages... everywhere you go, and that's Nature herself."

"Nature is doing everything in perfect harmony... [W]herever you see and whichever [way] you look, there is something fundamental happening, and there are thousands and tens of thousands of laws of nature that are being satisfied at the same time... [M]any of those laws of Nature are... yet unknown to humans, but it's amazing how coordinated Nature is. It's working all the time! So even when you are fed up, and you close your books, and your professor leaves the room, and go into vacation time, and your internet is down, and so on, you think science stops existing and it stops existing for humans, but Nature keeps going."

"It's possible to argue... [T]here are wonderful musicians, let's talk about... western classical music... nowadays... but... compared with the time of Bach, Mozart and Beethoven, composition in classical music has gone down. ...It's possible to argue that the concept and the belief in genius killed classical music composition. It's extremely... discouraging to be told, "You shouldn't compose unless you can be Beethoven." ...[T]he concept of the genius is an invention of the... German idealistic philosophers. People didn't talk about genius before, and people... simply didn't have the concept and it wasn't part of people's thinking. ...[L]ook at ...Italian Baroque composers... They didn't care about talent or genius but they're creating wonderful music... just on the spot. ...[T]hey didn't have to be tragic. They don't have to have a dramatic life. ...You just do it because you like it, and the same with mathematics."

"The other side... of this observation is that.... whichever [way] you look, and whatever you listen to, and wherever you cast your mind... in that part of the universe that you are observing Nature is doing something. So nothing is easier... to discover than science because science is happening all around you. It's just a matter of opening up your mind a little bit, and making a little bit of effort, and... you have to have an eye for surprises, but humans are born to be surprised, and programmed by Mother Nature to be curious... So you just pay attention, and pause, and relax... [E]specially, you shouldn't worry about what other people think, and what your social standing is. If you are interested in something, it's interesting, and if you're not interested in something, it's not interesting. But you should just keep looking, and everywhere you look, you reach out with your right arm, you reach out your left arm. You stick out your left foot and right foot. Everywhere you reach, there is a bit of science in there... [S]o you meet science all over the place. It's very easy."

"[L]ife is very short and the universe is a wonderful place, and there is so much to see, and so much to experience, and so much to become more intelligent about... [T]he only way you can do it is to have your personal (however modest)... experience of various phenomena... happenings and... events. ...[T]elling about something (this is a meta-comment about something) instead of doing the actual thing, is the worst way to approach science... I'm not going to tell anyone about this and deprive them of the pleasure of seeing the phenomenon themselves."

"You can Google my name, and ... There are lots of videos that they put out online... and you can watch these. However, even that is only a substitute. There's nothing that replaces your own touch. Trying things yourself, and indeed noticing curiosities in nature itself."

"Watching videos is much better than a stupid person like me telling you about this, so that's really the worst possible way to proceed, but even watching videos is no good. You should really try those things yourself and... discover things yourself. There's so much, so much out there."

"I'm fortunate enough to be friends and personally acquainted with some of the leading mathematicians of our age, but... I have never met a genius. They are all understandable. They are wonderful, wonderful people, and they really love what they are doing, and their creations... open up a whole world for you... but I don't think... I ever met a genius. ...In practical terms, it's much more useful to ...focus on other things. So that's why I'm skirting around your question on innate ability."

"[T]he question I wanted to be asked and which I have never been asked is, "What is the question you have been wanting to be asked, but you have not been asked?""

"When you learn mathematics, you learn a lot of definitions. And let's say that you have a certain number of definitions - maybe you learn 100 definitions. Also, there are a number of theorems, and a number of examples to which the theorems apply. Now, a good piece of mathematics should have many more theorems than definitions. And you should have many more examples than theorems - that's a good situation. Unfortunately, everywhere in the world, it happens that in textbooks, in classrooms - You learn 100 definitions (you have memorize definitions!) And then you learn 10 theorems; And then there is only one example. It should be that you have one definition, ten theorems, and 100 or even 10,000 examples to which the theorems apply."

"[T]here are lots of things that one does which are essential, indespensable for survival and which is foundational for everything else, about which people never ask... "What's exciting about it?" What's exciting about breathing for example. ...[I]f you stop breathing, you are no longer. ...You're aware of breathing sometimes. It's not that you're completely unconcsiously invisible, but you don't ask that question. What's exciting about... living itself? Of course there are ups and downs. There are dramas in life, but people don't live because it's exciting. People live because it's natural for them and because that's what they want to do, despite everything sometimes, or in some lucky cases, because of some things. ...But people live because it's a basic and natural way of existing as humans, as indeed, biological creatures... [S]cientists, when they are unhampered and unencumbered by those dictates of sociology... where you have to publish in certain ways because you want to enhance your career, because you want to achieve some status, because you want to... ensure you have a certain standard of living and so on. If they are doing science where they do science because, almost, they have to, because that's their existence... If I lost my job... I have to be able to live somehow, but let's assume that I have some kind of income, and I have to move to and live in isolation. I think after... the initial period of being really depressed... "Why am I stuck here?" and so on, I think I'd end up doing science, because that's... who I am."

"Draw pictures, draw pictures! As a guideline, when I do research in any area (fluid mechanics, geometry, dynamical systems, topology, combinatorics, representation theory), I always draw pictures when I'm doing research. I'm drawing one picture every few minutes, so by the end of the day, after maybe six or seven hours, I have maybe 30, 40 pictures, if not more. So in a week that's hundreds. You should be drawing lots and lots of pictures, trying lots of pictures. Some of these pictures can be in your head, but you should start by drawing lots of real pictures, on paper. But not a few pictures. Not tens of pictures. Hundreds of pictures, please, hundreds. Because that's how we can, eventually, listen to Mozart's music - in mathematics!"

"[I]t's just that mathematics is an unforgiving subject where any misunderstanding, any lack of understanding shows immediately, whereas in the rest of human endeavors you can keep going by faking for quite a long time. So in that way, yes, the language frames how you understand mathematics, but in that very very practical way. ...[T]he best way to improve your chance of future advance in mathematics is to practice, and improve your native language."

"I don't believe that I'm a good communicator. I believe that lots of other people are simply very bad communicators... I don't think other people are thinking. It's completely common sense. I have no intention of claiming any credit for what I do, and if you think this passionately, and if your agenda is not some of the other things I described earlier... [I]f your agenda is to share surprises and to share, if possible, some of the joy to make people understand, there are obvious things that you can do... I'm very surprised that people aren't doing it... [I]t's absolutely obvious to anybody."

"In science we... tend to be interested in things that have been already labeled "interesting." ...[W]e ...think science happens in institutionalized contexts, and that the latest fashions and the "cutting edge" ...is where science occurs... [P]eople who get interested in science often read... books that tell you about the cutting edge... and they get excited, but it's not that they have had an intimate contact with science and got excited. It's rather that sociologically they have been told to be excited about something that's supposed to be exciting. ...They haven't had any exposure to "theory X" but they... are told hero stories... romantic stories... But those... "sciences in flower"... are already blossoming. ...[T]hey have lots and lots of intricate structures up there and [are] connected to lots and lots of things. But at the same time, as with plants, we should look at "sciences in sprout." ...We have the impression that when we stop doing science and go on holiday, or close up our offices and shut down the laboratories for the weekend, science stops happening. And when you close the textbooks and the professor says, "OK, end of class!" you can forget about science... and it stops happening. But that's not true. There's something that keeps practicing science 24 hours a day, 7 days a week, nonstop everywhere in the world, everywhere in the universe, and that's called Nature! If you take... even this blob of air in front of me... there are so many beautiful and intricate and unbelievably complicated, complex s that are dancing together and trying to satisfy one another, and succeeding and satisfying this huge... network of patterns. That is science! It's amazing, and conversely, there is nothing easier to discover than science. ...Everywhere I look, there must be science, because we live in this universe. We cannot even escape living in this universe. We need... imagination and a little bit of patience because you often fail, but especially... we need to look, imagine and maybe a willingness to be trained in acquiring better vision, which is called scientific education. ...It's wonderful that people get interested in science because they're supposed to be interested in science and read... and so on, but that they also try in daily life, phenomena around them, however modest. It would be nice if they started noticing sciences in sprout."

"If you... came back from a very nice trip... Lots of adventures and lots of wonderful experience... and... relaxing one evening... with your family, and you tell your stories, your family are drawn in... I can already...imagine hearing... laughter and... clapping hands and gasps of breath... [Y]ou're communicating very well... [Y]ou do the same thing with science. It's not difficult at all. Absolutely not! In fact the onus is on the other side. Why are people so incompetent? ...[B]ecause their agenda is somewhere else and... who can blame them? ...As humans you want to have a comfortable life. You want to have some... socially recognized position and... security... and the society requires that you communicate in a certain way, which is not at all the way science should be communicated, if your agenda is not one of those."

"[J]ust as many people... correctly worry about biodiversity, I get... emotional and upset... whenever linguistic diversity in particular, and cultural diversity in general, decreases... is threatened... [T]he history of evolution tells us that... you get interesting diversity and... life forms because of . Whenever diversity decreases and one single species or... idea or... way of doing things starts taking over, usually the world is headed for destruction. ...Monkeys that call themselves humans might do some optimization calculations... in their foolishness, and they say, "Oh, ...we have times this ...and that means we have to do it this way. Everyone should be behaving this way..." and so on... [T]hen they end up doing this and in some sense the invention of money doomed us to go in that direction. But I do believe that that way lies madness. ...[F]or me, madness means you abandoned diversity and ...everyone started running in the same direction, and that's really dangerous. So I am... a great partisan of people doing things their own cultural ways, and I don't want, for example, English to take over the entire world."

"Different cultures... until recently, used... science in different styles... [M]athematics, which is supposed to be the most universal of these... If you do zoology or geology or things like that which are geographically constrained, different countries might so things differently, but mathematics is... as universal as any human endeavor can get... [N]onetheless... the Russians... write and think about mathematics in a way very different from how Americans thought and wrote, and the French wrote... and thought mathematics in a way very different from how the Japanese did, and so on... [Y]ou can tell instantly which school, which culture, it came from."

"Many people say mathematics is very difficult to learn, and so it is, and it's probably one of the most difficult things that you can learn, and besides, human brains are not really well adapted to mathematics. It's designed for doing other things, but a lot of mathematical difficulties that people encounter... are actually linguistic. ...[T]here is a definition, a very very precise way of thinking about the limits, and continuity and so on, which... goes under the name of epsilon and delta. So for every epsilon there exists a delta such that... and blah, blah, blah... [T]his is a stumbling block for just about everyone, but when I came into mathematics as an adult... I felt no difficulty whatsoever. In fact I didn't even notice that it was supposed to be difficult. That's because I had been very rigorously trained in the use of languages, as a linguist. ...[S]o the idea that if you change the order quantifiers, of course the meaning changes completely. It was trivial, of course... Compared with the task of taking apart the syntax of somebody like Thucydides... whose sentence continued for a page, with subordinate clause upon subordinate clause... By the way, he writes really clearly, but in a complicated . ...[C]ompared to that kind of thing, the language of mathematics was very very easy. ...[T]here is nothing to it."

"[M]ost people don't have sufficient mastery of their native language. They never had the experience. They don't have... enough practice of careful use of their own native language. ...[Y]ou speak really carefully, making sure that you understand absolutely everything that you are saying and every word and every phrase counts... [N]o... people just blah, blah, blah... talk away. ...[I]f you have a really careful habit of careful use of language... most of the difficulties of mathematics will go away."

"[W]hen I did my PhD, it was in very very pure mathematics and I still love that field, ...algebraic topology ...but then ...I started moving into more physical subjects and... started doing experiments... I thought this was an opportunity. Until then I had lots of... friends and family who were not scientists, and who didn't have any mathematical background, but... with pure mathematics it's very difficult to convey the excitement of computing s... [W]ith physics I decided that every time I finish a project, write a paper or even figure out something, I should design a toy that... captures... joy that I have had, and can share it with people... [T]hen it became quite successful, and it became the other way around. Now I look around and... realize that there's science all around and so I start from the toys... I try to... discover one every month... I was given most of them because my good friends send me toys... but I have... stumbled on... 1/3 of them myself, and... depending on the public lecture... I got... maybe a dozen and... try to tell a story. ...[S]ome of the collections are more cohesive stories than others, but ...whatever I take, I start seeing connections ...And as with the larger nature, so with my toy collection, there are lots and lots of inner connections that I'm waiting to discover; and I usually can."

"We know money is the root of all evil, but it didn't actually stop evil from happening in Cambodia, in fact."

"It is here, at this very moment when the first utterly trivial differential equation is solved, that the secret form of words is revealed that makes modern science possible."

"The derivative is an artifact, the first of the great concepts of modern science that fails conspicuously to correspond to anything in real life."

"Stepping forward, I step back, the two steps, one forward and one back, canceling one another so that after they have been completed, I am where I started, having done something but accomplished little, a useful metaphor for a great many activities in life."

"A mathematical argument, once understood, is in its capacity to compel belief a miracle of enlightened life."

"In the twelfth century, for example, Bhāskara demonstrated correctly that \sqrt{3} + \sqrt{12} = 3\sqrt{3}, an achievement, I might add, utterly beyond the collective intellectual power, say, of the English department at Duke University. (It is pleasant to imagine members of the department sitting together in a long lecture hall, Marxists to one side, deconstructionists to the other, abusing one another roundly as they grapple with the problem.)"

"I have written this book in isolation, hardly talking to a soul, but unoppressed as well by campus codes or creeds, free to say what I want and when I want. It is a measure of the degradation that has overtaken American academic life that I should feel obliged to boast of such circumstances."

"Then he said what I knew—what I had always known—he would say. It is what the dead always say, and it is the only thing they say. “Remember me.”"

"“Any idiot,” he said calmly but with immense conviction, “can learn anything in mathematics. It requires only patience.”"

"I want to denaturalize the present."

"Any claim about…the level of colonial violence, requires not just assumptions about the scale of violence that would have occurred absent colonial rule but also a careful measure of that violence relative to the population, security threat, and security resources in a given territory. One is hard-pressed, to take a prominent example, to find a single example of such care in measurement in the vast critical cholarship on the British counter-insurgency campaign against the Mau in Kenya from 1952 to 1960…At the very least, it is incumbent on scholars to show that the brutalities unleashed by the British in this campaign were not the likely result of a proportionate response given the context and scale of the threat. If this supposedly solid case is wobbly, what does it tell us about the lesser ‘violence’ often cited as invalidating colonialism?"

"One main challenge of this research is to properly enumerate the things that matter and then to assign them weights, weights that presumably varied with time and place."

"Eminent scholars repeatedly make the logically contradictory claim that colonialism was both too disruptive and not disruptive enough."

"Millions of people moved closer to areas of more intensive colonial rule, sent their children to colonial schools and hospitals, went beyond the call of duty in positions in colonial governments, reported crimes to colonial police, migrated from non-colonized to colonized areas, fought for colonial armies, and participated in colonial political processes – all relatively voluntary acts. Indeed, the rapid spread and persistence of Western colonialism with very little force relative to the populations and areas concerned is prima facie evidence of its acceptance by subject populations compared to the feasible alternatives... In most colonial areas, subject peoples either faced grave security threats from rival groups or they saw the benefits of being governed by a modernized and liberal state."

"Of course colonial governance can only return with the consent of the country in question. The nationalist leaders in developing countries are probably not eager to see this happen. But the people- given those decades of ‘anti-colonial disaster’- possibly are."

"After I failed to win consideration for inclusion in the special issue, the Third World Quarterly editor Shahid Qadir sent my article for normal peer review. It received one positive and one negative review. Qadir, as was his prerogative, decided to run it but as a “viewpoint” rather than “research” article, with my consent."

"At least in the initial phases, legitimacy will be demonstrated not by the holding of a plebiscite or by the support of organized and broadly representative groups but simply by the ability of the intervening state to win compliance from key actors and get the job done."

"Research that is careful in conceptualizing and measuring controls, that establishes a feasible counterfactual, that includes multiple dimensions of costs and benefits weighted in some justified way, and that adheres to basic epistemic virtues often finds that at least some if not many or most episodes of Western colonialism were a net benefit, as the literature review by Juan and Pierskalla shows. Such works have found evidence for significant social, economic, and political gains under colonialism: expanded education, improved public health, the abolition of slavery, widened employment opportunities, improved administration, the creation of basic infrastructure, female rights, enfranchisement of untouchable or historically excluded communities, fair taxation, access to capital, the generation of historical and cultural knowledge, and national identify formation, to mention just a few dimensions."

"The overwhelming consensus among our colleagues who are experts in history and political science that Gilley’s research is not merely unpopular but rather discredited."

"He must be treated with utter disgust, with unsurpassed revulsion. He must be ostracized, publicly shamed and humiliated."

"Not only should we not accept Gilley’s general pro-colonial explanation of the poor performance of many post-colonial African nations since he provides us with no good reason to do so, we do have good reason to believe that their poor performance is a legacy of their colonial subjection."

"Whatever we think about Gilley’s article, then, the idea that colonialism can be summarized by reference to a gruesome picture of a Congolese peasant, a trite ‘what if it happened to you’ scenario, and the cheap trick of its ‘tantamount to’ holocaust denial is absurd."

"The problem with Gilley’s case for colonialism is the lack of rigor, his inability or unwillingness to vigorously and transparently challenge his own beliefs, his own values and his own fears – in a word, his perspective."

"By 1891, six years into the attempt to build the EIC, the whole project was on the verge of bankruptcy. It would have been easy for Léopold to raise revenues by sanctioning imports of liquor that could be taxed or by levying fees on the number of huts in each village, both of which would have caused harm to the native population. A truly “greedy” king, as Hochschild repeatedly calls him, had many fiscal options that Léopold did not exercise."

"The rubber quotas imposed on natives in this 15 percent of the territory were enforced by native soldiers working for the companies or for the EIC itself. In many areas, the rubber came with ease and the natives prospered. The rubber station at Irengi, for instance, was known for its bulging stores and hospitable locals, whose women spent a lot of time making bracelets and where “no one ever misses a meal,” noted the EIC soldier George Bricusse in his memoirs. Elsewhere, however, absent direct supervision, and with the difficulties of meeting quotas greater, some native soldiers engaged in abusive behavior to force the collection. Bricusse noted these areas as well, especially where locals had sabotaged rubber stations and then fled to the French Congo to the north. In rare cases, native soldiers kidnapped women or killed men to exact revenge. When they fell into skirmishes, they sometimes followed long-standing Arab and African traditions by cutting off the hands or feet of the fallen as trophies, or to show that the bullets they fired had been used in battle. How many locals died in these frays is unclear, but the confirmed cases might put the figure at about 10,000, a terrible number."