Princeton University Alumni

"Two, the State needs to work with industry to rapidly develop and manufacture diagnostic tests, personal protection equipment, medications and ventilators."

"Concurrently the government needs to do five things. One, there needs to be clear messaging about behavioural changes aimed not just at the public but also the police."

"Responses cannot be one-size-fits-all and will need to be tailored to local needs. Agriculture is a state subject and states and district administrators should have flexibility and be encouraged to be innovative and not punished for thinking out of the box."

"At the same time, given India’s population density, the cramped and squalid conditions in which tens of millions people live, not only will social distancing have limited effectiveness (household members of every infected person will be at high risk), but the loss of livelihoods and access to will impose significant human costs. The short-term tradeoff between lives and livelihoods is manifest and nobody really knows where the precise balance lies. Too limited a lockout period risks the lives of potentially hundreds of thousands of people; too restrictive a lockout could result in the eruption of serious ."

"The threat from a rapid diffusion of the coronavirus disease (Covid-19) initially threatened to become India’s most severe since the Spanish Flu, which killed almost 15 million people a century ago. Increasingly, however, it is spiraling into an economic crisis and could easily spin out of control into a humanitarian crisis. Prime Minister Narendra Modi’s speech conveyed a clear sense of the gravity of the situation. Given the structural constraints — India’s population density, weak health and sanitation infrastructure, and limited resources more generally — the need to slow the spread of infection is paramount. Whether the decision to lockdown [sic] the country for 21 days should have come earlier, should have been made with more preparation, should have been longer or shorter in duration, will be intensely debated, but its need is unequivocal."

"You can always find a shock of beauty or meaning in what life you have left."

"People think you're Jesus because you've gone through something special. They treat you like you've got special knowledge, or they treat you a little bit like Frankenstein. Of course, those two responses are related. Neither of them is accurate. But that's the kind of vibe you can get — a lot of us who have disabilities know very well."

"Let death be what takes us, not lack of imagination."

"We make something normal, we call it a problem, we pathologize it, and then we go to war with it. Sometimes that works pretty well, and oftentimes it works not at all. In the case with end of life and death, it's a mix. Medical science and our understanding of health has advanced, and we are able to live longer, and we have pushed back on nature in all sorts of ways that I'm happy for…But the bad news is we just keep orphaning this subject of death, and it becomes less and less familiar and then more and more surprising and gets harder and harder than it needs to be."

"By facing mortality, it seems to inform how you live. So, the secret is that facing death has a lot to do with living well…"

"Leaning into the subject of suffering, leaning into the subject of mortality, was directly therapeutic for me. It wasn’t an intellectual interest or a recreational thought...Getting through my day required me to lean into it, and that’s where I just saw all this beauty that comes from it."

"... these technologies are a kind of training wheels, or a test run, or a pretend version ... of the connectivity we actually have anyway ... so we build the Internet & we say ... you see, this is what it's like to be connected ... now, you are connected (on telecommunications & social media, &c)"

"When the hedge-funders asked me the best way to maintain the authority over their security forces after the 'event', I suggested that their best bet would be to treat those people really well, right now. They should be engaging with their security staffs as if they were members of their own family. And the more they can expand this ethos of inclusivity to the rest of their business practices, supply-chain management, sustainability efforts and wealth distribution, the less chance there will be of an 'event' in the first place."

"This is a book about the role of slavery and the slave trade in the events leading up to 4 July 1776 in igniting the rebellion that led to the founding of the United States of America. ... It is a story that does not see the founding of the U.S.A. as inevitable—or even a positive development: for Africans (or indigenes) most particularly."

"To the extent that 1776 led to the resultant U.S., which came to captain the African Slave Trade—as London moved in an opposing direction toward a revolutionary abolition of this form of property—the much-celebrated revolt of the North American settlers can fairly be said to have eventuated as a counter-revolution of slavery."

"Even when one posits this economic conflict as overriding all others in sparking revolt, the larger point was that it was slavery that was driving these fortunes, particularly in the North American colonies."

"Ironically, the founders of the republic have been hailed and lionized by left, right, and center for—in effect—creating the first apartheid state."

"On 22 June 1772 in a London courtroom ... the presiding magistrate, Lord Mansfield, had just made a ruling that suggested that slavery, the blight that had ensnared so many, would no longer obtain, at least not in England. A few nights later, a boisterous group of Africans, numbering in the hundreds, gathered for a festive celebration. ... Others were not so elated, particularly in Virginia, where the former “property” in question in this case had been residing. “Is it in the Power of Parliament to make such a Law? Can any human law abrogate the divine? The Law[s] of Nature are the Laws of God,” wrote one querulously questioning writer. Indicating that this was not a sectional response, a correspondent in Manhattan near the same time assured that this ostensibly anti-slavery ruling “will occasion a greater ferment in America (particularly in the islands) than the Stamp Act itself,” a reference to another London edict that was then stirring controversy in the colonies. The radical South Carolinian William Drayton—whose colony barely contained an unruly African majority—was apoplectic about this London decision, asserting that it would “complete the ruin of many American provinces.”"

"Happer is a former Princeton physics professor who co-founded the group in 2015. Before that, he chaired the George Marshall Institute—dissolved around the same time of the CO2 Coalition's founding—and developed a reputation as one of the nation's premier climate skeptics."

"It’s important to note the person behind this attempt to chill our defense agencies from understanding and managing climate risk is Dr. Will Happer. Dr. Happer testified before Congress in December 2015 that the world has too little Carbon Dioxide and is too cold – an extreme, fringe view even for the tiny number of scientists who call themselves climate skeptics. This is a clumsy attempt to force the entire federal government to conform to a bizarre view thoroughly rejected by the vast majority of scientists."

"Happer, who worked at the Energy Department under George H.W. Bush and joined the White House in September to work on “emerging technologies,” is not formally trained as a climate scientist."

"Before he founded the CO2 Coalition, Happer chaired the George Marshall Institute and developed a reputation as one of the nation's premier climate "skeptics." The Institute received $865,000 from ExxonMobil between 1998 and 2011. (Elsewhere, ExxonMobil-funded think tanks have been found offering scientists $10,000-a-pop to undermine climate reports.) With a degree in physics from Princeton, Happer is unusually qualified to serve in this area—the various other deniers I spoke to for the story had degrees like a bachelor's in political science or a PhD in geography—but he is a professional denier all the same."

"...the public in general doesn't realize that from the point of view of geological history, we are in a CO2 famine.... There is no problem from CO2. The world has lots and lots of problems, but increasing CO2 is not one of the problems. So [the accord] dignifies it by getting all these yahoos who don't know a damn thing about climate saying, 'This is a problem, and we're going to solve it.' All this virtue signaling. You can read about it in the Bible: Pharisees and hypocrites and phonies."

"Temperatures have not risen very much, and most of the temperature rise is probably completely natural, and has nothing to do with increasing CO2. Industrialization probably played a small role, but I think it's very hard to tell how much."

"I am trying to explain to my fellow Americans the serious damage that will be done to us, and indeed to the whole world, by cockamamie policies to ‘save the planet’ from CO2."

"There’s a whole area of climate so-called science that is really more like a cult. It’s like Hare Krishna or something like that. They’re glassy-eyed and they chant. It will potentially harm the image of all science."

"I like to call this the CO2 anti-defamation league, because, there is the CO2 molecule, and it has undergone decade after decade of abuse, for no reason. We’re doing our best to try and counter this myth that CO2 is a dangerous pollutant. It’s not a pollutant at all. . . . We should be telling the scientific truth, that more CO2 is actually a benefit to the earth."

"Shut up...The demonisation of carbon dioxide is just like the demonisation of the poor Jews under Hitler. Carbon dioxide is actually a benefit to the world, and so were the Jews."

"We know that carbon dioxide has been a much larger fraction of the earth's atmosphere than it is today, and the geological record shows that life flourished on land and in the oceans during those times. The incredible list of supposed horrors that increasing carbon dioxide will bring the world is pure belief disguised as science."

"I, and many other scientists, think the warming will be small compared the natural fluctuations in the earth’s temperature, and that the warming and increased CO2 will be good for mankind."

"The CIA owns everyone of any significance in the major media."

"The somewhere we're goin' to, and got to go to if we don't want to get wiped out, it's somewhere everlastingly and eternally ahead! It's like to-morrow; when we get there we aren't there; we got to keep goin', and we got to everlastingly and eternally keep goin' – and goin' fast! If we don't, the Almighty hasn't got a bit o' use for us; He turns us right into dust and scattered old bones, and nothin's left of our whole country and our finest cities except some street paving and a few cellars with weeds in 'em."

"I'm not sure he's wrong about automobiles," he said. "With all their speed forward they may be a step backward in civilization — that is, in spiritual civilization. It may be that they will not add to the beauty of the world, nor to the life of men's souls. I am not sure. But automobiles have come, and they bring a greater change in our life than most of us suspect."

"If we would stand up and be counted on the side of reason, we ought to drop terms like 'pseudoscience' and 'unscientific' from our vocabulary; they are just hollow phrases which do only emotive work for us."

"The conformal invariance of the Yang-Mills equations in four dimensions greatly facilitates the study of the temporal asymptotic behavior of their solutions."

"The real numbers are the dependable breadwinner of the family, the complete ordered field we all rely on. The complex numbers are a slightly flashier but still respectable younger brother: not ordered, but algebraically complete. The quaternions, being noncommutative, are the eccentric cousin who is shunned at important family gatherings. But the octonions are the crazy old uncle nobody lets out of the attic: they are nonassociative."

"Quantum theory may be formulated using Hilbert spaces over any of the three associative normed division algebras: the real numbers, the complex numbers and the quaternions. Indeed, these three choices appear naturally in a number of axiomatic approaches. However, there are internal problems with real or quaternionic quantum theory. Here we argue that these problems can be resolved if we treat real, complex and quaternionic quantum theory as part of a unified structure. Dyson called this structure the "three-fold way". ... This three-fold classification sheds light on the physics of time reversal symmetry, and it already plays an important role in particle physics."

"The most popular approach to quantum gravity is string theory. Despite decades of hard work by many very smart people, it's far from clear that this theory is successful. It's made no predictions that have been confirmed by experiment. In fact, it's made few predictions that we have any hope of testing anytime soon! Finding certain sorts of particles at the big new particle accelerator near Geneva would count as partial confirmation, but string theory says very little about the details of what we should expect. In fact, thanks to the vast "landscape" of string theory models that researchers are uncovering, it keeps getting harder to squeeze specific predictions out of this theory."

"Besides their possible role in physics, the octonions are important because they tie together some algebraic structures that otherwise appear as isolated and inexplicable exceptions."

"Class field theory can be divided into two parts, local and global. In each part it is the study of all the abelian extensions of a certain base field. The underlying philosophy is to describe all abelian extensions in terms of objects residing within, or close to, the base field."

"It was not until my second year as a doctoral student that I began to understand that mathematics was an ever-expanding universe. My thesis advisor at Princeton was Emil Artin, one of the great algebraists of the century. Unfortunately, or perhaps fortunately, he offered me no advice in the selection of a thesis topic. I think it was a fluke that I got started at all. But once I did, a whole new world opened up, to which I would devote a vast amount of time and energy for over thirty years."

"The spinor genus is due to Eichler. His early results (1952) established the theory over the rational field and also, in certain special cases, over a number field. Kneser (1956) extended this to number fields in general. At about the same time Watson obtained Eichler's results by elementary methods over the rational field."

"Algebraic geometry has developed in waves, each with its own language and point of view. The late nineteenth century saw the function-theoretic approach of Riemann, the more geometric approach of Brill and Noether, and the purely algebraic approach of Kronecker, Dedekind, and Weber. The Italian school followed with Castelnuovo, Enriques, and Severi, culminating in the classification of algebraic surfaces. Then came the twentieth-century "American" school of Chow, Weil, and Zariski, which gave firm algebraic foundations to the Italian intuition. Most recently, Serre and Grothendieck initiated the French school, which has rewritten the foundations of algebraic geometry in terms of schemes and cohomology, and which has an impressive record of solving old problems with new techniques. Each of these schools has introduced new concepts and methods."

"Why do I paint? In my work as a mathematician, form, structure, and economy of expression are important. In music, add tone quality, balance and harmony. And now in painting, these aesthetic values are enhanced by color, contrast, and composition."

"It doesn't matter how long it takes, if the end result is a good theorem."

"A “good theorem,” as Tate puts it, lasts forever. Once proved, it will always stay proved, and other mathematicians are free to use it and build on it as they please, sometimes to great effect."

"Since I was a teenager I had an interest in number theory. Fortunately, I came across a good number theory book by L. E. Dickson, so I knew a little number theory. Also I had been reading Bell’s histories of people like Gauss. I liked number theory. It’s natural, in a way, because many wonderful problems and theorems in number theory can be explained to any interested high-school student. Number theory is easier to get into in that sense. But of course it depends on one’s intuition and taste also."

"The improved understanding of the equations of hydrodynamics is general in nature; it applies to all quantum field theories, including those like quantum chromodynamics that are of interest to real world experiments. I think this is a good (though minor) example of the impact of string theory on experiments. At our current stage of understanding of string theory, we can effectively do calculations only in particularly simple — particularly symmetric — theories. But we are able to analyse these theories very completely; do the calculations completely correctly. We can then use these calculations to test various general predictions about the behaviour of all quantum field theories. These expectations sometimes turn out to be incorrect. With the string calculations to guide you can then correct these predictions. The corrected general expectations then apply to all quantum field theories, not just those very symmetric ones that string theory is able to analyse in detail."

"String theory work done in India is pretty good. … There’s no other country with a GDP per capita comparable to India’s whose string theoretic output is anywhere as good. In fact, the output is better than any country in the European Union, but at the same time not comparable to the EU’s as a whole. So you get an idea of the scale: reasonably good, not fantastic. The striking weakness of research in India is that research happens by and large only in a few elite institutions. But in the last five years, it has been broadening out a bit. TIFR and the Harish-Chandra Research Institute (HRI) have good research groups; there are some reasonably good young groups in Indian Institute of Science (IIS), Bengaluru; Institute of Mathematical Sciences, Chennai; some small groups in the Chennai Mathematical Institute, IIT-Madras, IIT-Bombay, IIT-Kanpur, all growing in strength, The Indian Institute of Science Education and Research (IISER), Pune, has also made good hires in string theory."

"Although quantum theory involves the use of nonlocal states, such as wave packets and entangled states, there is nothing in the theory, or in the real world so far as it is accurately described by quantum theory, that corresponds to the sorts of instantaneous nonlocal influences which have often been thought to arise in the situation envisaged in the EPR paradox, or implied by the fact that quantum theory violates Bell inequalities."