# Edward Witten

Jump to navigation
Jump to search

**Edward Witten** (born August 26, 1951) is an American theoretical physicist and professor at the Institute for Advanced Study, who is widely known as “the most brilliant physicist of his generation.” He is a leading researcher in string theory. In 1990, Witten won the Fields Medal, the most prestigious award in pure mathematics.

## Quotes

[edit]- sorted chronologically

**It is very possible that a proper understanding of string theory will make the space-time continuum melt away.... String theory is a miracle through and through.**- as quoted by K.C. Cole, "A Theory of Everything"
*New York Times Magazine*(1987) Oct.18

- as quoted by K.C. Cole, "A Theory of Everything"

- Vibrating strings in 10 dimensions is just a weird fact... An explanation of that weird fact would tell you why there are 10 dimensions in the first place.
- as quoted by K.C. Cole, "A Theory of Everything"
*New York Times Magazine*(1987) Oct.18

- as quoted by K.C. Cole, "A Theory of Everything"

**I don't think that any physicist would have been clever enough to have invented string theory on purpose... Luckily, it was invented by accident.**- as quoted by K.C. Cole, "A Theory of Everything"
*New York Times Magazine*(1987) Oct.18

- as quoted by K.C. Cole, "A Theory of Everything"

**String theory is extremely attractive because gravity is forced upon us.**All known consistent string theories include gravity, so**while gravity is impossible in quantum field theory as we have known it, it is obligatory in string theory.**- as quoted by Michio Kaku,
*Hyperspace: A Scientific Odyssey Through Parallel Universes, Time Warps, and the 10th Dimension*(1995)

- as quoted by Michio Kaku,

**Most people who haven't been trained in physics probably think of what physicists do as a question of incredibly complicated calculations, but that's not really the essence of it. The essence of it is that physics is about concepts, wanting to understand the concepts, the principles by which the world works.**- "Edward Witten" interview,
*Superstrings: A Theory of Everything?*(1992) ed. P.C.W. Davies, Julian Brown

- "Edward Witten" interview,

**Quantum mechanics... developed through some rather messy, complicated processes stimulated by experiment. While it's a very rich and wonderful theory, it doesn't quite have the conceptual foundation of general relativity.**Our problem in physics is that everything is based on these two different theories and when we put them together we get nonsense.- "Edward Witten" interview,
*Superstrings: A Theory of Everything?*(1992) ed. P.C.W. Davies, Julian Brown

- "Edward Witten" interview,

- In Newton's day the problem was to write something which was correct - he never had the problem of writing nonsense, but by the twentieth century we have a rich conceptual framework with relativity and quantum mechanics and so on. In this framework it's difficult to do things which are even internally coherent, much less correct. Actually, that's fortunate in the sense that it's one of the main tools we have in trying to make progress in physics.
**Physics has progressed to a domain where experiment is a little difficult... Nevertheless, the fact that we have a rich logical structure which constrains us a lot in terms of what is consistent, is one of the main reasons we are still able to make advances.**- "Edward Witten" interview,
*Superstrings: A Theory of Everything?*(1992) ed. P.C.W. Davies, Julian Brown

- "Edward Witten" interview,

**String theory at its finest is, or should be, a new branch of geometry. ...I, myself, believe rather strongly that the proper setting for string theory will prove to be a suitable elaboration of the geometrical ideas upon which Einstein based general relativity.**- "Edward Witten" interview,
*Superstrings: A Theory of Everything?*(1992) ed. P.C.W. Davies, Julian Brown

- "Edward Witten" interview,

**I think one has to regard it as a long term process. One has to remember that String theory, if you choose to date it from the Veneziano model, is already eighteen years old**... that quantum electrodynamic theory towards which Planck was heading [in 1900], took fifty years to emerge.- "Edward Witten" interview,
*Superstrings: A Theory of Everything?*(1992) ed. P.C.W. Davies, Julian Brown

- "Edward Witten" interview,

**I would expect that a proper elucidation of what string theory really is all about would involve a revolution in our concepts of the basic laws of physics - similar in scope to any that occurred in the past.**- "Edward Witten" interview,
*Superstrings: A Theory of Everything?*(1992) ed. P.C.W. Davies, Julian Brown

- "Edward Witten" interview,

- It's been said that string theory is part of the physics of the twenty-first century that fell by chance into the twentieth century. That's a remark that was made by a leading physicist about fifteen years ago. ...String theory was invented essentially by accident in a long series of events, starting with the Veneziano model...
**No one invented it on purpose, it was invented in a lucky accident. ...By rights, string theory shouldn't have been invented until our knowledge of some of the areas that are prerequisite... had developed to the point that it was possible for us to have the right concept of what it is all about.**- "Edward Witten" interview,
*Superstrings: A Theory of Everything?*(1992) ed. P.C.W. Davies, Julian Brown

- "Edward Witten" interview,

- It was clear that if I didn't spend the rest of my life concentrating on string theory, I would simply be missing my life's calling.
- as quoted by John Horgan,
*The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age*(1996)

- as quoted by John Horgan,

- Even though it is, properly speaking, a postprediction, in the sense that the experiment was made before the theory,
**the fact that gravity is a consequence of string theory, to me, is one of the greatest theoretical insights ever.**- as quoted by John Horgan,
*The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age*(1996)

- as quoted by John Horgan,

**Good wrong ideas are extremely scarce... and good wrong ideas that even remotely rival the majesty of string theory have never been seen.**- as quoted by John Horgan,
*The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age*(1996)

- as quoted by John Horgan,

**Generally speaking, all the really great ideas of physics are really spin-offs of string theory... Some of them were discovered first, but I consider that a mere accident of the development on planet earth.**On planet earth, they were discovered in this order [general relativity, quantum field theory, superstrings, and supersymmetry]... But I don't believe, if there are many civilizations in the universe, that those four ideas were discovered in that order in each civilization.- as quoted by John Horgan,
*The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age*(1996)

- as quoted by John Horgan,

- If supersymmetry plays the role in physics that we suspect it does, then it is very likely to be discovered by the next generation of particle accelerators, either at Fermilab... or at CERN... Discovery of supersymmetry would be one of the real milestones in physics, made even more exciting by its close links to still more ambitious theoretical ideas. Indeed,
**supersymmetry is one of the basic requirements of "string theory," which is the framework in which theoretical physicists have had some success in unifying gravity with the rest of the elementary particle forces.**Discovery of supersymmetry would would certainly give string theory an enormous boost.- Foreward, written June 30, 1999, to
*Supersymmetry: Unveiling the Ultimate Laws of Nature*(2000) by Gordon Kane

- Foreward, written June 30, 1999, to

- Just around the same time that the string picture was formed, asymptotic freedom was discovered and made possible, in QCD, a more precise and successful theory of the strong interactions. Yet there has always been a striking analogy between QCD and string theory. If the hypothesis of quark confinement in QCD is true in its usual form, than a widely separated quark and antiquark are joined by a “color flux tube.” This has an obvious analogy to the notion of a meson as a string with charges at its ends, as assumed in string theory. Explaining this analogy would mean understanding quark confinement. This would be quite a nice achievement, since it is a longstanding sore point in theoretical physics that despite real experiments and computer simulations supporting the quark confinement hypothesis and despite a lot of ingenious work explaining qualitative criteria for quark confinement and why this notion is natural, there is no convincing, pencil and paper demonstration of quark confinement in QCD.
- Edward Witten (October, 2001). Why strings?.

- Even before string theory, especially as physics developed in the 20th century, it turned out that
**the equations that really work in describing nature with the most generality and the greatest simplicity are very elegant and subtle**.- in a NOVA interview
*Viewpoints on String Theory, Edward Witten*, July 2003.

- in a NOVA interview

- It was found [in the 1970s], unexpectedly and without anyone really having a concept for it, that the rules of perturbation theory can be changed in a way that makes relativistic quantum gravity inevitable rather than impossible. The change is made by replacing point particles by strings. Then Feynman graphs are replaced by Riemann surfaces, which are smooth - unlike the graphs, which have singularities at interaction vertices. The Riemann surfaces can degenerate to graphs in many different ways. In field theory, the interactions occur at the vertices of a Feynman graph. By contrast, in string theory, the interaction is encoded globally, in the topology of a Riemann surface, any small piece of which is like any other. This is reminiscent of how non-linearities are encoded globally in twistor theory.
- "The Past and Future of String Theory" in
*The Future of Theoretical Physics and Cosmology: Celebrating Stephen Hawking's Contributions to Physics*(2003) ed. G.W. Gibbons, E.P.S. Shellard & S.J. Rankin

- "The Past and Future of String Theory" in

- Replacing particles by strings is a naive-sounding step, from which many other things follow. In fact, replacing Feynman graphs by Riemann surfaces has numerous consequences: 1. It eliminates the infinities from the theory. ...2. It greatly reduces the number of possible theories. ...3. It gives the first hint that string theory will change our notions of spacetime. Just as in QCD, so also in gravity, many of the interesting questions cannot be answered in perturbation theory. In string theory, to understand the nature of the Big Bang, or the quantum fate of a black hole, or the nature of the vacuum state that determines the properties of the elementary particles, requires information beyond perturbation theory... Perturbation theory is not everything. It is just the way the [string] theory was discovered.
- "The Past and Future of String Theory" in
*The Future of Theoretical Physics and Cosmology: Celebrating Stephen Hawking's Contributions to Physics*(2003) ed. G.W. Gibbons, E.P.S. Shellard & S.J. Rankin

- "The Past and Future of String Theory" in

- ... one thing that's worth mentioning, though, it that apart from the dream of understanding physics at a deeper level involving gravity, work in string theory has been useful in shedding lights on more conventional problems in quantum field theory and even in condensed matter physics and as well with applications to mathematics. Apart from its intrinsic interest, those successes are one of the things that tend to give us confidence that we're on the right track. Because, speaking personally, I find it implausible that a completely wrong new physics theory would give rise to useful insights about so many different areas.
- (April 23, 2024)"Dirac Conversation: Edward Witten".
*Int'l Center for Theoretical Physics*. (interview by ICTP director Atish Dabholkar; quote at 19:56 of 45:59 in video)

- (April 23, 2024)"Dirac Conversation: Edward Witten".

## Quotes about Witten

[edit]- The past decade has seen a remarkable renaissance in the interaction between mathematics and physics. This has been mainly due to the increasingly sophisticated mathematical models employed by elementary particle physicists, and the consequent need to use the appropriate mathematical machinery. In particular, because of the strongly non-linear nature of the theories involved, topological ideas and methods have played a prominent part. ...

In all this large and exciting field, which involves many of the leading physicists and mathematicians in the world, Edward Witten stands out clearly as the most influential and dominating figure. Although he is clearly 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 suprised the mathematical community by a brilliant application of physical insight leading to new and deep mathematical ideas.- Michael Atiyah, "On the work of Edward Witten".
*Proceedings of the International Congress of Mathematicians (Kyoto, 1990)*.**1**. 1990. pp. 31–35.

- Michael Atiyah, "On the work of Edward Witten".

- For example, Ed Witten recently derived a formula for Donaldson invariants on Kähler manifolds using a twisted version of supersymmetric Yang-Mills theory in four dimensions. His argument depends on the existence of a mass gap, cluster decomposition, spontaneous symmetry breaking, asymptotic freedom, and gluino condensation.

- In the spring of 1985 Ed Witten, one of the most brilliant of young physicists at Princeton University, announced that he would give a talk. ...it was clear that this talk would be an extraordinary occasion. ...our seminar room was packed with people, some old and famous, some young, all eager with expectations. Witten spoke very fast for an hour and a half without stopping. It was a dazzling display of virtuosity. It was also, as Witten remarked quietly at the end, a new theory of the universe. ...When Witten came to the end... The listeners sat silent. ...There were no questions. Not one of us was brave enough to stand up and reveal the depths of our ignorance. ...I describe this scene because it gives a picture of what it means to explore the universe at the highest level of abstraction.
**Ed Witten is taking a big chance.**He has moved so far into abstraction that few even of his friends know what he is talking about. ...He did not invent superstrings. ...**Ed Witten's role is to build superstrings into a mathematical structure which reflects to an impressive extent the observed structure of particles and fields in the universe. After they heard him speak, many members of his audience went back to their desks and did the homework they should have done before, reading his papers and learning his language.**The next time he talks, we shall understand him better.**Next time, we shall perhaps be brave enough to ask questions.**- Freeman Dyson,
*Infinite in All Directions: Gifford Lectures Given at Aberdeen, Scotland April--November 1985*(2004)

- Freeman Dyson,

- Witten's excitement arose from the fact that the theory passed several crucial tests which other theories had failed. To have found a theory of the universe which is not mathematically self-contradictory is already a considerable achievement.
- Freeman Dyson,
*Infinite in All Directions: Gifford Lectures Given at Aberdeen, Scotland April--November 1985*(2004)

- Freeman Dyson,

- Our Witten, which art in Princeton,

Hallowed be thy name.

Thy Nobel come,

Thy will be done,

In CERN as it is in the US.

Give us this day our daily string,

And forgive us our theory,

As we forgive those who do phenomenology.

Lead us not into experiment,

And deliver us from tests.

For thine is the arXiv,

Hep-th and math-AG,

For ever and ever,

Amen- Adam Falkowski, "CERN TH 2007"

- Enter superstring theory. The concept that particles are really tiny strings dates from the 1960s, but it took on wings in 1974, when
**John Schwarz... and Joel Scherk... came to terms with what had been an ugly blemish in their calculations. String theory kept predicting the existence of a particle with zero mass and a spin of two. Schwarz and Scherk realized that this unwelcome particle was nothing other than the graviton**, the quantum carrier of gravitational force (Although there is no quantum theory of gravity yet, it is possible to specify some of the characteristics of the quantum particle thought to convey it.) This was liberating:**The calculations were saying not only that string theory***might*be the way to a fully unified account of all particles and forces but that one could not write a string theory*without*incorporating gravity. Ed Witten... recalled that this new constituted "the greatest intellectual thrill of my life."- Timothy Ferris,
*The Whole Shebang: A State of the Universe Report*(1998)

- Timothy Ferris,

- In the high carrels of theoretical physics, where intelligence is taken for granted,
**Witten is regarded as preternaturally, almost forbiddingly, smart**. ...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, he came to science in a roundabout fashion.- Timothy Ferris,
*The Whole Shebang: A State of the Universe Report*(1998)

- Timothy Ferris,

- The Theory of Everything, if you dare be bold,

Might be something more than a string orbifold.

While some of your leaders have got old and sclerotic,

Not to be trusted alone with things heterotic,**Please heed our advice that you are not smitten—****The Book is not finished, the last word is not Witten.**- Sheldon Lee Glashow with Ben Bova,
*Interactions : a Journey through the Mind of a Particle Physicist and the Matter of this World*(1988)

- Sheldon Lee Glashow with Ben Bova,

- A crucial observation, central to the second superstring revolution initiated by Witten and others in 1995, is that string theory actually includes ingredients with a variety of different dimensions: two-dimensional Frisbee-like constituents, three-dimensional blob-like constituents, and even more exotic possibilities to boot.
- Brian Greene,
*The Elegant Universe*(2003)

- Brian Greene,

- In the mid-1990s, Witten, based on his own insights and previous work by Michael Duff... and Chris Hull and Paul Townsend... gave convincing evidence that... String theory... to most string theorists' amazement, actually requires
*ten*space dimensions and one time dimension, for a total of*eleven*dimensions.- Brian Greene,
*The Elegant Universe*(2003)

- Brian Greene,

- Edward Witten is fond of declaring that string theory had already made a dramatic and experimentally confirmed prediction: "String theory had the remarkable property of predicting gravity." What Witten means by this is that both Newton and Einstein developed theories of gravity because their observations of the world clearly showed them that gravity exists, and that, therefore, it required an accurate and consistent explanation. On the contrary, a physicist studying string theory—even if he or she was completely unaware of general relativity—would be inexorably led to it by the string framework.
- Brian Greene,
*The Elegant Universe*(2003)

- Brian Greene,

- Work by Strominger and Witten showed that the masses of the particles in each family depend upon... the way in which the boundaries of the various multidimensional holes in the Calabi-Yau shape intersect and overlap with one another. ...as strings vibrate through the extra curled-up dimensions, the precise arrangement of the various holes and the way in which the Calabi-Yau shape folds around them has a direct impact on the possible resonant patterns of vibration. ...
**as with the number of families, string theory can provide us with a framework for answering questions—such as why the electron and other particles have the masses they do—on which previous theories are completely silent.**...carrying through with such calculations requires that we know which Calabi-Yau space to take for the extra dimensions.- Brian Greene,
*The Elegant Universe*(2003)

- Brian Greene,

- In the mid-1980s Philip Candelas, Gary Horowitz, Andrew Strominger, and Edward Witten... discovered that each hole—the term used in a precisely defined mathematical sense—contained within the Calabi-Yau shape gives rise to a
*family*of lowest-energy string vibrational patterns. ...among these preferred Calabi-Yau shapes are ones that also yield just the right number of messenger particles as well as just the right electric charges and nuclear force properties to match the particles [listed in the book] ...- Brian Greene,
*The Fabric of the Cosmos*(2003)

- Brian Greene,

- In the spring of 1995... Drawing on the work of a number of string theorists (including Chris Hull, Paul Townsend, Ashoke Sen, Michael Duff, John Schwarz and many others),
**Edward Witten—who for decades has been the world's most renowned string theorist—uncovered a hidden unity that tied all five string theories together. Witten showed that rather than being distinct, the five theories are actually just five different ways of mathematically analyzing a***single*theory. ...The unifying master theory has tentatively been called*M-theory*.- Brian Greene,
*The Fabric of the Cosmos*(2003)

- Brian Greene,

**Much as Kaluza found that a universe with five spacetime dimensions provided a framework for unifying electromagnetism and gravity, and much as string theorists found that a universe with ten spacetime dimensions provided a framework for unifying quantum mechanics and general relativity, Witten found that a universe with eleven spacetime dimensions provided a framework for unifying all string theories.**- Brian Greene,
*The Fabric of the Cosmos*(2003)

- Brian Greene,

- Between sessions at a physics conference, I asked a number of attendees:
**Who is the smartest physicist of them all? ...the name mentioned most often was Witten's.**He seemed to evoke a special kind of awe, as though he belonged to a category unto himself.**He is often likened to Einstein; one colleague reached even further back**for a comparison,**suggesting that Witten possessed the greatest mathematical mind since Newton.**- John Horgan,
*The End of Science: Facing the Limits of Knowledge in the Twilight of the Scientific Age*(1996)

- John Horgan,

**Edward Witten... dominates the world of theoretical physics. Witten is currently the "leader of the pack," the most brilliant high-energy physicist, who sets trends in the physics community the way Picasso would set trends in the art world. Hundreds of physicists follow his work religiously to get a glimmer of his path-breaking ideas.**- Michio Kaku,
*Hyperspace: A Scientific Odyssey through Parallel Universes, Time Warps, and the 10th Dimension*(1994)

- Michio Kaku,

- The boundaries of physics have been changing. Now scientists ask not only how the world works (a question the Standard Model answers) but why it works that way (a question the Standard Model cannot answer). Einstein asked "why" earlier in the century, but only in the past decade or so have the "why" questions become normal scientific research in particle physics, rather than philosophical afterthoughts. One ambitious approach to "why" is known as
*string theory,*which is formulated in an eleven-dimensional world. Work on string theory has proceeded so far by study of the theory itself, rather than via the historical fruitful interplay of experiment and theory.**As Edward Witten remarks... string theory predicts that nature should be supersymmetric.**Supersymmetry is a surprising and subtle idea—the idea that the equations representing basic laws of nature don't change if certain particles in the equations are interchanged with one another.- Gordon Kane,
*Supersymmetry: Unveiling the Ultimate Laws of Nature*(2000)

- Gordon Kane,

**He never does calculations except in his mind.**I will fill pages with calculations before I understand what I'm doing. But Edward will sit down only to calculate a minus sign, or a factor of two.- Chiara Nappi quoted by Robert P. Crease & Charles C. Mann,
*The Second Creation: Makers of the Revolution in Twentieth-century Physics*(1996)

- Chiara Nappi quoted by Robert P. Crease & Charles C. Mann,

- The positive energy theorem was for half a century or more an open challenge to relativists. Many attempts were made to prove flat spacetime was stable, but none completely succeeded completely until a majestic tour de force of geometric reasoning of Shoen and Yau. This was followed two years later by a proof of Witten, which was as elegant as it was short. It is this proof of Witten’s that we take as a template... for the quantum theory.
- Lee Smolin, "Positive energy in quantum gravity"
*arXiv*(Jun 10, 2014) arXiv:1406.2611v1

- Lee Smolin, "Positive energy in quantum gravity"

- We shouldn't toss comparisons to Einstein around too frequently, but when it comes to Witten...
**He's head and shoulder above the rest. He's started whole groups of people on new paths. He produces elegant, breathtaking proofs which people gasp at, which leave them in awe.**- Samuel Treiman, as quoted by K.C. Cole, "A Theory of Everything"
*New York Times Magazine*(1987) Oct.18

- Samuel Treiman, as quoted by K.C. Cole, "A Theory of Everything"

- My stay was nearly over when one 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.
- Ramamurti Shankar, John Randolph Huffman Professor of Physics at Yale.
*Conceptual Foundations of Quantum Field Theory*(1999), p. 48.

- Ramamurti Shankar, John Randolph Huffman Professor of Physics at Yale.

- The MacArthur Foundation chose Witten in 1982 for one of its earliest “genius” grants, and he is probably the only person that virtually everyone in the theoretical physics community would agree deserves the genius label. He has received a wide array of honors, including the most prestigious award in mathematics, the Fields Medal, in 1990. The strange situation of the most talented person in theoretical physics having received the mathematics equivalent of a Nobel Prize, but no actual Nobel Prize in physics, indicates both how unusual a figure Witten is, and also how unusual the relationship between mathematics and physics has become in recent years.

When I was a graduate student at Princeton, one day I was leaving the library perhaps thirty feet or so behind Witten. The library was underneath a large plaza separating the mathematics and physics buildings, and he went up the stairs to the plaza ahead of me, disappearing from view. When I reached the plaza he was nowhere to be seen, and it is quite a bit more than thirty feet to the nearest building entrance. While presumably he was just moving a lot faster than I was, it crossed my mind at the time that a consistent explanation for everything was that Witten was an extraterrestrial being from a superior race who, since he thought no one was watching, had teleported back to his office.

More seriously, Witten’s accomplishments are very much a product of the combination of a huge talent and a lot of hard work. His papers are uniformly models of clarity and of deep thinking about a problem, of a sort that very few people can match. Anyone who has taken the time to try to understand even a fraction of his work finds it a humbling experience to see just how much he has been able to achieve. He is also a refreshing change from some of the earlier generations of famous particle theorists, who could be very entertaining, but at the same time were often rather insecure and not known always to treat others well.- Peter Woit,
*Not Even Wrong*(2006)

- Peter Woit,

- After Einstein’s dramatic success with general relativity in 1915, he devoted most of the rest of his career to a fruitless attempt to unify electromagnetism and gravity using the sorts of geometric techniques that had worked in the case of general relativity. We now can see that this research program was seriously misguided, because Einstein was ignoring the lessons of quantum mechanics. To understand electromagnetism fully one must deal with quantum field theory and QED in one way or another, and Einstein steadfastly refused to do this, continuing to believe that a theory of classical fields could somehow be made to do everything. Einstein chose to ignore quantum mechanics despite its great successes, hoping that it could somehow be made to go away. If Witten had been in Einstein’s place, I doubt that he would have made this mistake, since he is someone who has always remained very involved in whatever lines of research are popular in the rest of the theoretical community. On the other hand, this example does show that genius is no protection against making the mistake of devoting decades of one’s life to an idea that has no chance of success.
- Peter Woit,
*Not Even Wrong*(2006)

- Peter Woit,

## External links

[edit]Categories:

- Physicists from the United States
- 1951 births
- Living people
- People from Baltimore
- MacArthur Fellows
- Fields Medalists
- National Medal of Science laureates
- Princeton University alumni
- Princeton University faculty
- Harvard University faculty
- University of Oxford faculty
- California Institute of Technology faculty
- Crafoord Prize winners