By Xiuxiong Chen, Professor of Mathematics, Stony Brook University I met Professor Eugenio Calabi in the Fall of 1989, a couple of months after I arrived on the University of Pennsylvania campus. We hit it off quite nicely, as he was a zealous lecturer and loved to go to the blackboard, while I was … Read more
By Charles L. KaneChristopher H. Browne Distinguished Professor of Physics University of Pennsylvania Matter can arrange itself in the most ingenious ways. In addition to the solid, liquid and gas phases that are familiar in classical physics, electronic phases of matter with both useful and exotic properties are made possible by quantum mechanics. In the … Read more
By Graham Farmelo Fellow, Churchill College, University of Cambridge, U.K.Adjunct Professor of Physics, Northeastern University, Boston, MA Miracle of miracles—that’s how the great physicist Frank Yang described the discovery that some of the beautiful structures of modern mathematics precisely describe our universe’s underlying order. This link between the concrete world of physics and the abstractions … Read more
Spenta R. Wadia is Founding Director and Infosys Homi Bhabha Chair Professor at the International Center for Theoretical Sciences of the Tata Institute of Fundamental Research in Bangalore, India. His main research interests are in elementary particle physics, string theory and quantum gravity. Here is an excerpt from an interview during Spenta’s visit to SCGP.
By Juan Maldacena Carl P. Feinberg Professor, School of Natural Sciences Institute for Advanced Study, Princeton NJ Juan Maldacena is Carl P. Feinberg Professor at the Institute for Advanced Study in Princeton. After receiving his Ph.D. from Princeton in 1996, Juan Maldacena became associate professor of physics at Harvard in 1997. In November of that … Read more
Geometry, from the ancient Greek geo (earth) and metron (measurement), is often considered a universal quality in human thinking. In fact, this idea of an innate ability to “know” geometry dates back to Plato. In the dialogue Meno, written about 380 BC by Plato, the philosopher Socrates draws out an accurate answer to a geometric … Read more
Carl Schoonover’s acclaimed book Portraits of the Mind is a fascinating visual odyssey exploring how we investigate the workings of the human brain through images—from medieval sketches and 19th century drawings by the founder of neuroscience, to state-of-the-art techniques that fuel research today. Schoonover is a postdoctoral research scientist in the Axel Laboratory at Columbia … Read more
By George Sterman, Director of the C.N. Yang Institute for Theoretical Physics Most of us would agree that addition and subtraction are simpler than multiplication and division, at least for big numbers. And this is not just for people who lack an affinity for math. When quantitative astronomy began in earnest, astronomers like Tycho Brahe … Read more
By Kenji Fukaya Recently there has been a discussion among mathematicians, as well as in press and several blogs, covering the developments in symplectic geometry. Professor Fukaya expressed interest in giving his opinion and we are happy to present it here: The set of the solutions of the equation x2 + y2 – z2 = … Read more
By Simon Donaldson If we have four objects—say A, B, C, D—there are just three ways of dividing them into pairs: (AB)(CD) (AC)(BD) (AD)(BC). The salient property is that 3 is less than 4. This simple fact expresses something special about the number 4. For example if we take 6 objects there are 10 ways to divide … Read more
