Scientists From Massachusetts

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April 10, 2026

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April 10, 2026

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"Sometime toward the end of my second year, I started working with Gell-Mann. I went to Gell-Mann and he gave me a problem to work on and suggested I start working with fixed source theory of K-particles, where he wanted me to do things involving strong and weak interactions. And it's when I read about fixed source theory that I began to learn about renormalization group and realized it could be applied to fixed source theory, and I don't know whether there were papers that I read about renormalization group and fixed source theory, or I worked it out for myself, but in playing around with this, sort of trying to learn what was going on, I discovered that there were great simplifications that took place when you took the fixed source equation and took them to high energies, and when you did a leading log approximation. In the end, I discovered that those equations, simplified at the high energies -- you could get exact solutions. That was part of my thesis. And that was the initial thing that sparked my interest in the renormalization group. I remember when I presented my thesis to a seminar, and this was when Feynman was there, but not Gell-Mann. I went through all this exciting mathematics and toward the end, someone said, "Yes, that's fine, but what good is it?" I remember Feynman's answer as "Don't look a gift horse in the mouth!""

- Kenneth G. Wilson

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"One of the facts of nature is that there is what's called parity violation, which means that the fundamental laws are not invariant under mirror reflection. For example, a neutrino always spins clockwise and not counterclockwise, so it would look wrong viewed in a mirror. When you try to write down a fundamental theory with parity violation, mathematical inconsistencies often arise when you take account of quantum effects. This is referred to as the anomaly problem. It appeared that one couldn't make a theory based on strings without encountering these anomalies, which, if that were the case, would mean strings couldn't give a realistic theory. Green and I discovered that these anomalies cancel one another in very special situations. When we released our results in 1984, the field exploded. That's when Edward Witten [a theoretical physicist at the Institute for Advanced Study in Princeton], probably the most influential theoretical physicist in the world, got interested. Witten and three collaborators wrote a paper early in 1985 making a particular proposal for what to do with the six extra dimensions, the ones other than the four for space and time. That proposal looked, at the time, as if it could give a theory that is quite realistic. These developments, together with the discovery of another version of superstring theory, constituted the first superstring revolution."

- John Henry Schwarz

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