Based on these interviews, he compiled a list of ten dimensions of complexity-ten pairs of apparently antithetical characteristics that are often both present in the creative minds. The list includes:...
This was undoubtedly one of symmetry's greatest success stories. Glashow, Wienberg, and Salam managed to unmask the electromagnetic and weak forces by recognizing that underneath the differences in th...
The forces of nature are color blind. Just as an infinite chessboard would look the same if we interchanged black and white, the force between a green quark and a red quark is the same as that between...
The Greek excellence in mathematics was largely a direct consequence of their passion for knowledge for its own sake, rather than merely for practical purposes. A story has it that when a student who...
Our mathematics is a combination of invention and discoveries. The axioms of Euclidean geometry as a concept were an invention, just as the rules of chess were an invention. The axioms were also suppl...
In other words, Birkhoff proposed a formula for the feeling of aesthetic value: M = O / C. The meaning of this formula is: For a given degree of complexity, the aesthetic measure is higher the more or...
In mathematics, if you are of quick mind, you can get to the frontline of cutting-edge research very quickly. In some other domains you may have to read entire thick volumes first. Moreover, if you ha...
Here, however, is where his genius truly took off. Galois managed to associate with each equation a sort of genetic code of that equation-the Galois group of the equation-and to demonstrate that the p...
Group theory has been called by the noted mathematics scholar James R. Newman the supreme art of mathematical abstraction. It derives its incredible power from the intellectual flexibility afforded by...
Unfortunately, I do not find Tegmark's line of reasoning to be extremely compelling. The leap from the existence of an external reality (independent of humans) to the conclusion that, in Tegmark's wor...
Through the works of Weinberg, Glashow, and Salam on the electroweak theory and the elegant framework developed by the physicists David Gross, David Politzer, and Frank Wilczek for quantum chromodynam...
This development had dramatic philosophical consequences. As in the case of the non-Euclidean geometries in the nineteenth century, there wasn't just one definitive set theory, but rather at least fou...
There were also many cases of feedback between physics and mathematics, where a physical phenomenon inspired a mathematical model that later proved to be the explanation of an entirely different physi...
In the late 1960's, physicists Steven Weinberg, Abdus Salam, and Sheldon Glashow conquered the next unification frontier. In a phenomenal piece of scientific work they showed that the electromagnetic...
The spirit of revolution and the power of free thought were Percy Shelley's biggest passions in life.One could use precisely the same words to describe Galois. On one of the pages that Galois had left...
In it, Porphyry says about Pythagoras: He himself could hear the harmony of the Universe, and understood the music of the spheres, and the stars which move in concert with them, and which we cannot he...