It may not have been noticed around here, but the world just lost one of its true geniuses, Freeman Dyson. Dyson played a critical role in the understanding of quantum electrodynamics (QED), a theory of light that makes predictions that agree with experiment to about one part in a trillion, in the early 1950s. As an example of his math abilities, this is an offhand comment he once made at lunch where he worked:
If you take this number: 105263157894736842 and move the 2 at the right hand end of it to the left hand end of it, like this: 210526315789473684, you get exactly double the number:
105263157894736842 + 105263157894736842 = 210526315789473684
105263157894736842 is the smallest number for which this trick works.
The word “genius” gets bandied about a lot and so has been degraded. But Freeman Dyson was a true genius. For those who are interested in what he did, look for this book: “QED and the men who made it: Dyson, Feynman, Schwinger and Tomonaga.” It is not an easy read by any means, but it will give you an idea of the incredible intellectual firepower that went into the development of QED.