Word: godell
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...Kurt Godel was born in 1906 in Brunn, then part of the Austro-Hungarian Empire and now part of the Czech Republic, to a father who owned a textile factory and had a fondness for logic and reason and a mother who believed in starting her son's education early. By age 10, Godel was studying math, religion and several languages. By 25 he had produced what many consider the most important result of 20th century mathematics: his famous "incompleteness theorem." Godel's astonishing and disorienting discovery, published in 1931, proved that nearly a century of effort by the world...
...appreciate Godel's theorem, it is crucial to understand how mathematics was perceived at the time. After many centuries of being a typically sloppy human mishmash in which vague intuitions and precise logic coexisted on equal terms, mathematics at the end of the 19th century was finally being shaped up. So-called formal systems were devised (the prime example being Russell and Whitehead's Principia Mathematica) in which theorems, following strict rules of inference, sprout from axioms like limbs from a tree. This process of theorem sprouting had to start somewhere, and that is where the axioms came in: they...
...last book on my nightstand, and the one furthest out of my normal range, is called Godel, Escher, Bach, by Douglas R. Hofstader. It won the Pulitzer Prize in the early 1980s and ties together math, art and music through images of endlessly looping equations, drawings and musical canons. I've slugged through about 200 pages of it. Although it's starting to get into deep computer theory, which is difficult to read, it's still interesting...
...forever inaccessible to computers. The reason is that all digital computers operate according to algorithms, or sets of rules that prescribe how to solve problems. Yet there are problems that cannot be approached by any system of rules, a fact shown in the 1930s by the mathematician Kurt Godel. Godel's theorem establishes that in any mathematical system there must be certain propositions that are obviously true but that can never be proved within the rules of the system...
Dyson's good cheer seems rigorously earned. For 35 years he has been a professor at the Institute for Advanced Study in Princeton, N.J., where his colleagues have included the likes of Albert Einstein, J. Robert Oppenheimer, Kurt Godel and John von Neumann. Dyson has had an intimate look at upheavals of contemporary science ranging from advances in particle physics and molecular biology to space travel and artificial intelligence. His long career in the ivory tower has not made him a reflexive defender of his elite brotherhood. "I detest and abhor," he writes, "the academic snobbery which places pure scientists...