Word: theorems
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Dates: during 1990-1999
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...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's greatest mathematicians was doomed to failure...
...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...
...Were the above 100 percent readings three days later just a fluke, or were they the output of a normally functioning system? What's truly going on? Perhaps inquiries should be forwarded to British mathematician Andrew Wiles, who gained celebrity for his complicated proof of Fermat's Last Theorem, to see if he can provide a solution. Of course, I myself have discovered a remarkable little explanation, but unfortunately this column is too short to contain...
...addition to being elected to the National Academy of Sciences in 1982, Mazur has been awarded the Cole Prize for a theorem concerning elliptic curves...
Mazur is well-known for his work on topology, and his accomplishments in the area of number theory are widely seen as a factor in the 1996 proof of Fermat's Last Theorem by Andrew Wiles...