Archives - Mathematics: Page 13
Author: paul carson (Mon Oct 02, 2006 5:23 pm)
Title: Mathematics
“Some of the harshest attacks on The End of Science came from scientists whose fields I had not bothered to investigate (or, from their perspective, to denigrate). Mathematician John Casti complained in a review in the journal Nature that “there is no chapter on the end of mathematics”. I had planned to include such a chapter; I just ran out of time and energy”.
“By one interpretation of modern mathematical thinking, thee are in principle no limits to mathematics. Kurt Gödel’s incompleteness theorem established that any complex system of axioms gives rise to questions that cannot be answered with those axioms. By adding to their base of axioms, mathematicians can keep expanding the realm within which they play, posing new conjectures and constructing new proofs, forever. The question is whether anyone will be able to comprehend those proofs”.
“Possibly the largest conventional proof ever constructed is the classification of finite simple groups, also called the enormous theorem. In its original form, it consisted of some 500 separate papers totaling over 10,000 pages, written by more than 100 mathematicians over 30 years. Perhaps the only person who really understood the proof was Daniel Gorenstein of Rutgers University, who served as a kind of general contractor for the project. He died in 1992”.
“A growing number of mathematical proofs are constructed with the help of computers, which can carry out calculations far beyond the capability of mere mortals. Mathematician Gregory Chaitin warns that many of the computer generated mathematical truths discovered in the future will be random facts, true for no reason apparent to the human mind and offering no insight or understanding. So yes, mathematics can probably continue forever, but our machines might be the only ones able to understand it”. (John Horgan, 2006)
In the case of Mathematics even paper and pencil mathematical proofs probably will continue for ever and we humans will most probably be able to understand them.
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