HPS391H1 Chapter Notes - Chapter 8: Kempe Chain, Mathematical Proof, Probability Theory
29 Apr 2016
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Mathematical legitimacy of computer is debated -> many mathematicians denied that computers could figure in proofs. Doubt of computer proofs makes most sense in a foundational milieu where math proofs are expected to be a priori construction which guarantee their conclusions. Canonical method of checking proofs, reading them over, and verifying doesn"t apply to computer proofs. Hard copies of proofs unobtainable due to amount of computer time required to print them out. Evidence of the validity of computer result is quasi-empirical. Some foundationalists refuse to admit computer proofs to normal mathematics on the grounds that it would change the fundamental character of mathematics. On the other hand quasi-empiricists state that computer proofs = normal mathematics on the grounds that normal math was quasi-empirical. This debate had a breakthrough in 1976 when appel, haken, and koch proved the four-color. Four-color conjecture (four colors suffice to color every map) was well-known but appel, haken, and koch"s proof was computer-dependent.
