A Philosophical Controversy over

Moghaddam Heydari, Gholam Hossein

A Philosophical Controversy over "Proof" in Mathematics

Document Type : Research Article

Author

Gholam Hossein Moghaddam Heydari

Faculty member of the Humanities Research Institute

Abstract

The Four-Color Conjecture_ that four colors suffice to color every map was a longstanding conjecture well known to every mathematician. It was clearly in the mainstream of mathematics. The year 1976 saw a complete solution to this conjecture. However this proof was essentially dependent on computer. It could not be looked over, reviewed, verified directly by a rational agent. Other mathematicians could not check it by hand. The proof was formalizable but it was not surveyable. This proof is no traditional proof. Is the computer proof really a mathematical proof? The answer to the question leads to serious philosophical problems. Such use of computers in mathematics introduced empirical experiments into mathematics and finally Experimental Mathematics journal published in 1992. The following essay describes the computer proof of the Four-Color Theorem and traces out its philosophical significance.

Keywords

The Four-Color Conjecture

Mathematical Proof

Formalizable

Surveyable

Experimental Mathematics

منابع

الف- فارسی

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ب- لاتین

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http://www-groups.dcs.st-and.ac.uk/~history/PrintHT/The_four_colour_theorem.html

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