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Volume 8, Issue 2
2001

I have a passion for proving. In my view, proving is the essence of mathematics. As soon as we ask "why?" we start proving. Proving is cultivated reasoning. Mathematics cannot be defined by the objects studied but only by its method, which is proving. Formal proving, the basis of computer-supported proving, will drastically change the way we do mathematics. Computing is a special case of proving, and proving is a special case of computing. Actually, computing and proving are two of the three main aspects of formal mathematical activity. The third aspect is solving. Proving, solving, and computing naturally correspond to the way free variables in formulae are considered: They can be universally quantified, existentially quantified, or left free for substitution.

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