This talk reports on the author's experience in teaching college mathematics students the basics of logic and proof in preparation for their transitioning to upper-level proof-based mathematics courses, following that up with a philosophical and historical analysis of mathematicians' attitudes toward such a project going back to nineteenth- and twentieth-century developments in logic and foundations (De Morgan, Boole, Frege, Russell, and Hilbert). The natural deduction approach to logic and inference developed in the mid-twentieth century by Jaskowski and Fitch is recommended as a much better focused approach for learning how to do proofs in mathematics. This idea is systematically developed in the first part of the author's 2019 textbook Introduction to Discrete Mathematics via Logic and Proof.
Jongsma, Calvin, "Logic and Proof for Mathematics: A Twentieth Century Perspective" (1987). ACMS Conference Proceedings 1987. 5.
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