Our community (appropriately defined) is facing a great challenge to reevaluate the role of proof in light of the growing power of current computer systems, of modern mathematical computing packages and of the growing capacity to data-mine on the internet. Add to that the enormous complexity of many modern mathematical results such as the Poincaré conjecture, Fermat’s last theorem, and the classification of finite simple groups. As the need and prospects for inductive mathematics blossom, the need to ensure the role of proof is properly founded remains undiminished. I share with Polya the view that “[I]ntuition comes to us much earlier and with much less outside influence than formal arguments · · · Therefore, I think that in teaching (high school age youngsters we should emphasize intuitive insight more than, and long before, deductive reasoning. ” — George Polya (1887-1985) [15, 2 p. 128] He goes on to reaffirm, nonetheless, that proof should certainly be taught

ABSTRACT I will argue that the mathematical community (appropriately defined) is facing a great challenge to re-evaluate the role of proof in light of the power of current computer systems, of modern mathematical computing packages and of the growing capacity to data-mine on the internet. With great challenges come great opportunities. I intend to illustrate the current challenges and opportunities for the learning and doing of mathematics. As the prospects for inductive mathematics blossom, the need to make sure that the role of proof is properly founded remains undiminished.

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