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Exploratory experimentation: digitally-assisted discovery and proof

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posted on 2025-05-08, 14:35 authored by Jonathan Michael Borwein
The mathematical community (appropriately defined) faces a great challenge to re-evaluate the role of proof in light of the power of current computer systems, the sophistication of modern mathematical computing packages, and the growing capacity to data-mine on the internet. Added to those are the enormous complexity of many modern mathematical results such as the Poincaré conjecture, Fermat’s last theorem, and the classification of finite simple groups. With great challenges come great opportunities. Here, I survey the current challenges and opportunities for the learning and doing of mathematics. As the prospects for inductive mathematics blossom, the need to ensure that the role of proof is properly founded remains undiminished. Much of this material was presented as a plenary talk in May 2009 at the National Taiwan Normal University Workshop for ICMI Study 19 “On Proof and Proving in Mathematics Education.”

History

Source title

Proof and Proving in Mathematics Education: the 19th ICMI Study

Pagination

69-96

Series details

New ICMI Study Series-15

Publisher

Springer

Place published

Dordrecht, Germany

Language

  • en, English

College/Research Centre

Faculty of Science and Information Technology

Rights statement

The final publication is available at www.springerlink.com

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