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Mathematics by Experiment: Plausible Reasoning in the 21st Century, extended second edition, A K
 2008. EXPERIMENTATION AND COMPUTATION 19
, 2008
"... If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics. (Kurt Gödel, 1951) Paper Revised 09–09–04 This paper is an extended version of a presentation made at ICME10, related work is elab ..."
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Cited by 41 (18 self)
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If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics. (Kurt Gödel, 1951) Paper Revised 09–09–04 This paper is an extended version of a presentation made at ICME10, related work is elaborated in references [1–7]. 1 I shall generally explore experimental and heuristic mathematics and give (mostly) accessible, primarily visual and symbolic, examples. The emergence of powerful mathematical computing environments like Maple and Matlab, the growing
FROM TROTSKY to GÖDEL: a LIFE
, 2004
"... If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics. ..."
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If mathematics describes an objective world just like physics, there is no reason why inductive methods should not be applied in mathematics just the same as in physics.
Ten Computational Challenge Problems
"... Moreover a mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock our efforts. It should be to us a guidepost on the mazy path to hidden truths, and ultimately a reminder of our pleasure in the successful solution. · · · Besides it is an error ..."
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Moreover a mathematical problem should be difficult in order to entice us, yet not completely inaccessible, lest it mock our efforts. It should be to us a guidepost on the mazy path to hidden truths, and ultimately a reminder of our pleasure in the successful solution. · · · Besides it is an error to believe that rigor in the proof is the enemy of simplicity.