deduction
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enThe origins of proof III: Proof and puzzles through the ages
http://plus.maths.org/content/origins-proof-iii-proof-and-puzzles-through-ages
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Jon Walthoe </div>
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For millennia, puzzles and paradoxes have forced mathematicians to continually rethink their ideas of what proofs actually are. <strong>Jon Walthoe</strong> explains the tricks involved and how great thinkers like Pythagoras, Newton and Gödel tackled the problems. </div>
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<div class="pub_date">September 1999</div>
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<p>In the Millennia since Euclid, people's conceptions of mathematical proof have been revolutionised. From the discovery of Calculus and the rise of abstract mathematics, to Gödel's amazing discovery. There have been many changes and a few surprises along the way.</p><p><a href="http://plus.maths.org/content/origins-proof-iii-proof-and-puzzles-through-ages" target="_blank">read more</a></p>http://plus.maths.org/content/origins-proof-iii-proof-and-puzzles-through-ages#comments9axiomcalculusdeductionGödel's Incompleteness Theoreminductionirrational numberparadoxproofrational numberRussell's ParadoxTue, 31 Aug 1999 23:00:00 +0000plusadmin2394 at http://plus.maths.org/contentThe origins of proof
http://plus.maths.org/content/origins-proof
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Kona Macphee </div>
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Starting in this issue, PASS Maths is pleased to present a series of articles about proof and logical reasoning. In this article we give a brief introduction to deductive reasoning and take a look at one of the earliest known examples of mathematical proof. </div>
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<div class="pub_date">January 1999</div>
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<p><b>What is proof?</b> Philosophers have argued for centuries about the answer to this question, and how (and if!) things can be proven; no doubt they will continue to do so! Mathematicians, on the other hand, have been using "working definitions" of proof to advance mathematical knowledge for equally long.</p>
<p>Starting in this issue, PASS Maths is pleased to present a series of articles introducing some of the basic ideas behind proof and logical reasoning and showing their importance in mathematics.</p><p><a href="http://plus.maths.org/content/origins-proof" target="_blank">read more</a></p>http://plus.maths.org/content/origins-proof#comments7axiomdeductionEuclid's ElementspremiseproofFri, 01 Jan 1999 00:00:00 +0000plusadmin2385 at http://plus.maths.org/content