hilbert problems
https://plus.maths.org/content/taxonomy/term/584
enCantor and Cohen: Infinite investigators part II
https://plus.maths.org/content/cantor-and-cohen-infinite-investigators-part-ii
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Richard Elwes </div>
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<b>Richard Elwes</b> continues his investigation into Cantor and Cohen's work. He investigates the <i>continuum hypothesis</i>, the question that caused Cantor so much grief. </div>
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<div class="pub_date">June 2008</div>
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<h1>The continuum hypothesis</h1>
<p><i>This is one half of a two-part article telling a story of two mathematical problems and two men: Georg Cantor, who discovered the strange world that these problems inhabit, and Paul Cohen (who died last year), who eventually solved them. This article explores what is known as the continuum hypothesis, while <a href="/issue47/features/elwes1">the other article</a> explores the axiom
of choice.<p><a href="https://plus.maths.org/content/cantor-and-cohen-infinite-investigators-part-ii" target="_blank">read more</a></p>https://plus.maths.org/content/cantor-and-cohen-infinite-investigators-part-ii#comments47axiomcontinuum hypothesishilbert problemshistory of mathematicsinfinitylogicphilosophy of mathematicsset theorywhat is infinityZermelo-Fraenkel axiomatisation of set theorySun, 01 Jun 2008 23:00:00 +0000plusadmin2330 at https://plus.maths.org/contentWe must know, we will know
https://plus.maths.org/content/we-must-know-we-will-know
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Rebecca Morris </div>
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<b>Runner up in the general public category</b>. Great minds spark controversy. This is something you'd expect to hear about a great philosopher or artist, but not about a mathematician. Get ready to bin your stereotypes as <b>Rebecca Morris</b> describes some controversial ideas of the great mathematician David Hilbert. </div>
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<div class="pub_date">December 2006</div>
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<p style="color:purple;"><b><i>This article is a runner-up in the general public category of the Plus new writers award 2006.</i></b></p>
<p><i>"It seems that there was a mathematician who had become a novelist. 'Why did he do that?' people in Göttingen marvelled. 'How can a man who was a mathematician write novels?' 'But that is completely simple,' Hilbert said. 'He did not have enough imagination for mathematics, but he had enough for novels.' "</i></p><p><a href="https://plus.maths.org/content/we-must-know-we-will-know" target="_blank">read more</a></p>https://plus.maths.org/content/we-must-know-we-will-know#comments41axiomEuclidean geometryGödel's Incompleteness Theoremhilbert problemshistory of mathematicslogicphilosophy of mathematicsFri, 01 Dec 2006 00:00:00 +0000plusadmin2295 at https://plus.maths.org/contentThe music of the primes
https://plus.maths.org/content/music-primes
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Marcus du Sautoy </div>
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Following on from his article 'The prime number lottery' in last issue of <i>Plus</i>, Marcus du Sautoy continues his exploration of the greatest unsolved problem of mathematics: The <b>Riemann Hypothesis</b>. </div>
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<div class="pub_date">January 2004</div>
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<p><i>Many people have commented over the ages on the similarities between mathematics and music. Leibniz once said that "music is the pleasure the human mind experiences from counting without being aware that it is counting". But the similarity is more than mere numerical. The aesthetics of a musical composition have much in common with the best pieces of mathematics, where themes are
established, then mutate and interweave until we find ourselves transformed at the end of the piece to a new place.<p><a href="https://plus.maths.org/content/music-primes" target="_blank">read more</a></p>https://plus.maths.org/content/music-primes#comments28harmonichilbert problemsimaginary numberlogarithmic integralmathematics and musicprime numberRiemann hypothesisRiemann zeta functionThu, 01 Jan 2004 00:00:00 +0000plusadmin2241 at https://plus.maths.org/contentStruggling for sixteen
https://plus.maths.org/content/struggling-sixteen
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A new attempt to solve Hilbert's 16th problem is causing controversy. </div>
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<div class="pub_date">16/12/2003</div>
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<p>"Who of us would not be glad to lift the veil behind which the future lies hidden" - so started David Hilbert's 1900 lecture outlining the 23 open problems he challenged the mathematical community to solve in the following century.<p><a href="https://plus.maths.org/content/struggling-sixteen" target="_blank">read more</a></p>https://plus.maths.org/content/struggling-sixteen#commentsalgebraic geometryhilbert problemsmathematics in the mediaTue, 16 Dec 2003 00:00:00 +0000plusadmin2519 at https://plus.maths.org/contentThe prime number lottery
https://plus.maths.org/content/prime-number-lottery
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Marcus du Sautoy </div>
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Marcus du Sautoy begins a two part exploration of the greatest unsolved problem of mathematics: The <b>Riemann Hypothesis</b>. In the first part, we find out how the German mathematician Gauss, aged only 15, discovered the dice that Nature used to chose the primes. </div>
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<div class="pub_date">November 2003</div>
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<p>David Hilbert</p><p><a href="https://plus.maths.org/content/prime-number-lottery" target="_blank">read more</a></p>https://plus.maths.org/content/prime-number-lottery#comments27Fibonacci numberhilbert problemslogarithmprime numberRiemann hypothesisSat, 01 Nov 2003 00:00:00 +0000plusadmin2237 at https://plus.maths.org/contentHow maths can make you rich and famous: Part II
https://plus.maths.org/content/how-maths-can-make-you-rich-and-famous-part-ii
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Chris Budd </div>
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One million dollars is waiting to be won by anyone who can solve one of the grand mathematical challenges of the 21st century. In the second of two articles, Chris Budd looks at the well-posedness of the <b>Navier-Stokes equations</b>. </div>
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<div class="pub_date">May 2003</div>
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<h2>A brief history of problem-solving</h2>
<p>Despite the impression given by many textbooks, teachers and internet articles, we understand much less about mathematics than is commonly thought. In fact, maths is littered with problems that we cannot solve.<p><a href="https://plus.maths.org/content/how-maths-can-make-you-rich-and-famous-part-ii" target="_blank">read more</a></p>https://plus.maths.org/content/how-maths-can-make-you-rich-and-famous-part-ii#comments25aerodynamicsangle trisectioncircle-squaringClay Institute Millennium Prize Problemsdoubling the cubeFermat's Last Theoremfluid mechanicshilbert problemsmathematical modellingnavier-stokes equationsWed, 30 Apr 2003 23:00:00 +0000plusadmin2223 at https://plus.maths.org/content