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September 2009
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history of mathematics

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Daniel Bernoulli (1700-1782) discovered the relationship between the density of a fluid in a pipe, the speed it is travelling in the pipe and the pressure exerted by the fluid against the walls of the pipe. This is the story of what happened.

Tags: bernoulli equation : history of mathematics


Tags: history of mathematics : Babbage's Engines


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Bill Casselman writes about the intriguing amateur mathematician Henry Perigal, who took his elegant proof of Pythagoras' Theorem literally to his grave - by having it carved on his tombstone.

Tags: history of mathematics : Henry Perigal : pythagoras' theorem : dissection proof : cut-and-shift proof : congruence : tessellation : Pythagoras tiling : lattice tiling


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In 1694, a famous discussion between two of the leading scientists of the day - Isaac Newton and David Gregory - took place on the campus of Cambridge University. The discussion concerned the kissing problem, but it was to be another 260 years before the problem was finally solved.

Tags: history of mathematics : plane geometry : packing : kissing problem : Isaac Newton : David Gregory


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100 years after the birth of Paul Dirac, mathematicians and physicists gather to celebrate his beautiful work.

Tags: history of mathematics : public understanding of mathematics : Dirac's equation


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Richard Elwes continues his investigation into Cantor and Cohen's work. He investigates the continuum hypothesis, the question that caused Cantor so much grief.

Tags: history of mathematics : axiom : logic : set theory : Zermelo-Fraenkel axiomatisation of set theory : hilbert problems : infinity : continuum hypothesis


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Fibonacci, famous for the Fibonacci sequence, also introduced the decimal system into Europe.

Tags: history of mathematics : Fibonacci number : limit : golden ratio : sequence


Tags: history of mathematics : three-dimensional packing : sphere packing problem : Kepler's conjecture


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When Kurt Gödel published his incompleteness theorem in 1931, the mathematical community was stunned: using maths he had proved that there are limits to what maths can prove. This put an end to the hope that all of maths could one day be unified in one elegant theory and had very real implications for computer science. John W Dawson describes Gödel's brilliant work and troubled life.

Tags: history of mathematics : logic : Gödel's Incompleteness Theorem


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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 Rebecca Morris describes some controversial ideas of the great mathematician David Hilbert.

Tags: history of mathematics : axiom : Euclidean geometry : logic : hilbert problems : incompleteness theorem


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Being good at mental arithmetic isn't going to gain you much street cred these days. But, as Owen Daniel explains, not so long ago it was a sure route to fame and fortune — even if you were a horse.

Tags: history of mathematics : arithmetic : mental arithmetic


If you thought you knew what geometry is all about, then this issue of Plus may change your mind. We explore a strange point-less geometry of spacetime, find out about hyperbolic geometry's amazing fractals, celebrate a geometric formula named after Leonhard Euler, the most prolific mathematician of all time, and try to calculate pi. This issue also contains the first ever Plus teacher package and, to celebrate our tenth birthday, continues our series on the history of Plus.

Tags: mathematics education : history of mathematics : four-colour theorem : computer science : incompleteness theorem : plus birthday


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Leonhard Euler was one of the most prolific mathematicians of all time. This year marks the 300th anniversary of his birth. Robin Wilson starts off a four part series on Euler with a look at his life and work.

Tags: history of mathematics : geometry : harmonic series : topology : Euler : infinite series : Euler year


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How to count without counting

Tags: history of mathematics : arithmetic : mathematics in sport : tallying


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What's the nature of infinity? Are all infinities the same? And what happens if you've got infinitely many infinities? In this article Richard Elwes explores how these questions brought triumph to one man and ruin to another, ventures to the limits of mathematics and finds that, with infinity, you're spoilt for choice.

Tags: history of mathematics : axiom : logic : set theory : Russell's Paradox : Zermelo-Fraenkel axiomatisation of set theory : infinity : axiom of choice


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Peter Macgregor explores the beautiful world of the infinite.

Tags: history of mathematics : infinity : transfinite number


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Johannes Kepler (1571-1630) is now chiefly remembered as a mathematical astronomer who discovered three laws that describe the motion of the planets. J.V. Field continues our series on the origins of proof with an examination of Kepler's astronomy.

Tags: history of mathematics : gravity : proof : ellipse : astronomy : geometry : Kepler's three laws of planetary motion : error


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According to one mathematician, god created the whole numbers, with everything else being the work of humanity. Why, then did god not equip us with a good way of writing them down? Chris Hollings reveals that our number system, much used but rarely praised, is in fact a work of genius and took millennia to evolve.

Tags: history of mathematics : Babylonian mathematics : number system


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When it comes to describing natural phenomena, mathematics is amazingly — even unreasonably — effective. In this article Mario Livio looks at an example of strings and knots, taking us from the mysteries of physical matter to the most esoteric outpost of pure mathematics, and back again.

Tags: history of mathematics : philosophy of mathematics : knot : knot theory


What's the risk of climate change or passive smoking? Why do penguins rotate their eggs? What makes mathematicians reach out for god? And how did we evolve the maths behind these questions? Find some answers in this political, psychological, philosophical and physical issue of Plus, and do some real sums with our interactive checker board.

Tags: women in mathematics : bernoulli equation : history of mathematics : astronomy : noether's theorem : computer programming : computer science : calculus : bernoulli : st. petersburg paradox : group theory : galileo : Newton : copernicus : kepler : leibniz : bernoulli number : plus birthday : Kepler's three laws of planetary motion


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Alexander Grothendiek turns 80

Tags: history of mathematics : Fermat's Last Theorem : number theory : algebraic geometry