Historically, women have not enjoyed educational equality. Indeed, Oxford only began awarding degrees to women in the 1920s.  Even today the number of women receiving degrees in mathematics is half that of men. In turn, this lack of access has seeded a widely held, but fallacious, view that men are inherently better skilled at numerate subjects. Despite many studies into sex difference in mathematical ability, the differences have been found to be insignificant. Moreover, studies have shown that reminding women that men are 'better' at mathematics actually causes them to underperform.  This would suggest that it is largely social factors which determine how attractive mathematics is to women; if there is a wide perception that women cannot be mathematicians then they will not become mathematicians. In order, therefore, to promote women in mathematics, it is extremely important to highlight the achievements of those who have bucked the historical trends. One such woman whose life and work should be championed is Emmy Noether.

Pascal's approach does not assume that God gives us any indication of his (for Pascal God was male) existence during our lifetime. But what if there is a god, or some sort of a superior being, who does interact with us in this world? A superior being that plays games with us? In this article we take a rather unusual approach, asking if mathematical game theory can help shed some light on these questions.

Here’s my theory: Some students struggle with economics because they do not fully understand the mathematical tools economists use. Profs do not know how their students were taught mathematics, what their students know, what their students don’t know - and have no idea how to help their students bridge those gaps.

The nature of mathematics is elucidated by one mathematician’s account of how a memory word used by drummers in ancient India led him to the classic problem of the traveling salesman’s route

Maybe you don't understand what the equation says.  Maybe you understand it in theory, but every time you try to apply it in practice you get mixed up trying to remember the difference between p(a|x) and p(x|a), and whether p(a)*p(x|a) belongs in the numerator or the denominator.  Maybe you see the theorem, and you understand the theorem, and you can use the theorem, but you can't understand why your friends and/or research colleagues seem to think it's the secret of the universe.  Maybe your friends are all wearing Bayes' Theorem T-shirts, and you're feeling left out.  Maybe you're a girl looking for a boyfriend, but the boy you're interested in refuses to date anyone who "isn't Bayesian".  What matters is that Bayes is cool, and if you don't know Bayes, you aren't cool.

Oliver Humpage takes us on a full tilt race to, er, zero, in this explanation of his favourite equation, Euler's Identity.

Giant Steps – A music animated short film (2:15 minutes) to John Coltrane’s masterpiece.<br />
When I listen to music I see colors and shapes and when I watch visual art I hear sounds. I wanted to express my sensing of shapes, colors and music in this short animation.<br />
I chose this piece because I’ve struggled to play it for many years and I wanted to gain a deeper understanding of it.“Giant Steps” was also a major breakthrough in the history of Jazz music.  It was the first time that music was based on symmetrical patterns, which stemmed from a mathematical division of the musical scale.<br />
I translated Coltrane’s mathematical approach to architecture. His musical theme defines a space and the musical improvisation is like someone drifting in that imaginary space.

How could bees of little brain come up with anything as complex as a dance language? The answer could lie not in biology but in six-dimensional math and the bizarre world of quantum mechanics.

This book is as vital today as it was when it was first published in 1954. An invaluable exploration of grossly distorted graphs, correlation/causation confusion, and sucky sampling.

"Clouds are not spheres, mountains are not cones, coastlines are not circles, and bark is not smooth, nor does lightning travel in a straight line." So writes acclaimed mathematician Benoit Mandelbrot in his path-breaking book The Fractal Geometry of Nature. Instead, such natural forms, and many man-made creations as well, are "rough," he says. To study and learn from such roughness, for which he invented the term fractal, Mandelbrot devised a new kind of visual mathematics based on such irregular shapes. Fractal geometry, as he called this new math, is worlds apart from the Euclidean variety we all learn in school, and it has sparked discoveries in myriad fields, from finance to metallurgy, cosmology to medicine. In this interview, hear from the father of fractals about why he disdains rules, why he considers himself a philosopher, and why he abandons work on any given advance in fractals as soon as it becomes popular.

Easily incorporate computational thinking into your curriculum with these classroom-ready lessons, examples, and programs. For more resources, including discussion forums and news, visit our ECT Discussion Forums.

Aimed at teaching mathematics students how to program using their knowledge of mathematics, the entire books emphasis is on "how to think" when programming. Three methods for constructing an algorithm or a program are used: manipulation and enrichment of existing code; use of recurrent sequences; deferral of code writing, in order to deal with one difficulty at a time. Many theorems are mathematically proved and programmed, and the text concludes with an explanation of how a compiler works and how to compile "by hand" little programs. Intended for anyone who thinks mathematically and wants to program and play with mathematics.

On the evening of June 20th, several hundred physicists, including a Nobel laureate, assembled in an auditorium at the Friendship Hotel in Beijing for a lecture by the Chinese mathematician Shing-Tung Yau. In the late nineteen-seventies, when Yau was in his twenties, he had made a series of breakthroughs that helped launch the string-theory revolution in physics and earned him, in addition to a Fields Medal—the most coveted award in mathematics—a reputation in both disciplines as a thinker of unrivalled technical power.

It is the best, most accessible work ever in the philosophy of mathematics. It is also beautifully conceived and executed. For those who want to know what philosophical analysis is, this is among the best example ever produced. He succeeded in laying the foundation for the stunning advances in mathematical logic in the 20th century that themselves provided frameworks for modern theories both of computation and of linguistically encoded information.

It turns out that even simple equations can have such complicated behaviour that, in practice, it’s impossible to predict the outcome, which is described as ‘chaotic’. And what’s interesting is that we’ve found this in lots of different areas: from biology to genetics, to computer science and physics, and even in evolutionary systems.

Complexity is saying that sometimes out of simple equations you can get complex behaviours that may not be random but perhaps structured. So the question then is how it is possible to predict where complexity emerges? Complexity the book is concerned with the creation of an institute in Santa Fe to address these questions…from evolutionary systems to cities, to financial markets.

Sync investigates the concept of universal harmony. The drive to synchronization is one of the most far-reaching phenomena in the universe, encompassing people, planets, atoms, animals and a whole lot more. But the laws of Thermodynamics seem to dictate the opposite - that nature should degenerate toward entropy. This is not so, as magnificent small and large structures like galaxies and cells keep assembling themselves in perfect harmony.

Consulting and collecting numbers has been a feature of human affairs since antiquity-from the pyramids to tax collection to head counts for military service-but not until the Scientific Revolution in the seventeenth century did social numbers such as births, deaths and marriages begin to be analysed. The Triumph of Numbers explores how numbers have come to assume a leading role in science, in the operations and structure of government, in the analysis of society, in marketing and in many other aspects of daily life. The late I.B. Cohen shows how number problems of government, science and engineering led to the invention of the computer. He shines a new light on familiar figures like Thomas Jefferson, Ben Franklin and Charles Dickens, and he reveals Florence Nightingale as a passionate statistician. Cohen has left us with an engaging and accessible history of numbers, and an appreciation and understanding of the essential nature of statistics.

Documents the calculation, numerical value, and use of the ratio from 2000 B.C. to the modern computer age, detailing social conditions in eras when progress was made.

This is one of the best-written popular science books to have come this way for quite a while... Seife has a neat turn of phrase, an easy yet respectful familiarity with his subject that helps the maths slip down easily. --Nicholas Lezard, 'The Guardian'

This is an extraordinary book by an extraordinary author. Mathematics teacher Georges Ifrah spent a decade travelling around the world researching the origins of numbers, supporting himself by working as a waiter, taxi-driver and night clerk. The result is The Universal History of Numbers, an impressively detailed account of pretty much every aspect of the emergence and evolution of counting from the Cro-Magnons of 25,000 BC through Babylonian, Greek and Roman times to the metric system and beyond.

The journalist and author says three things define our number system: only ten digits, zero to nine; a place value system, which isn’t true of Roman numerals; and the use of zero, because zero enables easy multiplication and it then becomes feasible for the lay person to calculate.

RT @tcarmody: Excited to hear that @mathpunk's alt-math unbook on DIY science is on its way from YES! to HELL YES!: http://bit.ly/alMLdO

Reading mathematics too quickly results in frustration.  A half hour of concentration in a novel might net the average reader 20-60 pages with full comprehension, depending on the novel and the experience of the reader.  The same half hour in a math article buys you 0-10 lines depending on the article and how experienced you are at reading mathematics. There is no substitute for work and time.  You can speed up your math reading skill by practicing, but be careful.  Like any skill, trying too much too fast can set you back and kill your motivation.  Imagine trying to do an hour of high-energy aerobics if you have not worked out in two years.  You may make it through the first class, but you are not likely to come back.  The frustration from seeing the experienced class members effortlessly do twice as much as you, while you moan the whole next day from soreness, is too much to take.

Any set of five points in the plane in general position has a subset of four points that form the vertices of a convex quadrilateral.

The Ulam spiral, or prime spiral (in other languages also called the Ulam cloth) is a simple method of graphing the prime numbers that reveals a pattern. It was discovered by the mathematician Stanislaw Ulam in 1963, while he was doodling on scratch paper at a scientific meeting.

'Gary Foshee, a collector and designer of puzzles from Issaquah near Seattle walked to the lectern to present his talk. It consisted of the following three sentences: "I have two children. One is a boy born on a Tuesday. What is the probability I have two boys?"'

"Pennsylvania mathematicians have found solutions to a 140-year-old, 7-dimensional equation that were not known to exist for more than a century despite its widespread use in modeling the behavior of gases."

Steven Strogatz moves on to imaginary numbers as part of his series on teaching mathematics to adults.

Tom Henderson is the self-described 'mathpunk'. He argues that the world is stacked against the general public's lack of mathematical understanding. He tries to get students interested in maths and foster real understanding and awareness rather than memorisation of formulae: 'the steps'.

He discusses mathematics in the context of things that humans are likely to be interested in: social conflict, sex and beauty.

How film-makers have (consciously or otherwise) adopted the 1/f fluctuation to reflect human attention spans.

Stephen Strogatz explores negative numbers in his series of excellent articles teaching basic mathematical principles.

"A host of new studies suggests that the two number systems, the bestial and celestial, may be profoundly related, an insight with potentially broad implications for math education."

"Learning on Sesame Street, as in school, means learning Right Answers, and as in school, Right Answers come from grown-ups. We see children figuring things out. As in school, we hear children responding, without much animation or imagination, to leading questions put by adults. But we rarely see them figuring things out; in fact, we rarely see children doing anything."

Fascinating piece on looking at cities through mathematical eyes - what laws define how our cities grow?