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The influence of Pythagoras in mathematics and philosophy remains strong today, as do the Themysteries surrounding the great Greek philosopher. Like philosophy and religion, the science of mathematics can change the way we perceive the world and has a massive impact on our lives. Pythagoras’ philosophy influenced both Plato and Aristotle, and through them his ideas were fundamental in Western philosophy. In his life 2,500 years ago, the Greek philosopher combined philosophy, mathematics, and religion, and his work and ideas are still influential to this day. The Pythagorean theorem remains fundamental in mathematics, and is taught in schools across the...

Mathematician Per Enflo, who solved a huge chunk of the 'invariant subspaces problem' decades ago, may have just finished his work.This article was originally published at The Conversation. The publication contributed the article to Space.com's Expert Voices: Op-Ed & Insights. Nathan Brownlowe, Senior Lecturer in the School of Mathematics and Statistics at the University of Sydney. Two weeks ago, a modest-looking paper was uploaded to the arXiv preprint server with the unassuming title "On the invariant subspace problem in Hilbert spaces". The paper is just 13 pages long and its list of references contains only a single entry. The paper...

At an American Mathematical Society meeting, high school students presented a proof of the Pythagorean theorem that used trigonometry—an approach that some once considered impossibleTwo high school students have proved the Pythagorean theorem in a way that one early 20th-century mathematician thought was impossible: using trigonometry. Calcea Johnson and Ne’Kiya Jackson, both at St. Mary’s Academy in New Orleans, announced their achievement last month at an American Mathematical Society meeting. “It’s an unparalleled feeling, honestly, because there’s just nothing like it, being able to do something that ... people don’t think that young people can do,” Johnson told WWL-TV, a...

A nearly 60-year-old mathematical problem has finally been solved. The story began last fall when David Smith, a retired print technician from Yorkshire, England, came upon a shape with a tantalizing property. The life-long tiling enthusiast discovered a 13-sided shape — dubbed the hat — that is able to fill the infinite plane without overlaps or gaps in a pattern that not only never repeats but also never can be made to repeat. This elusive shape is known to mathematicians as an aperiodic monotile or an einstein, a clever pun that takes its name from the German words ein and...

An amateur mathematician in the United Kingdom may have solved a 60-year-old problem in geometry, garnering the attention of researchers. CNN reported David Smith, a retired printing technician, has discovered a shape known as an “einstein,” which can be tiled over a surface without the pattern repeating. The outlet noted mathematicians first began working on this problem in the 1960s. Smith and three coauthors, Joseph Samuel Myers, Craig S. Kaplan, and Chaim Goodman-Strauss, published a paper explaining Smith’s finding. Smith, who says he is “always looking for an interesting shape,” wrote a blog post to serve as a “scrapbook” of...

An ancient clay tablet shows that the Babylonians used Pythagorean triples to measure accurate right angles for surveying land.Students may not believe that Pythagoras’ Theorem has real-world uses, but a 3,700-year-old tablet proves that their maths teachers are right. The artifact, named Si.427, shows how ancient land surveyors used geometry to draw boundaries accurately. Discovered in central Iraq in 1894, Si.427 sat in a museum in Istanbul for over a century. Now, mathematician Dr Daniel Mansfield from the University of New South Wales, Australia, has studied the clay tablet and uncovered its meaning. “Si.427 dates from the Old Babylonian (OB)...

Si.427 is a hand tablet from 1900-1600 BC, created by an Old Babylonian surveyor. It’s made out of clay and the surveyor wrote on it with a stylus. Credit: Must credit UNSW Sydney ========================================================================================== A UNSW mathematician has revealed the origins of applied geometry on a 3700-year-old clay tablet that has been hiding in plain sight in a museum in Istanbul for over a century. The tablet – known as Si.427 – was discovered in the late 19th century in what is now central Iraq, but its significance was unknown until the UNSW scientist’s detective work was revealed today. Most...

At 28, Peter Scholze is uncovering deep connections between number theory and geometry. In 2010, a startling rumor filtered through the number theory community and reached Jared Weinstein. Apparently, some graduate student at the University of Bonn in Germany had written a paper that redid “Harris-Taylor” — a 288-page book dedicated to a single impenetrable proof in number theory — in only 37 pages. The 22-year-old student, Peter Scholze, had found a way to sidestep one of the most complicated parts of the proof, which deals with a sweeping connection between number theory and geometry. “It was just so stunning...

Mysterious structures found deep inside a French cave are the work of Neanderthal builders who lived in the region more than 100,000 years before modern humans set foot in Europe. The extraordinary constructions are made from nearly 400 stalagmites that have been yanked from the ground and stacked on top of one another to produce rudimentary walls on the damp cave floor. The most prominent formations are two ringed walls, built four layers deep in places, which appear to have been propped up with stalagmites wedged in place as vertical stays. The largest of the walls is nearly seven metres...

Deep in a dark cave in southwestern France lie half a dozen mysterious structures that scientists believe were built by Neanderthals 176,000 years ago -- about 140,000 years before the first modern humans arrived in Europe. The structures, described Wednesday in the journal Nature, are located in what is known as the Bruniquel Cave. They are made of roughly 400 pieces of stalagmites, all roughly, almost eerily, the same size. Archaeologists say these mineral formations were probably broken off the cave floor by ancient hands and then deliberately arranged into two large rings and a series of four round piles...

Mathieu Ossendrijver of Humboldt University in Berlin found the tablet while combing through the collections at the British Museum. The written record gives instructions for estimating the area under a curve by finding the area of trapezoids drawn underneath. Using those calculations, the tablet shows how to find the distance Jupiter has traveled in a given interval of time. Until now, this kind of use of trapezoids wasn't known to exist before the 14th century. ... By 400 B.C. Babylonian astronomers had worked out a coordinate system using the ecliptic, the region of the sky the sun and planets move...

A Jewel at the Heart of Quantum Physics Artist’s rendering of the amplituhedron, a newly discovered mathematical object resembling a multifaceted jewel in higher dimensions. Encoded in its volume are the most basic features of reality that can be calculated — the probabilities of outcomes of particle interactions. Physicists have discovered a jewel-like geometric object that dramatically simplifies calculations of particle interactions and challenges the notion that space and time are fundamental components of reality.“This is completely new and very much simpler than anything that has been done before,” said Andrew Hodges, a mathematical physicist at Oxford University who has...

BIRMINGHAM, Ala. (AP) -- The Secret Service questioned an Alabama teacher after school officials said he used an hypothetical example of shooting at the president to teach geometric angles.

This article is also available as a podcast. A Gömböc is a strange thing. It looks like an egg with sharp edges, and when you put it down it starts wriggling and rolling around with an apparent will of its own. Until quite recently, no-one knew whether Gömböcs even existed. Even now, Gábor Domokos, one of their discoverers, reckons that in some sense they barely exists at all. So what are Gömböcs and what makes them special? Balancing act The defining feature of a Gömböc is the fact that it's got just two points of equilibrium: one is stable and...

A French-Russian mathematician has won the Abel Prize today for his work on advanced forms of geometry. The winner of the 6 million Norwegian kroner (US$920,000) prize, Mikhail Leonidovich Gromov, has held a permanent appointment at the Institute of Advanced Scientific Studies (IHES) outside Paris since 1982. The Abel committee cited Gromov specifically for his contributions to three sub-disciplines of modern geometry: the study of Riemannian space, symplectic geometry, and groups of polynomial growth. Gromov is "renowned among mathematicians for his original approach", says Ian Stewart, a mathematician at the University of Warwick in Coventry. Among other things, modern geometers...

Hundreds of years ago in Japan, people offered thanks to the gods by sacrificing a horse or a pig. Horses and pigs, however, were valuable and expensive, so poor folks had a hard time expressing their gratitude. So they came up with a solution: Rather than sacrificing a horse, they would simply draw a painting of a horse on a wooden tablet and hang it in the temple. Then someone, most likely an impoverished samurai, realized that horses and pigs were hardly the only thing that could be drawn on a tablet. He had the idea of painting something original,...

The mosques of the medieval Islamic world are artistic wonders and perhaps mathematical wonders as well. A study of patterns in 12th- to 17th-century mosaics suggests that Muslim scholars made a geometric breakthrough 500 years before mathematicians in the West. Peter J. Lu, a physics graduate student at Harvard University, noticed a striking similarity between certain medieval mosque mosaics and a geometric pattern known as a quasi crystal—an infinite tiling pattern that doesn’t regularly repeat itself and has symmetries not found in normal crystals (see video below). Lu teamed up with physicist Paul Steinhardt of Princeton University to test the...

My 9th grader needs to write a 10 page term paper for her 10th grade honors math class. (Which I find strange). Anyway she is having a difficult time choosing a topic - it cannot be a biography. She was thinking about writing about math used in computer graphics, but she is having a difficult time finding sources that are written anywhere near her level. She needs at least one text as a source - it cannot all be from the internet. Any of you math teachers, general brainiacs, computer geniuses etc. out there who could offer suggestions on a...

Close window Published online: 22 February 2007; | doi:10.1038/news070219-9 Islamic tiles reveal sophisticated mathsMuslim artists were 500 years ahead of western researchers.Philip Ball The pattern on the Darb-i Imam shrine, built in 1453, is almost identical to Penrose tilings, discovered in 1973. Click here for a larger image K. Dudley and M. Elliff The complex geometrical designs used centuries ago in Islamic art and architecture were planned with a tiling system that was not discovered in the West until five centuries later, two physicists have claimed. Islamic tiling patterns were put together not with a compass and ruler, as...

Hyperbolic space is an unimaginable concept, unless you're a Latvian mathematician who's handy with needle and yarn. ___ On a Thursday night in Ithaca, New York, Daina Taimina, an ebullient blond mathematician at Cornell University, sits at her kitchen table with her husband, David Henderson, a Cornell professor of geometry. In front of her sits a big Chinese bowl filled with crinkled forms made of gray, blue, red, and purple yarn. Reaching into the bowl, Taimina pulls out a woozy multicolored surface, the likes of which would have delighted Dr. Seuss. "This is an octagon with a 45 degree angle...