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355 posts tagged with Mathematics.

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355 posts tagged with Mathematics.

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## Who is Alexander Grothendieck?

Who is Alexander Grothendieck? [PDF]

*This lecture is concerned not with Grothendieck's mathematics but with his very unusual life on the fringes of human society. In particular, there is, on the one hand, the question of why at the age of forty-two Grothendieck first of all resigned his professorship at the Institut des Hautes Etudes Scientifiques (IHES); then withdrew from mathematics completely; and finally broke off all connections to his colleagues, students, acquaintances, friends, as well as his own family, to live as a hermit in an unknown place. On the other hand, one would like to know what has occupied this restless and creative spirit since his withdrawal from mathematics.*## It's more free maths!

Online Encyclopedia of Mathematics Edited by Michiel Hazewinkel (CWI, Amsterdam), and originaly published in dead tree form in 2002, now free to browse and poke into. [more inside]

## Bite me, Larry Summers.

No gender differences found in math performance. None. Not on average, at least in countries where the sexes are treated equally. And no, not at the highest, outlier levels of mathematical ability, either, despite what some believe.
And not in number of undergrad math degrees earned. And not in terms of complex problem solving ability. Just plain not.

## Rock the streets

Whether you want to learn to lace shoes, tie shoelaces, stop shoelaces from coming undone, calculate shoelace lengths or even repair aglets, Ian's Shoelace Site has the answer!

## A "Harmonious" Path

Accidental Astrophysicists: "They started with algebra and ended up learning about gravitational lensing (PDF)." [Via linkfilter]

## A Woolen Reef

## Reality

The Reality Tests. "A team of physicists in Vienna has devised experiments that may answer one of the enduring riddles of science: Do we create the world just by looking at it?"

## Behind Door Number One...

The Monty Hall Problem has struck again, and this time it’s not merely embarrassing mathematicians. If the calculations of a Yale economist are correct, there’s a sneaky logical fallacy in some of the most famous experiments in psychology." The NY Times' John Tierney reports on new research into cognitive dissonance as examined through the famous Monty Hall Problem. [A previous MetaFilter thread about the Monty Hall Problem: Let's Make A Deal!]

## Would you like to play a game?

Fun and games with mathematics and mathematical puzzles (e.g. heart basket, Rubik's Cube, Rubik's Magic, hypercubes, and more) in both English and (with yet more content in) German.

## Adventures in Balrog Math

## Cut The Knot

Interactive mathematics miscellany and puzzles, including 75 proofs of the Pythagorean Theorem, an interactive column using Java applets, and eye-opening demonstrations. (Actually, much more.)

## Swarm

From Ants to People, an Instinct to Swarm. Carl Zimmer looks at the work of Iain Couzin. [Via The Loom.]

## The Pope with the Robotic Head

Gerbert D'Aurillac: mathemetician and engineer, Pope, ghost, and meddler with dark forces. [more inside]

## Why did Sumerians use base 60 mathematics?

An hour has 60 minutes and a minute has 60 seconds because the Sumerians used a base 60 counting system. Why

*60*? A plausible explanation is that they could count to 12 with one hand, and to 60 with both hands. Alternate explanations from the MacTutor History of Mathematics archive.## Exotic Names for Exotic Shapes.

The Johnson Solids are a set of 92 semi-regular polyhedra, all of which are uniquely named and numbered. Except for the familiar square pyramid they all have exotic names like the Hebesphenomegacorona. A Hebesphenomegacorona in space. Number 26, the Gyrobifastigium, is unique in that if copies of itself are properly stacked together they will leave no gaps, thus making it the only space filling Johnson Solid.

## Writings on Reckoning

The

*Suan shu shu*(筭數書) is an ancient Chinese collection of writings on mathematics discovered together with other texts [Chinese, incl. image of bamboo slips from same excavation] when in 1983 archaeologists opened a tomb at Zhangjiashan in Hubei believed closed in 186 BCE. Main link includes a downloadable full translation with commentary of this earliest extant Chinese work on mathematics by noted China scholar Dr Christopher Cullen.## Life is complex: it has both real and imaginary components

More than fifty selected articles from

*The Princeton Companion of Mathematics*(username:*Guest*, password:*PCM*) — a thematically-organized compendium of mathematics and mathematicians from Fields Medal-winner Tim Gowers. [via, previously]## A Map of the Cat

Richard P. Feynman

**{**Information Junkie**→**PhD**→**Atomic Bomber**→**Professor/Lecturer on Physics + Mathematical Artist [DIY] + Nanotech Knowledgist**→**33.3% Nobel laureate + QEDynamic Speaker + Tiny Machinist + Challenger of Conclusions + Best-Selling Writer –**X**– Busted [outside Tuva]**→**Star Trek TNG Shuttlecraft**↓**Pepsi Black/Blue**↑**U.S. Postage Stamp**}**∞## driven mad by paradoxes

Dangerous Knowledge, BBC. In this one-off documentary, David Malone looks at four brilliant mathematicians - Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing - whose genius has profoundly affected us, but which tragically drove them insane and eventually led to them all committing suicide.

## art with a lot of concept

Fate, Absolute Life and Death, the Aleph, the Zeitgeist, the sinking of the Atlantis, the World Trade Center, the formation of the universe...what more could you want from art? There's probably already been a been a post on this guy, Paul Laffoley, but I should hope more people could get a glance at some of this man's work. Crazy or brilliant, you make your decision. A video from his website.

## Mathematics vs. Democracy: A Clear Winner or a Tie Game?

The Marquis de Condorcet and Admiral Jean-Charles de Borda were two men of the French Enlightenment who struggled with how to design voting systems that accurately reflected voters' preferences. Condorcet favored a method that required the winner in a multiparty election to win a series of head-to-head contests, but he also discovered that his method easily led to a paradoxes that produced no clear winners. The Borda method avoids the Condorcet paradox by requiring voters to rank choices numerically in order of preference, but this method is flawed because the withdrawal of a last-place candidate can reverse the election results. Mathematicians in the 19th century attempted to design better voting systems, including Lewis Carroll, who favored an early form of proportional representation. Economist Kenneth Arrow argued that designing a perfect voting system was futile, because his "impossibility theorem" proved that it's impossible to design a non-dictatorial voting system that fulfills five basic criteria of fairness. (more inside)

## Evolution and Cooperation

In Games, an Insight Into the Rules of Evolution. Carl Zimmer writes about Martin Nowak (previously mentioned here), a mathematical biologist who uses games to understand how cooperation evolved. [Via MindHacks.]

## You say Viagra, I say \/!@&2^

How Many Ways Can You Spell V1@gra? Building on previous research (Cockerham, 2004), Brian Hayes attempts to find the limits of Viagra-spammer ingenuity.

## Math + Vishnu = Really Fast Math

*What is the square of 85? In an instant, a 17-year-old boy said without blinking, "7,225."*

*Kamlesh Shetty had used a trick from a quaint concept called Vedic math, a compilation of arithmetic shortcuts believed to have been written by ancient Indians who lived centuries before Christ, during a glorious period in Indian history called the Vedic Age.*More on Vedic math. Still more. And there's a similar system called the Trachtenberg system, invented in a Nazi concentration camp. Where were these guys when I was in the third grade struggling with my times tables?

## Mathematics in Movies

## Aptitude Schmaptitude!: innumeracy in America

Aptitude Schmaptitude!

*While the state of mathematical incompetence in this country has been much lamented, most famously in Paulos's brilliant 1988 book Innumeracy, it is still tacitly accepted . . . Being incompetent in math has become not only acceptable in this widely innumerate culture, it has almost become a matter of pride. No one goes around showing off that he is illiterate, or has no athletic ability, but declarations of innumeracy are constantly made without any embarrassment or shame.*## The Narrow Road

The Narrow Road : in which a professional mathematician guides you through pure mathematics (and touches on tangential issues).

## Chinese chemists will eat us all

Win £500 from the Royal Society of Chemistry (or a place on a Chinese science undergraduate course) if your math skills are up to it.

## E8 Structure Decoded

Math Team Solves the Unsolvable E8

"If you thought writing calculations to describe 3-D objects in math class was hard, consider doing the same for one with 248 dimensions. Mathematicians call such an object E

"If you thought writing calculations to describe 3-D objects in math class was hard, consider doing the same for one with 248 dimensions. Mathematicians call such an object E

_{8}, a symmetrical structure whose mathematical calculation has long been considered an unsolvable problem. Yet an international team of math whizzes cracked E_{8}'s symmetrical code in a large-scale computing project, which produced about 60 gigabytes of data. If they were to show their handiwork on paper, the written equation would cover an area the size of Manhattan."## Images of Aggregation

Images of Aggregation "These works come from a study of organic natural forms and their relationship to simple mathematical rules." See videos, and also, Images of Flow. [via]

## My blog is smarter than your blog.

Alain Connes has a blog. Terry Tao also has a blog. Two Fields medalists blog on open problems, their views on mathematics, and Tomb Raider. Timothy Gowers doesn't have a blog, but does have a compendium of informal essays on topics like Why is multiplication commutative? If you prefer pictures to words: Faces of Mathematics.

## Music of golden proportions

Zelda and the Golden Ratio. A fascinating examination of the music from Nintendo's Zelda games, and the recurring appearances of 0.618, the bisection point on a line at which the relationship of the shorter segment to the longer one is the same as that of the longer section to the whole line.

## The scholarship on whether Pythagoras wrote "Beans, Beans, the Musical Fruit" remains inconclusive.

Everything you know about Pythagoras is wrong (except the bit about the beans). Less the golden-thighed Einstein of the Ancient World and more the L. Ron Hubbard of Magna Graecia. [Last link has some rude words]

## Origeometry

What if Euclid had been Japanese? There are traditionally stated and proved theorems

*about*origami. And MetaFilter has previously explored modular origami (as well as the boring old artistic kind), which has a geometric foundation. However, origami itself is a powerful mathematical framework that allows one to, for instance, solve the famously insoluable problem of trisecting an angle. More generally: Traditional geometry solves quadratic equations, origami solves cubic ones. (Many more mathematical items about and using origami can be found in the excellent mathematics teachers' book: Project Origami: Activities for Exploring Mathematics, most of which are unfortunately not findable online).## In Soviet Russia, sponge soaks you

Dr. Jeannine Mosely finishes building a level-3 Menger sponge from business cards. You can also build your own, though Dr. Mosely warns, "[a] level 4 sponge would require almost a million cards and weigh over a ton. I do not believe it could support its own weight — so a level 3 is the biggest sponge we can hope to build." (related)

## Let them eat cake... fairly.

Mathematicians in the 1940s became curious about Fair Division, thus birthing an entire branch of mathematics concerned with cutting cakes. Recently, this man came up with a new method, purported to be the most fair yet. Hard to disbelieve, coming from the topologist who has mastered shoelaces, although arguably he's missing the point.

## Kinseyian mathematics, of a kind

The "Darwinian paradox" of homosexuality presents the conundrum of how a potential genetic basis for homosexual behavior could provide a survival benefit to offpsring and extend through generations, when sexual reproduction would seem to place strong selection pressure against such a "gene". Recently developed mathematical models (PDF) from researchers Sergey Gavrilets and William Rice not only show how a "gay gene" might proliferate within a population, but also provides testable hypotheses, including predictions of "widespread bisexuality" (subscription req'd).

## Operation Kaprekar

Mysterious number 6174. An excellent recreational math article.

## Gallery

## Nullity and Perspex Machines

Dr James Anderson, from the University of Reading's computer science department, claims to have defined what it means to divide by zero. It's so simple, he claims, that he's even taught it to high school students [via Digg]. You just have to work with a new number he calls Nullity (RealPlayer video). According to Anderson's site The Book of Paragon, the creation, innovation, or discovery of nullity is a step toward describing a "perspective simplex, or perspex [ . . . ] a simple physical thing that is both a mind and a body." Anderson claims that Nullity permits the definition of transreal arithmetic (pdf), a "total arithmetic . . . with no arithmetical exceptions," thus removing what the fictional dialogue No Zombies, Only Feelies? identifies as the "homunculus problem" in mathematics: the need for human intervention to sort out "corner cases" which are not defined.

## Good times, good times!

Autodidactic goodies on a budget: Free computer books and online lectures, seminars and instructional materials from a variety of renowned institutions.

## Of course, I'm illiterate!

Platonic Realms is an online math academy. It features a searchable encyclopedia with extended articles on things from Cantor's Theorem to Zeno's Paradox of the Tortoise and Achilles. You'll also find minitexts, such as "Coping with Math Anxiety" and "The Mathematical Art of M.C. Escher". Last but not least, a searchable math quotes database.

## Sorry, but I can't find "Story of Your Life"

## Interview of Grigory Perelman

Grigory Perelman, awarded the Fields Medal for his work on the Poincare Conjecture, talks to the New Yorker.

## Proofs and Pictures: The Role of Visualization in Mathematical and Scientific Reasoning

Proofs and Pictures: The Role of Visualization in Mathematical and Scientific Reasoning [video] "The picture is a telescope for looking into Plato's heaven." -- James Brown [cached]

## paging dr. perelman

Grisha Perelman, where are you? Perelman has quite possibly solved one of mathematics biggest mysteries, Poincaré’s conjecture, but has since disappeared.

## Turing: The Final Years

Among his collected works, in the few, short years before mathematician Alan Turing was driven to suicide, he published

*"The Chemical Basis of Morphogenesis"*, theorizing how a standing wave-like distribution of "cannibal" and "missionary" chemicals might explain how plants and animals develop their shape and pigmentation. Blogger Jonathan Swinton focuses on this more obscure aspect of Turing's research, and reviews some of his posthumous and unpublished efforts — including one of the earliest known examples of digital computation applied to the field of biology.## More than you ever wanted to know about nothing at all

The Zero Saga contains a great deal of information about the concept of zero, and its relation to other numbers and concepts in mathematics. It was linked in Good Math, Bad Math; which contains a variety of other informative articles on the numbers that capture our imaginations. (

**Note:**You may want to skip past part 4 of the Zero Saga, as it contains replies to the site, and as such should probably be at the bottom of the page. But, to compensate, the comments on Good Math are better than most blogs I've read.)## The Moving Sofa Constant

The Moving Sofa Constant. We have noticed you have a small personal problem with sofas. You move them and get them stuck in hallways. But it's nothing a little math won't fix.

## Minimum sudoku

Minimum Sudoku. It is believed (though not proven) that the minimum number of entries in a Sudoku grid that will lead to a unique solution is 17. Gordon Royle of the University of Western Australia has collected 36,628 "minimum Sudoku" grids. Additional reading: an article in American Scientist on determining the difficulty of a Sudoku problem; Wikipedia article on the mathematics of Sudoku; the Sudoku Programmers' Forum on Sudoku mathematics.