47 posts tagged with math *and* maths. (View popular tags)

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Hyperreal numbers: infinities and infinitesimals - "In 1976, Jerome Keisler, a student of the famous logician Tarski, published this elementary textbook that teaches calculus using hyperreal numbers. Now it's free, with a Creative Commons copyright!" (pdf—25mb :) [more inside]

posted by kliuless on Sep 17, 2014 - 28 comments

posted by kliuless on Sep 17, 2014 - 28 comments

Norbert Wiener: The Eccentric Genius Whose Time May Have Finally Come (Again) - "The most direct reason for Wiener's fall to relative obscurity was the breakthrough of a young mathematician and engineer named Claude Shannon." [more inside]

posted by kliuless on Jul 11, 2014 - 12 comments

posted by kliuless on Jul 11, 2014 - 12 comments

Math or Maths? A few minutes with Dr Lynne Murphy (an American linguist in England) should clear this right up. Via Numberphile.

posted by R. Mutt on Apr 30, 2014 - 116 comments

posted by R. Mutt on Apr 30, 2014 - 116 comments

Computers are providing solutions to math problems that we can't check - "A computer has solved the longstanding Erdős discrepancy problem! Trouble is, we have no idea what it's talking about — because the solution, which is as long as all of Wikipedia's pages combined, is far too voluminous for us puny humans to confirm." (via; previously ;)

posted by kliuless on Apr 12, 2014 - 24 comments

posted by kliuless on Apr 12, 2014 - 24 comments

Finite time blowup for an averaged three-dimensional Navier-Stokes equation - "[Terence Tao] has shown that in an alternative abstract universe closely related to the one described by the Navier-Stokes equations, it is possible for a body of fluid to form a sort of computer, which can build a self-replicating fluid robot that, like the Cat in the Hat, keeps transferring its energy to smaller and smaller copies of itself until the fluid 'blows up.' " [1,2,3] (previously)

posted by kliuless on Mar 9, 2014 - 15 comments

posted by kliuless on Mar 9, 2014 - 15 comments

Network Theory Overview - "The idea: nature and the world of human technology are full of networks! People like to draw diagrams of networks. Mathematical physicists know that in principle these diagrams can be understood using category theory. But why should physicists have all the fun? This is the century of *understanding living systems and adapting to life on a finite planet*. Math isn't the main thing we need, but it's got to be part of the solution... so one thing we should do is develop a unified and powerful theory of networks." (via ;)

posted by kliuless on Mar 2, 2014 - 17 comments

posted by kliuless on Mar 2, 2014 - 17 comments

It's a bit late for the holiday, but math(s) comedian Helen Arney sings about her Christmas wish -- the largest known Mersenne Prime, Mersenne 48. [more inside]

posted by GenjiandProust on Dec 28, 2013 - 1 comment

posted by GenjiandProust on Dec 28, 2013 - 1 comment

Closing in on the twin prime conjecture (Quanta) - "Just months after Zhang announced his result, Maynard has presented an independent proof that pushes the gap down to 600. A new Polymath project is in the planning stages, to try to combine the collaboration's techniques with Maynard's approach to push this bound even lower." [more inside]

posted by kliuless on Dec 1, 2013 - 16 comments

posted by kliuless on Dec 1, 2013 - 16 comments

posted by motty on Jun 27, 2013 - 42 comments

Is there any point to the 12 times table? [more inside]

posted by Cat Pie Hurts on Jun 27, 2013 - 159 comments

posted by Cat Pie Hurts on Jun 27, 2013 - 159 comments

In August of last year, mathematician Shinichi Mochizuki reported that he had solved one of the great puzzles of number theory: the ABC conjecture (previously on Metafilter). Almost a year later, no one else knows whether he has succeeded. No one can understand his proof.

posted by painquale on May 10, 2013 - 59 comments

posted by painquale on May 10, 2013 - 59 comments

Using computer systems for doing mathematical proofs - "With the proliferation of computer-assisted proofs that are all but impossible to check by hand, Hales thinks computers must become the judge." [more inside]

posted by kliuless on Mar 16, 2013 - 25 comments

posted by kliuless on Mar 16, 2013 - 25 comments

"Draw some random points on a piece of paper and join them up to make a random polygon. Find all the midpoints and connecting them up to give a new shape, and repeat. The resulting shape will get smaller and smaller, and will tend towards an ellipse!" [code to make this in Mathematica] [a version which allows you to watch the process step by step, with 10 vertices or 100]

posted by ocherdraco on Dec 3, 2012 - 65 comments

posted by ocherdraco on Dec 3, 2012 - 65 comments

The Nature of Computation - Intellects Vast and Warm and Sympathetic: "I hand you a network or graph, and ask whether there is a path through the network that crosses each edge exactly once, returning to its starting point. (That is, I ask whether there is a 'Eulerian' cycle.) Then I hand you another network, and ask whether there is a path which visits each node exactly once. (That is, I ask whether there is a 'Hamiltonian' cycle.) How hard is it to answer me?" (via) [more inside]

posted by kliuless on Dec 1, 2012 - 19 comments

posted by kliuless on Dec 1, 2012 - 19 comments

Morton and Vicary on the Categorified Heisenberg Algebra - "In quantum mechanics, position times momentum does not equal momentum times position! This sounds weird, but it's connected to a very simple fact. Suppose you have a box with some balls in it, and you have the magical ability to create and annihilate balls. Then there's one more way to create a ball and then annihilate one, than to annihilate one and then create one. Huh? Yes: if there are, say, 3 balls in the box to start with, there are 4 balls you can choose to annihilate after you've created one but only 3 before you create one..." [more inside]

posted by kliuless on Jul 21, 2012 - 78 comments

posted by kliuless on Jul 21, 2012 - 78 comments

FatFonts creates numerical fonts where the amount of ink/pixels for each number is in direct proportion to its value.

posted by fearfulsymmetry on May 14, 2012 - 23 comments

posted by fearfulsymmetry on May 14, 2012 - 23 comments

In Russian roulette, is it best to go first? | The Mathematics of Tetris | What is the result of infinity minus infinity? [more inside]

posted by Foci for Analysis on May 14, 2012 - 30 comments

posted by Foci for Analysis on May 14, 2012 - 30 comments

Geometrically the irrationality of the square root of 2 means that there is no integer-by-integer square whose area is twice the area of another integer-by-integer square. A visual proof that the square root of 2 is irrational (not found in previous visual proof post.)

posted by Obscure Reference on May 9, 2012 - 39 comments

posted by Obscure Reference on May 9, 2012 - 39 comments

Science through yarn: Wooly Thoughts. The Home of Mathematical Knitting, including knitted klein bottles and hyperbolic planes. The Museum of Scientifically Accurate Fabric Brain Art (previously). Much, much, more on knitting, crochet and quilting used to visualize complex theories in topology, probability, chaos and fractals. [more inside]

posted by Bora Horza Gobuchul on Nov 6, 2011 - 8 comments

posted by Bora Horza Gobuchul on Nov 6, 2011 - 8 comments

Beaded Polyhedra ❂ More beadwork (mathematical and otherwise) by Gwen Fisher ❂ Still more beadwork galleries at beAdinfinitum ❂ Three-dimensional finite point groups and the symmetry of beaded beads [pdf - some algebra, but lots of illustrations]

posted by Wolfdog on Jul 19, 2011 - 6 comments

posted by Wolfdog on Jul 19, 2011 - 6 comments

A thread full of proofs without words at MathOverflow and quite a lot more of them courtesy of Google Books.

posted by Wolfdog on Jul 18, 2011 - 22 comments

posted by Wolfdog on Jul 18, 2011 - 22 comments

New math theories reveal the nature of numbers [1,2] - "We prove that partition numbers are 'fractal' for every prime. These numbers, in a way we make precise, are self-similar in a shocking way. Our 'zooming' procedure resolves several open conjectures, and it will change how mathematicians study partitions." (/.|via) [more inside]

posted by kliuless on Jan 22, 2011 - 45 comments

posted by kliuless on Jan 22, 2011 - 45 comments

The OEIS Movie is simply a slideshow of one thousand plots from the Online Encyclopedia of Integer Sequences, at two plots per second with sequence-generated music. [more inside]

posted by Wolfdog on Dec 2, 2010 - 12 comments

posted by Wolfdog on Dec 2, 2010 - 12 comments

A Brief History of Mathematics is a BBC series of ten fifteen-minute podcasts by Professor Marcus du Sautoy about the history of mathematics from Newton and Leibniz to Nicolas Bourbaki, the pseudonym of a group of French 20th Century mathematicians. Among those covered by Professor du Sautoy are Euler, Fourier and Poincaré. The podcasts also include short interviews with people such as Brian Eno and Roger Penrose.

posted by Kattullus on Dec 1, 2010 - 11 comments

posted by Kattullus on Dec 1, 2010 - 11 comments

A brief tour of the mysteriously universal laws of mathematics and nature. [more inside]

posted by kliuless on Oct 24, 2010 - 33 comments

posted by kliuless on Oct 24, 2010 - 33 comments

How do you calculate Pi? Build a supercomputer. *The Mountains of Pi*, a New Yorker profile of the mathematician (sic) the Chudnovsky brothers. Warning: the article is from 1992, and internet is missing its definite article. (Previously)

posted by OmieWise on Sep 9, 2010 - 31 comments

posted by OmieWise on Sep 9, 2010 - 31 comments

posted by Wolfdog on May 16, 2010 - 3 comments

Since its first printing in 1964, Abramowitz and Stegun's Handbook of Mathematical Functions has been a standard (and public domain) reference manual for special functions and applied mathematics. This week, NIST released its successor, the Digital Library of Mathematical Functions, online to the public.

posted by Upton O'Good on May 13, 2010 - 29 comments

posted by Upton O'Good on May 13, 2010 - 29 comments

Mathematics Illuminated is a set of thirteen surveys in varied topics in mathematics, nicely produced with video, text, and interactive Flash gadgets for each of the topics.

posted by Wolfdog on Apr 14, 2010 - 8 comments

posted by Wolfdog on Apr 14, 2010 - 8 comments

It's been called the most beautiful theorem in all of mathematics. [more inside]

posted by empath on Mar 9, 2010 - 48 comments

posted by empath on Mar 9, 2010 - 48 comments

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!

posted by Blazecock Pileon on Jun 27, 2008 - 22 comments

posted by Blazecock Pileon on Jun 27, 2008 - 22 comments

Symmetry. Shakespeare. Islamic medicine. Creative writing challenges. Four podcast series from University of Warwick.

posted by Wolfdog on Nov 18, 2007 - 2 comments

posted by Wolfdog on Nov 18, 2007 - 2 comments

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_{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."

posted by ericb on Mar 19, 2007 - 67 comments

"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

posted by ericb on Mar 19, 2007 - 67 comments

The Institute for Figuring presents the Crocheted Hyperbolic Coral Reef Project and Hyperbolic Crocheted Cacti and Kelp (more at this flickr gallery). If you secretly spend your evenings crocheting mathematical models, help build the coral reef or send a photo of your other creations to The People's Hyperbolic Gallery. (via Wonderland)

posted by madamjujujive on Sep 15, 2006 - 11 comments

posted by madamjujujive on Sep 15, 2006 - 11 comments

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.)

posted by Eideteker on Aug 3, 2006 - 11 comments

posted by Eideteker on Aug 3, 2006 - 11 comments

Gregory Chaitin's Meta Math! The Quest For Omega

"Okay, what I was able to find, or construct, is a funny area of pure mathematics where things are true for no reason, they're true by accident... It's a place where God plays dice with mathematical truth. It consists of mathematical facts which are so delicately balanced between being true or false that we're never going to know, and so you might as well toss a coin." From Paradoxes of Randomness.

"In my opinion, Omega suggests that even though maths and physics are different, perhaps they are not as different as most people think. To put it bluntly, if the incompleteness phenomenon discovered by Gödel in 1931 is really serious — and I believe that Turing's work and my own work suggest that incompleteness is much more serious than people think — then perhaps mathematics should be pursued somewhat more in the spirit of experimental science rather than always demanding proofs for everything." From Omega and why maths has no Theory Of Everythings.

[previously, see also, via]

posted by MetaMonkey on Apr 13, 2006 - 17 comments

"Okay, what I was able to find, or construct, is a funny area of pure mathematics where things are true for no reason, they're true by accident... It's a place where God plays dice with mathematical truth. It consists of mathematical facts which are so delicately balanced between being true or false that we're never going to know, and so you might as well toss a coin." From Paradoxes of Randomness.

"In my opinion, Omega suggests that even though maths and physics are different, perhaps they are not as different as most people think. To put it bluntly, if the incompleteness phenomenon discovered by Gödel in 1931 is really serious — and I believe that Turing's work and my own work suggest that incompleteness is much more serious than people think — then perhaps mathematics should be pursued somewhat more in the spirit of experimental science rather than always demanding proofs for everything." From Omega and why maths has no Theory Of Everythings.

[previously, see also, via]

posted by MetaMonkey on Apr 13, 2006 - 17 comments

Norman Wildberger's New Trigonometry Dr Norman Wildberger has rewritten the arcane rules of trigonometry and eliminated sines, cosines and tangents from the trigonometric toolkit. The First chapter of his new book, Divine Proportions, is online (.pdf).

posted by Kwantsar on Sep 25, 2005 - 21 comments

posted by Kwantsar on Sep 25, 2005 - 21 comments

Jim Loy's Mathematics Page is (among other things) a collection of interesting theorems (like Napoleon's Triangle theorem), thoughtful discussions of both simple and complex math, and geometric constructions (my personal favorite); the latter of which contains surprisingly-complex discussions on the trisection of angles, or the drawing of regular pentagons.

Similarly enthralling are the pages on Billiards (and the physics of), Astronomy (and the savants of), and Physics (and the Phlogiston Theory of), all of which are rife with illustrations and diagrams. See the homepage for much more.

If you like your geometric constructions big, try Zef Damen's Crop Circle Reconstructions.

posted by odinsdream on Sep 14, 2005 - 8 comments

Similarly enthralling are the pages on Billiards (and the physics of), Astronomy (and the savants of), and Physics (and the Phlogiston Theory of), all of which are rife with illustrations and diagrams. See the homepage for much more.

If you like your geometric constructions big, try Zef Damen's Crop Circle Reconstructions.

posted by odinsdream on Sep 14, 2005 - 8 comments

Java applets to help visualize various concepts in math, physics, and engineering

posted by Gyan on Sep 9, 2005 - 13 comments

posted by Gyan on Sep 9, 2005 - 13 comments

Mathematics Awareness Month - April 2005: Essays, DVD, Links. Prior MAMs.

posted by Gyan on Apr 1, 2005 - 7 comments

posted by Gyan on Apr 1, 2005 - 7 comments

Thinking Machine 4 *explores the invisible, elusive nature of thought. Play chess against a transparent intelligence, its evolving thought process visible on the board before you.*

From Martin Wattenberg (with Marek Walczak); they have been noted here before.

posted by e.e. coli on Oct 27, 2004 - 11 comments

From Martin Wattenberg (with Marek Walczak); they have been noted here before.

posted by e.e. coli on Oct 27, 2004 - 11 comments

Mathematician Henrik Lenstra was intrigued by a blank space in he middle of a drawing by MC Escher. Over two years he managed to describe the mathematical structure of the drawing, project what should go in the missing space and produce an extraordanary animation of the result.

posted by alms on Aug 6, 2002 - 32 comments

posted by alms on Aug 6, 2002 - 32 comments

The golden section (math, graphics) is an important relation used by artists and mathematicians, among others. I'm curious if any of you have good examples of recent use.

posted by lbergstr on Apr 15, 2002 - 45 comments

posted by lbergstr on Apr 15, 2002 - 45 comments

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