171 posts tagged with math *and* mathematics. (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

Middle East Peace Potential through Dynamics in Spherical Geometry: Engendering connectivity from incommensurable 5-fold and 6-fold conceptual frameworks. * This is an exploration of the hypothesis that unique belief systems depend for their coherence on distinctive patterns typically embodied in geometrical symbols in two dimensions. On the basis of that assumption, the case tentatively explored here is that of the "incommensurability" of the 5-fold Star of Islam and the 6-fold Star of David of Judaism...Mathematically these patterns cannot be readily combined. This issue is described in mathematics in terms of tiling...A set of hexagons and pentagons can however be uniquely fitted together as a particular three-dimensional polyhedron, namely the truncated icosahedron. * [more inside]

posted by leahwrenn on Aug 21, 2014 - 32 comments

posted by leahwrenn on Aug 21, 2014 - 32 comments

The Peg Solitaire Army is a problem spun off from a classic recreation, and yet another example of the golden ratio turning up where you least expect it. If you want to look at the game more deeply, George Bell's solitaire pages are the ne plus ultra: There's more about the solitaire army (and variants), ... [more inside]

posted by Wolfdog on Aug 15, 2014 - 6 comments

posted by Wolfdog on Aug 15, 2014 - 6 comments

Welcome to Al Zimmermann's Programming Contests. *You've entered an arena where demented computer programmers compete for glory and for some cool prizes.* The current challenge is just about to come to an end, but you can peruse the previous contests and prepare for the new one starting next month.

posted by Wolfdog on Aug 14, 2014 - 11 comments

posted by Wolfdog on Aug 14, 2014 - 11 comments

The 2014 Fields Medals have been awarded to Artur Avila, Manjul Bhargava, Martin Hairer, and Maryam Mirzakhani. Mirzakhani, a professor at Stanford, is the first woman to win math's highest prize, and Avila is the first South American. Erica Klarreich at Quanta Magazine has profiles of all four winners. [more inside]

posted by escabeche on Aug 12, 2014 - 35 comments

posted by escabeche on Aug 12, 2014 - 35 comments

The Foehr Reef is part of the worldwide Crochet Coral Reef Project. It was made by over 700 women and combines more than 4000 individual pieces of marine wonder. A short video shows its beauty [alternating English and German audio]. PDFs with pictures.
"The Crochet Coral Reef is a woolly celebration of the intersection of higher geometry and feminine handicraft, and a testimony to the disappearing wonders of the marine world." It originated out of a desire to increase awareness of environmental threats to the world's reefs and is a conjunction of art, environmentalism, and geometry. [more inside]

posted by travelwithcats on Aug 10, 2014 - 7 comments

posted by travelwithcats on Aug 10, 2014 - 7 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

Trio for Three Angles (1968) is one of many beautiful acclaimed visually-oriented short films with music by mathematical filmmakers Bruce and Katharine Cornwell, some animated by hand and some using early digital technology. It inspired three sequels: Similar Triangles (1975), Congruent Triangles (1976), and Journey to the Center of a Triangle (1978) (previously). [more inside]

posted by beryllium on Jul 6, 2014 - 5 comments

posted by beryllium on Jul 6, 2014 - 5 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

Each month, the Notices of the American Math Society runs a column called "What is...." which aims to explain an advanced mathematical concept in two pages, at a level accessible to a good undergrad math major. Armin Straub, a postdoc at Illinois, has collected them all in one place. [more inside]

posted by escabeche on Feb 26, 2014 - 33 comments

posted by escabeche on Feb 26, 2014 - 33 comments

Open warfare erupts in the world of mathematical biology, as Lior Pachter of UC-Berkeley writes three blog posts attacking two papers in Nature Bioscience, accusing one of them of being "dishonest and fraudulent": The Network Nonsense of Albert-Laszlo Barabasi, The Network Nonsense of Manolo Kellis, and Why I Read the Network Nonsense Papers. Kellis (MIT) and his co-authors respond (.pdf.)

posted by escabeche on Feb 12, 2014 - 53 comments

posted by escabeche on Feb 12, 2014 - 53 comments

Headlines from a Mathematically Literate World [more inside]

posted by Blasdelb on Dec 4, 2013 - 32 comments

posted by Blasdelb on Dec 4, 2013 - 32 comments

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

The Washington Post reports on a ridiculous mathematics test for first graders administered under New York's Common Core standards initiative. [Common Core previously.]

posted by Westringia F. on Nov 1, 2013 - 197 comments

posted by Westringia F. on Nov 1, 2013 - 197 comments

Revelations in the field of quantum physics have resulted in the discovery of the Amplituhedron, a jewel-like higher dimensional object whose volume elegantly predicts fundamental physical processes that took the brilliant Dr. Richard Feynman hundreds of pages of abstruse mathematics to describe.
The theoretical manifold not only enables simple pen-and-paper calculation of physics that would normally require supercomputers to work out, but also challenges basic assumptions about the nature of reality -- forgoing the core concepts of locality and unitarity and suggesting that space and time are merely emergent properties of a timeless, infinitely-sided "master amplituhedron," whose geometry represents the sum total of all physical interactions.
**More:** The 152-page source paper on arXiv [PDF] - Lead author Nima Arkani-Hamed's hour-long lecture at SUSY 2013 - Scans of Arkani-Hamed's handwritten lecture notes - A far more detailed lecture series "Scattering Without Space Time": one, two, three - Arkani-Hamed previously on MeFi - A hot-off-the-presses Wikipedia page (watch this space)

posted by Rhaomi on Sep 18, 2013 - 128 comments

posted by Rhaomi on Sep 18, 2013 - 128 comments

The Movie Math Quiz: Can you figure out which movies are being described by these mathematical equations?

posted by schmod on Sep 10, 2013 - 13 comments

posted by schmod on Sep 10, 2013 - 13 comments

Wonkblog has a new advice column called "Dear Dylan" where Dylan Matthews answers the usual advice column staples using game theory, mathematics and charts.

posted by reenum on Aug 25, 2013 - 30 comments

posted by reenum on Aug 25, 2013 - 30 comments

This Simple Math Puzzle Will Melt Your Brain

"Adding and subtracting ones sounds simple, right? Not according to the old Italian mathematician Grandi—who showed that a simple addition of 1s and -1s can give three different answers."

posted by andoatnp on Jul 2, 2013 - 61 comments

"Adding and subtracting ones sounds simple, right? Not according to the old Italian mathematician Grandi—who showed that a simple addition of 1s and -1s can give three different answers."

posted by andoatnp on Jul 2, 2013 - 61 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

Mathematicians Henry Segerman and Saul Schleimer have produced a triple gear, three linked gears in space that can rotate together. A short writeup of the topology and geometry behind the triple gear on the arXiv.

posted by escabeche on Apr 26, 2013 - 36 comments

posted by escabeche on Apr 26, 2013 - 36 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

The origins of plus and minus signs - "There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made – and betokeneth lesse."

posted by spbmp on Mar 12, 2013 - 30 comments

posted by spbmp on Mar 12, 2013 - 30 comments

Every film Pixar has produced has landed in the top fifty highest-grossing animated films of all time. What's their secret? Mathematics. Oh, and 22 Rules of Storytelling. [more inside]

posted by zarq on Mar 8, 2013 - 40 comments

posted by zarq on Mar 8, 2013 - 40 comments

Henry Reich of Minute Physics shares his favorite science blogs, video channels, and other resources on the web. (Minute Physics previously) [more inside]

posted by ocherdraco on Feb 8, 2013 - 5 comments

posted by ocherdraco on Feb 8, 2013 - 5 comments

Tim Gowers has announced a series of arXiv overlay journals called the Episciences Project that aim to exclude existing publishers from research publication in mathematics. As arXiv overlays, the Episciences Project avoids the editing and typesetting costs that existing open-access journals pay for using article processing charges. The French Centre pour la Communication Scientifique Directe (CCSD) is backing the remaining expenses, such as developing the platform. [more inside]

posted by jeffburdges on Jan 19, 2013 - 11 comments

posted by jeffburdges on Jan 19, 2013 - 11 comments

"The models we discuss belong to the class of two-variable systems with one delay for which appropriate delay stabilizes an unstable steady state. We formulate a theorem and prove that stabilization takes place in our case. We conclude that considerable (meaning large enough, but not too large) values of time delay involved in the model can stabilize love affairs dynamics." [more inside]

posted by bluefly on Jan 16, 2013 - 12 comments

posted by bluefly on Jan 16, 2013 - 12 comments

Numberphile is a website containing short videos (approx. 5-10 min.) about numbers and stuff. Mathematicians and physicists play around with the tools of their trade and explain things in simple, clear language. Learn things you didn't know you were interested in! Find out why 493-7775 is a pretty cool phone number! What's the significance of 42, anyway? What the heck is a vampire number? Why does Pac-Man have only 255 screens?
Suitable for viewing by everyone from intelligent and curious middle-schoolers to math-impaired adults. Browse their YouTube channel here. (Via)

posted by BitterOldPunk on Dec 29, 2012 - 20 comments

posted by BitterOldPunk on Dec 29, 2012 - 20 comments

Last night was the grand opening of the Museum of Mathematics in New York City, the only museum of its kind in North America. The video is narrated by MoMath's chief of content, mathematical sculptor George Hart (better known in some circles as Vi Hart's dad.) The sculpture of the space of three-note chords in the video is based on the work of Dmitri Tymoczko, and the lovely curved hammock of strings a visitor is sitting in at the end is a ruled quadric surface. Many more videos at the Museum of Mathematics YouTube channel. Coverage from the New Scientist. (Previously on MetaFilter.)

posted by escabeche on Dec 13, 2012 - 24 comments

posted by escabeche on Dec 13, 2012 - 24 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

posted by Rhaomi on Oct 27, 2012 - 14 comments

"Milgram and Bishop are opposed to reforms of mathematics teaching and support the continuation of a model in which students learn mathematics without engaging in realistic problems or discussing mathematical methods. They are, of course, entitled to this opinion, and there has been an ongoing, spirited academic debate about mathematics learning for a number of years. But Milgram and Bishop have gone beyond the bounds of reasoned discourse in a campaign to systematically suppress empirical evidence that contradicts their stance. Academic disagreement is an inevitable consequence of academic freedom, and I welcome it. However, responsible disagreement and academic bullying are not the same thing. Milgram and Bishop have engaged in a range of tactics to discredit me and damage my work which I have now decided to make public." Jo Boaler, professor of mathematics education at Stanford, accuses two mathematicians, one her colleague of Stanford, of unethical attempts to discredit her research, which supports "active engagement" with mathematics (aka "reform math") over the more traditional "practicing procedures" approach. [more inside]

posted by escabeche on Oct 18, 2012 - 119 comments

posted by escabeche on Oct 18, 2012 - 119 comments

What is the smallest prime? "It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime."

posted by escabeche on Sep 18, 2012 - 61 comments

posted by escabeche on Sep 18, 2012 - 61 comments

Robert MacPherson interviewed as part of the Simons Foundation's Science Lives series. MacPherson is among the founders of the modern theory of *singularities*, points like a kink in a curve where the geometry of a space stops being smooth and starts behaving badly. In the interview, MacPherson talks about cultural differences between math and music, his frustration with high school math, growing up gay in the South and life as a gay man in the scientific community, smuggling $23,000 in cash into post-Soviet Russia to help mathematicians there keep the lights on, catastrophe theory, perverse sheaves, how to be a successful graduate student, stuttering, and of course the development of the intersection homology theory for which he is most well-known.

posted by escabeche on Sep 12, 2012 - 5 comments

posted by escabeche on Sep 12, 2012 - 5 comments

Cliff Stoll makes glass Klein bottles. He also sells imported portraits of Gauss.

posted by madcaptenor on Aug 29, 2012 - 26 comments

posted by madcaptenor on Aug 29, 2012 - 26 comments

"The real satisfaction from mathematics is in learning from others and sharing with others." William Thurston, one of the greatest mathematicians of the 20th century, has died. He revolutionized topology and geometry, insisting always that geometric intuition and understanding played just as important a role in mathematical discovery as did the austere formalism championed by the school of Grothendieck. Thurston's views on the relation between mathematical understanding and formal proof are summed up in his essay "On Proof and Progress in Mathematics." [more inside]

posted by escabeche on Aug 22, 2012 - 32 comments

posted by escabeche on Aug 22, 2012 - 32 comments

Paul Lockhart, author of the famous Mathematician's Lament, has a new book coming out called Measurement, which tries to discuss mathematics "as an artful way of thinking and living". Lockhart discusses his passion for math and motives for writing the book in this video.

posted by Rory Marinich on Jul 31, 2012 - 17 comments

posted by Rory Marinich on Jul 31, 2012 - 17 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

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

H _ _ _ m _ n, Y a _ _ _ e e, _ _ t t _ _ _ h i p, _ h u t _ s & L a _ _ e r _ , R _ _ k , _ _ n d y _ _ _ _ , and _ _ r t s.

posted by Jasper Friendly Bear on Apr 7, 2012 - 28 comments

posted by Jasper Friendly Bear on Apr 7, 2012 - 28 comments

Amalie Noether: The Mighty Mathematician You’ve Never Heard Of

posted by jjray on Mar 27, 2012 - 49 comments

posted by jjray on Mar 27, 2012 - 49 comments

Conceptually talked about on MeFi previously, some basic Monte Carlo methods include the Inverse Transform Method (PDF) mentioned in the quoted paper, Acceptance-Rejection Sampling (PDFs 1,2), and integration with and without importance sampling (PDF).The year was 1945. Two earthshaking events took place: the successful test at Alamogordo and the building of the first electronic computer. Their combined impact was to modify qualitatively the nature of global interactions between Russia and the West. No less perturbative were the changes wrought in all of academic research and in applied science. On a less grand scale these events brought about a [renaissance] of a mathematical technique known to the old guard as statistical sampling; in its new surroundings and owing to its nature, there was no denying its new name of the Monte Carlo method (PDF).-N. Metropolis

posted by JoeXIII007 on Dec 17, 2011 - 13 comments