Mathematician Kenneth Appel has died at the age of 80. He is best known for having proved, with Wolfgang Haken, the four-color theorem, which states that only four colors are needed to have a map in which no two adjacent countries have the same color. [more inside]
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.
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]
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."
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]
Bayesian analysis shows redshirts are not most likely to die on Star Trek:TOS. Although Enterprise crew members in redshirts suffer many more casualties than crew members in other uniforms, they suffer fewer casualties than crew members in gold uniforms when the entire population size is considered. Only 10% of the entire redshirt population was lost during the three year run of Star Trek. This is less than the 13.4% of goldshirts, but more than the 5.1% of blueshirts. What is truly hazardous is not wearing a redshirt, but being a member of the security department. The red-shirted members of security were only 20.9% of the entire crew, but there is a 61.9% chance that the next casualty is in a redshirt and 64.5% chance this red-shirted victim is a member of the security department. The remaining redshirts, operations and engineering make up the largest single population, but only have an 8.6% chance of being a casualty.
Henry Reich of Minute Physics shares his favorite science blogs, video channels, and other resources on the web. (Minute Physics previously) [more inside]
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]
"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]
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)
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.)
Rosalind.info is a website with bioinformatics problems inspired by Project Euler (previously, previouslier.) [more inside]
"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]
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]
Maximum gravy: Vi hart, daughter of George & mathemusician at The Khan Academy, cooks mathematical potatoes to go along with a symmetrical Turduckenen. Have a delicious Thanksgiving. [more inside]
"We have little trouble recognizing that a chess grandmaster’s victory over a novice is skill, as well as assuming that Paul the octopus’s ability to predict World Cup games is due to chance. But what about everything else?" [Luck and Skill Untangled: The Science of Success]
From the somewhat arbitrary and dimensionful to the timeless classic, one man's subjective list of notable properties of specific numbers. [more inside]
She sat zazen, concentrating on not concentrating, until it was time to prepare for the appointment. Sitting seemed to produce the usual serenity, put everything in perspective. Her hand did not tremble as she applied her make-up; tranquil features looked back at her from the mirror. She was mildly surprised, in fact, at just how calm she was, until she got out of the hotel elevator at the garage level and the mugger made his play. She killed him instead of disabling him. Which was obviously not a measured, balanced action--the official fuss and paperwork could make her late. Annoyed at herself, she stuffed the corpse under a shiny new Westinghouse roadable whose owner she knew to be in Luna, and continued on to her own car. This would have to be squared later, and it would cost. No help for it--she fought to regain at least the semblance of tranquillity as her car emerged from the garage and turned north. Nothing must interfere with this meeting, or with her role in it. "Melancholy Elephants," an enthralling, Hugo Award-winning short story by Spider Robinson about a disciplined operative, a powerful senator, and a crucial mission to preserve humanity's most precious resource. (some spoilers inside) [more inside]
"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]
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."
N Is a Number: A Portrait of Paul Erdős is a 1993 documentary directed by George Paul Csicsery about the life of mathematician Paul Erdős. Paul Erdős (26 March 1913 -- 20 September 1996) was a Hungarian mathematician. Erdős published more papers than any other mathematician in history, working with hundreds of collaborators. He worked on problems in combinatorics, graph theory, number theory, classical analysis, approximation theory, set theory, and probability theory. He is also known for his "legendarily eccentric" personality. (Previously he was mostly a number)
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.
Shinichi Mochizuki believes that he has found a connection between prime numbers by developing a 500 page proof of the ABC conjecture [more inside]
The fine people over at the International Guild of Knot Tyers Forum talk knots. On Mars.
Cliff Stoll makes glass Klein bottles. He also sells imported portraits of Gauss.
"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]
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.
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]
Learning and Unlearning Math explores topic in mathematics from the perspective of a teacher. The author has developed series of articles on such varied topics as Multiplication, Quantity, Central Tendency, Math in Comics, and things not taught in schools. More recently, the blog has focused on the conventions for Mathematical Notation.
16 year old student from Germany solves 350 year old Isaac Newton puzzle Shourryya Ray, a 16-year-old German student, has cracked a puzzle that has stumped mathematicians since Sir Isaac Newton first posed the problem more than 350 years ago. The teen's solutions allow exact calculations of a trajectory under gravity and subject to air resistance. Bonus video of Neil Degrasse Tyson talking about Newton.
Free online graph paper generators: variations of squares, triangle, rhombus, and hexagonal, circular and polar, for drawing, gaming, writing, note-taking and much more. Blank Sheet Music (Flash) for all arrangements (PDF). Create and edit your own grids, probability and logarithmic graphs, petri-dish inserts and storyboards. Also, multilingual monthly and yearly calendars. Plus, more than you ever wanted to know about ISO paper dimensions and printable paper models of polyhedra. Prev-ious-ly.
That the conventional wisdom of 3,500 calories less is what it takes to lose a pound of weight is wrong. The body changes as you lose. Interestingly, we also found that the fatter you get, the easier it is to gain weight. An extra 10 calories a day puts more weight onto an obese person than on a thinner one. [more inside]
In Russian roulette, is it best to go first? | The Mathematics of Tetris | What is the result of infinity minus infinity? [more inside]
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.)
The trend of mathematics and physics towards unification provides the physicist with a powerful new method of research into the foundations of his subject, a method which has not yet been applied successfully, but which I feel confident will prove its value in the future. The method is to begin by choosing that branch of mathematics which one thinks will form the basis of the new theory. One should be influenced very much in this choice by considerations of mathematical beauty.  [more inside]
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.
"He is the kind of boy who is bound to be rather a problem in any school or community, being in some respects definitely anti-social." Alan Turing's school reports.
The Hacker Shelf is nice crowd-sourced guide to (legally) free books on various computational and mathematical subjects. The topics page gives you an idea of the breadth of material available.
What is the minimal number of clues necessary to create a uniquely solvable Sudoku puzzle? It turns out to be 17, though it took fancy symmetry arguments and nearly a year of computer time to prove it. But no need to read the paper when you can watch the video.
So, Nickelodeon, you tell us that Spongebob Squarepants lives in a pineapple upside down house at the bottom of the sea. Are you really sure about that? Beware of misleading your viewers about the universe, Nickelodeon! [more inside]
Need some quasiperiodic tilings? Alan Schoen has a smorgasbord of tilings of rhombuses with pentagonal, heptagonal, and nonagonal symmetry that come in many flavors. Be sure to check out his page on triply periodic minimal surfaces and the other curios at his Geometry Garret.
This is a radical statement about the Pyramid, especially on the internet because all web pages that I have been able to find that deal with the Pyramid, maintain that it was built and/or inspired by either God or space aliens. Most don't even consider that it could be a rational structure designed and built by normal people.
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. MetropolisConceptually 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).
An "Exciting Guide to Probability Distributions" from the University of Oxford: part 1, part 2. (Two links to PDFs)
S. Ekhad , E. Georgiadis, D. Zeilberger. "How to Gamble If You're In a Hurry." arXiv:1112.1645v1 (pdf), 7 Dec 2011. [more inside]