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585 posts tagged with Math.

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## The P vs. NP problem and its importance

The Status of the P Versus NP Problem

*It's one of the fundamental mathematical problems of our time, and its importance grows with the rise of powerful computers.*(via mr)## Figure 3. Basic model outbreak scenario. Susceptibles are quickly eradicated and zombies take over, infecting everyone.

## Parkinson's Law

Why bureaucracy, like gas, fills up all available space. From the archive of

*The Economist*, 1955 [via ArchiveDigger.]## A constant reminder

"This day may be celebrated in a variety of ways. Pause and give thought to the role that the number pi has played in your life. Imagine a world without pi. Attempt to memorise pi to as many decimal places as you can. If you're feeling creative, devise alternative values for pi. Go to a party (I will). Or just celebrate in the time-honoured fashion of ignoring Pi Approximation Day altogether."

Happy Pi Approximation Day. [more inside]

Happy Pi Approximation Day. [more inside]

## I will choose free will

The Free Will Theorem - "If there exist experimenters with (some) free will, then elementary particles also have (some) free will." (previously)

## Gimme That Old Time Derivation

The Cornell Historical Math Monographs archive has a great many famous papers, including works by De Morgan, Hamilton, Descartes (warning: French) and of course Lewis Carroll. [more inside]

## I am a strange loop.

Douglas Hofstadter's

*Gödel, Escher, Bach: An Eternal Golden Braid*has been recorded as a series of video lectures for MIT's Open Courseware project.## Beware of Oddity

## Theory versus Statistics, Financial Economics Edition.

Theory versus Statistics, Financial Economics Edition. "You can almost here the lament of this quant that the real math theory has been dead since 1980, and that it has all been applied and statistics ever since. It’s like Fischer Black was Kool Herc and Myron Scholes was Afrika Bambaataa, and they’d all go plug in their computers into lamp posts and do martingale representations in the streets and at house parties. And, of course, it was all ruined in 1979 when it went commercial." A response to The Last Temptation of Risk by Barry Eichengreen.

## Computable data* (conceivably knowable) about people

Stephen Wolfram discusses Wolfram|Alpha: Computational Knowledge Engine - at the same time Google Adds Search to Public Data, viz: "Nobody really paid attention to the two hour snorecast" -- like a cross between designing for big data and a glossary of game theory terms -- on Wolfram|Alpha (previously), yet the veil is being lifted nonetheless: "[on] a platonic search engine, unearthing eternal truths that may never have been written down before," cf. hunch & cyc (and in other startup news...) [via] [more inside]

## The five states of Texas

Following the recent uproar over Texas and the possibility of its secession (previously), Fivethirtyeight.com puts forward a theoretical division of Texas into five states: Plainland, Trinity, Gulfland, New Texas, and El Norte.

## Information doesn't want to be scale free

"the scale-free network modeing paradigm is largely inconsistent with the engineered nature of the Internet..." For a decade it's been conventional wisdom that the Internet has a scale-free topology, in which the number of links emanating from a site obeys a power law. In other words, the Internet has a long tail; compared with a completely random network, its structure is dominated by a few very highly connected nodes, while the rest of the web consists of a gigantic list of sites attached to hardly anything. Among its other effects, this makes the web highly vulnerable to epidemics. The power law on the internet has inspired a vast array of research by computer scientists, mathematicians, and engineers.
According to an article in this month's Notices of the American Math Society, it's all wrong. How could so many scientists make this kind of mistake? Statistician Cosma Shalizi explains how people see power laws when they aren't there: "Abusing linear regression makes the baby Gauss cry."

## I want my MathTV

MathTV is a real problem solver for many. It is also found on YouTube, and is free. Here is some background.

## Dolphins caught on film making art and doing science.

Dolphins at SeaWorld Orlando make and play with bubble rings. Others learn by watching. (SLYP) via [more inside]

## The On-Line Encyclopedia of Integer Sequences

Ever wondered what comes next, and why? The On-Line Encyclopedia of Integer Sequences has the answers. (Previously.)

## MacTutor History of Mathematics archive

The MacTutor History of Mathematics archive is an astounding collection of historical material on mathematics, especially biographies. (Previously: 1 2 3 4.)

## A vote for "The Indefatigable Frog" is a vote for posterity.

"Do you like fiction and mathematics? Are you interested in what our society thinks about mathematicians?" [more inside]

## All Things Mathematical

Somewhere between 538 and xkcd, Ask Doctor Math is an advice column for practical math questions. [more inside]

## Welcome to the Khan Academy

Sal Khan likes explaining things, and he's really good at it. Here he is on CNN giving an excellent explanation of the financial crisis. And here's a great explanation of Newton's Law of Gravitation. His YouTube channel has over 700 lectures and you leave understanding everything he talks about no matter the subject.

## S_estina

The sestina is an old poetic form invented by the troubadors; each of the thirty-nine lines ends with one of only six words, which gives the sestina a haunting, constricted feel. You might have read modern examples by Bishop or Auden, or the even more modern "WTF Sestina" by Meghann Marco. But you have probably never read a sestina which explains how to construct a sestina in the language of finite group theory. (.pdf link) Via excellent mathblog God Plays Dice.

## Exponential, what it do?

Division: Work it out! - these girls be spittin the math.

## A beautiful truthful mind

Brain reorganizes to make room for math. But does math easily lead to truth? Is it really just beauty?

## Would you like to buy an fuzzy multi-instanton knot?

"...the best place to hide bulls**t is in a refereed journal that’s not open-access!" The math-physics blog n-category cafe digs into the curious case of M.S. El Naschie. El Naschie is editor-in-chief of the journal Chaos, Solitons, and Fractals, published by the well-respected scientific publisher Elsevier and sold to academic libraries for US$4,520 a year. The problem? El Naschie has published 322 of his own papers in the journal -- papers that John Baez (of "This Week's Finds in Mathematical Physics" and "The Crackpot Index") describes as "vague, dreamlike imagery," "undisciplined numerology larded with impressive buzzwords," and "total baloney." Is El Naschie a reverse Sokal? Or a Markov process for producing random publishable papers? One thing's for sure -- he knows how to cure cancer.

## Two mathematicians walk into a bar...

A math professor was explaining a particularly complicated calculus concept to his class when a frustrated pre-med student interrupts him. "Why do we have to learn this stuff?" the pre-med blurts out. The professor pauses, and answers matter-of-factly: "Because math saves lives." "How?" demanded the student. "How on Earth does calculus save lives?" "Because," replied the professor, "it keeps certain people out of medical school."

## What is the largest prime factor of the sum of the favorited comments from all fibonacci-numbered MeFites?

"Project Euler is a series of challenging mathematical/computer programming problems that will require more than just mathematical insights to solve. Although mathematics will help you arrive at elegant and efficient methods, the use of a computer and programming skills will be required to solve most problems."

Started in 2001 as a sub-section of Maths Challenge, it has since grown large enough to become its own entity. It now boasts over 200 problems, many of them insanely difficult. [more inside]

Started in 2001 as a sub-section of Maths Challenge, it has since grown large enough to become its own entity. It now boasts over 200 problems, many of them insanely difficult. [more inside]

## The Mathemagician and Pied Puzzler, and others

*The Mathemagician and Pied Puzzler*(PDF, rough table of contents here) is a collection of puzzles created by members of the Gathering 4 Gardner Foundation, in tribute to the man himself (previously). Also freely available at the G4G site is

*Puzzle Craft*(PDF), by Stewart Coffin. (

*The Puzzling World of Polyhedral Dissections*, also by Coffin, is available here.)

## Quest for a true 3D Mandelbrot Fractal.

Quest for a true 3D Mandelbrot Fractal - a very nice exploration of Mandelbrot/Julia set fractals in various kinds of 3D space.

## Math Education: An Inconvenient Truth

Math Education: An Inconvenient Truth. How children learn (or: don't learn) math today. [more inside]

## Cryptarithms

MEFIEach letter corresponds to a number 0-9. The solution is unique. [more inside]

META

+ ASKME

-------

FILTER

## 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.*## Psychemathadelica!

How deep does the rabbit hole go? The Ultimate Fractal Video Project features animated zooms into the famous Mandelbrot Set. Some zoom in so far that, by the end of the dive, the first frame you had viewed would be as large as (or larger than) the known universe. | The animations are offered as .zip'd WMV files; lower-quality versions are viewable on FractAlkemist's YouTube page. [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.

## Dare frame thy fearful symmetry?

This week in mathematical physics, John Baez looks at the amazing tile patterns in the Alhambra in Granada, dividing the patterns into their characteristic Wallpaper Groups based on their symmetries. And if these patterns aren't good enough for you, try drawing your own with the Escher Web Sketch tool. [more inside]

## Virtual Thinking

Correlative Analytics -- or as O'Reilly might term the Social Graph -- sort of mirrors the debate on 'brute force' algorithmic proofs (that are "true for no reason," cf.) in which "computers can extract patterns in this ocean of data that no human could ever possibly detect. These patterns are correlations. They may or may not be causative, but we can learn new things. Therefore they accomplish what science does, although not in the traditional manner... In this part of science, we may get answers that work, but which we don't understand. Is this partial understanding? Or a different kind of understanding?" Of course, say some in the scientific community: hogwash; it's just a fabrication of scientifically/statistically illiterate pundits, like whilst new techniques in data analysis are being developed to help keep ahead of the deluge...

## How reliable is DNA in identifying suspects?

A discovery leads to questions about whether the odds of people sharing genetic profiles are sometimes higher than portrayed. Calling the finding meaningless, the FBI has sought to block such inquiry.

## Why Learn Algebra? I'm Never Likely to Go There.

EducationFilter: California becomes the first state to mandate all 8th graders take Algebra; in part because U.S. students constantly trail their peers from other nations in mathematics. At least one person thinks it's a bad idea ("If only 25 percent of this nation ever earns a college degree, why insist that all children take algebra in eighth grade?"). Here's the algebra curriculum 8th graders will have to learn. [more inside]

## 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!

## Pi(es) in a field

## A Woolen Reef

## Little boxes on the hillside

Friday ~~Flash~~ Java Fun - 'Building Houses With Side Views' Entertaining Java game/exercise/doodad. [more inside]

## Crank That Honor Roll

Smart Shorties is a new CD being marketed to teachers that takes the beats from popular rap songs and rewrites them to the multiplication tables, with the intent of improving kids' math skills. Forbes has a nice roundup on it's history, and NPR has done a featurette on it as well At the very least, it's certainly worth a listen for the chuckle potential, but in addition to that, it's an interesting example of the now-booming Edutainment industry, something that not only spans CD's, but also computer games and even standalone video game consoles.

also, Smart Shorties is certainly not the only "Hip-hop in the classroom" product out there, nor is it the first.

also, Smart Shorties is certainly not the only "Hip-hop in the classroom" product out there, nor is it the first.

## 3.14159265... and 99,992 digits to go!

Exercising your brain makes you smarter, and there is no better gym for it than the MentatWiki. [more inside]

## 15 bits of crypto should be enough for anybody

On May 13, security advisories published by Debian and Ubuntu revealed that, for over a year, their OpenSSL libraries have had a major flaw in their CSPRNG, which is used by key generation functions in many widely-used applications, which caused the "random" numbers produced to be extremely predictable. [lolcat summary] [more inside]

## Abstract concepts vs. concrete examples for teaching math

A new study in Science claims that teaching math is better done by teaching the abstract concepts rather than using concrete examples. From an article by the study authors in Science Mag (requires subscription):

*If a goal of teaching mathematics is to produce knowledge that students can apply to multiple situations, then presenting mathematical concepts through generic instantiations, such as traditional symbolic notation, may be more effective than a series of "good examples." This is not to say that educational design should not incorporate contextualized examples. What we are suggesting is that grounding mathematics deeply in concrete contexts can potentially limit its applicability. Students might be better able to generalize mathematical concepts to various situations if the concepts have been introduced with the use of generic instantiations.*## A Mathematician's Lament

“…if I had to design a mechanism for the express purpose of

*destroying*a child’s natural curiosity and love of pattern-making, I couldn’t possibly do as good a job as is currently being done — I simply wouldn’t have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education.” [more inside]## 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!]

## Matchbox Computing

"Once you've constructed your Hexapawn opponent, it's time to start playing against it... If you play this game repeatedly ... you'll quickly notice that your matchbox opponent plays better and better until it is unbeatable!" Martin Gardner created a game called Hexapawn, and also devised an artificially intelligent opponent you can build yourself out of matchboxes and colored beads. Bonus link: An interview with Martin Gardner.

## A road is a road is a road

Did you know that you can create a simple set of directions to your house that works

*no matter where the recipient starts from?*After 38 years this remarkable conjecture has now been proved by a 63-year old former security guard.## The Geometry of Music

The connection between mathematics and music is often touted in awed, mysterious tones, but it is grounded in hard-headed science. For example, mathematical principles underlie the organization of Western music into 12-note scales. And even a beginning piano student encounters geometry in the "circle of fifths" when learning the fundamentals of music theory. ...according to Dmitri Tymoczko, a composer and music theorist at Princeton University, these well-known connections reveal only a few threads of the hefty rope that binds music and math.The Geometry of Music

See also The Geometry of Musical Chords - Dmitri Tymoczko, Science 7 July 2006: Abstract

See also Dmitri Tymoczko, Composer and Music Theoristvia [more inside]

## golden ratio in the amen break

The Amen Break and the Golden Ratio by mathematics educator and author, Michael S. Schneider. Schneider, having already researched and written about the golden ratio extensively, noticed it right away when hearing the the amen break for the first time (amen break previously on the blue). While some composers have been known to intentionally incorporate fibonacci numbers and the golden ratio into their works, perhaps this is just another one of the many instances of the ratio showing up in nature.