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592 posts tagged with math.

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## Animated math

Essence of linear algebra - "[Grant Sanderson of 3Blue1Brown (now at Khan Academy) animates] the geometric intuitions underlying linear algebra, making the many matrix and vector operations feel less arbitrary." [more inside]

## "the naive approach is often to use a Gaussian blur"

Have you ever wondered what your graphics card is doing every time it displays one frame of a game? Turns out quite a lot. [more inside]

## xEuclidx

Compass-and-straightedge construction (aka Euclidean construction) is a method of drawing precise geometric figures using only a compass and a straightedge (like a ruler without the markings). MathOpenRef maintains a catalog of many common constructions, each with an explanatory animation and a proof. This YouTube video demonstrates how to construct almost every polygon that can be constructed using these methods. [more inside]

## Auditing Algorithms and Algorithmic Auditing

How big data increases inequality and threatens democracy - "A former academic mathematician and ex-hedge fund quant exposes flaws in how information is used to assess everything from creditworthiness to policing tactics, with results that cause damage both financially and to the fabric of society. Programmed biases and a lack of feedback are among the concerns behind the clever and apt title of Cathy O'Neil's book:

*Weapons of Math Destruction*." [more inside]## You are worth having coffee with.

Francis Su is a professor of mathematics at Harvey Mudd College and the first non-white president of the Mathematical Association of America. In 2013, he presented his Haimo Teaching Award lecture, The Lesson of Grace in Teaching. For Su, when we learn the lesson of grace—that we have dignity irrespective of accomplishments—and when we impart that lesson to our students, we make good teaching, enthusiastic learning, and honest evaluation possible. [more inside]

## Monumental Proof to Torment Mathematicians for Years to Come

Nearly four years after Shinichi Mochizuki (previously, previously, previously) unveiled an imposing set of papers (1, 2, 3, 4) that could revolutionize the theory of numbers, other mathematicians have yet to understand his work or agree on its validity — although they have made modest progress. [more inside]

## So, the unknowable kicks in

Logic hacking - "Writing shorter and shorter computer programs for which it's unknowable whether these programs run forever, or stop... the winner of the Busy Beaver Game for N-state Turing machines becomes unknowable using ordinary math - somewhere between N = 5 and N = 1919." [more inside]

## The lasting legacy of the "rocket girls" of JPL

California-based Jet Propulsion Laboratory (JPL) has been central to the US missile and rocket development and operations for decades, and from the beginning that technology's success rested on a corps of expert mathematicians, people known as computers. And from the beginning they were all women, in a time when such opportunities were few and far between. You can find pictures of them, but names have not been well-recorded ... until now. Nathalia Holt found many of those women and wrote about their experiences in her book,

*Rise of the Rocket Girls: The Women Who Propelled Us, from Missiles to the Moon to Mars*. [more inside]## "Hyperbolic" but not in the literary device sense

I know that you've gotten bored of roguelikes because they're so easy to wrap your head around and master, so here's one that takes place in hyperbolic space

## Why are we here? Because we're here.

Perhaps you've heard of the recent release of the 120-sided die, which is certainly impressive in its way but not really that… weird. If you're

*really*looking to stand out, why not order yourself some 34-sided dice?## When in doubt, do the math.

"

1) Buy experiences

2) Make it a treat

3) Buy time

4) Pay now, consume later

5) Invest in others

Five principles are four too many for a lazy reductionist, let’s see if we can identify some common themes and combine these ideas into a single framework that would lose all nuance and intricacy but be expressible as an equation. (Spoiler: of course we can, duh)."

*Happy Money*lists five principles of happy spending:1) Buy experiences

2) Make it a treat

3) Buy time

4) Pay now, consume later

5) Invest in others

Five principles are four too many for a lazy reductionist, let’s see if we can identify some common themes and combine these ideas into a single framework that would lose all nuance and intricacy but be expressible as an equation. (Spoiler: of course we can, duh)."

## Contact! Let's make contact!

"'Too many children think that scientists are all middle-aged white males in laboratory coats,' Edward Atkins,

*3-2-1 Contact*'s director of content, told*The New York Times*in 1983." The Kids' Show That Taught Me to Ask "Why?", an ode to 3-2-1 Contact. [more inside]## The New Astrology

Surveys indicate that economists see their discipline as ‘the most scientific of the social sciences’. What is the basis of this collective faith, shared by universities, presidents and billionaires? Shouldn’t successful and powerful people be the first to spot the exaggerated worth of a discipline, and the least likely to pay for it? In the hypothetical worlds of rational markets, where much of economic theory is set, perhaps. But real-world history tells a different story, of mathematical models masquerading as science and a public eager to buy them, mistaking elegant equations for empirical accuracy.

## A Riddle from 538

## Is this Prime?

The

*Is this prime?*game tests you as you sort numbers into prime and non-prime. Click Yes or No or type Y or N on the keyboard. Uses JavaScript. [more inside]## No, really, pi is wrong.

## "In short, they commuted but didn’t associate."

Happy π Day! And do you know what that means? Math puns today! Every day! In competitions, even. Don't like puns? Try other forms of math humor (or over-explain them to businesspeople)!

## What else have we missed about the primes?

## Conway's Game of Pi

John Horton Conway, known for his Game of Life among numerous other mathematical contributions, is partnering with Pizza Hut to release three original math problems at 8 AM EDT this coming Pi Day (March 14th), "varying in level of difficulty from high school to Ph.D. level". The first person to respond to each question with the correct answer will win 3.14 years of free pizza.

## When to stop dating and settle down, according to math

Optimal stopping is a math theory that can be used to solve real world decision problems. In the real world, it is often applied to help decide when to stop dating and get married.

## How Serious Computer Geeks Count On Their Fingers

How to count to 1000 on two hands Covers counting on your fingers in binary, a skill far more people should have. Be careful you don't offend anyone when you hit 4, 128 and especially 132. [more inside]

## "there are ten enthusiastic seconds in 6 weeks"

## More kids more math

"You wouldn’t see it in most classrooms, you wouldn’t know it by looking at slumping national test-score averages, but a cadre of American teenagers are reaching world-class heights in math—more of them, more regularly, than ever before." Peg Tyre in

*The Atlantic*covers the new wave of deeper, faster, and hopefully broader math education. [more inside]## Babylonian (Pre)Calculus!

Signs of Modern Astronomy Seen in Ancient Babylon - "Scientists have found a small clay tablet with markings indicating that a sort of precalculus technique was used to track Jupiter's motion in the night sky." [more inside]

## “may someday help in a more objective assignment of books...”

Scientists find evidence of mathematical structures in classic books. [The Guardian] James Joyce’s Finnegans Wake has been described as many things, from a masterpiece to unreadable nonsense. But it is also, according to scientists at the Institute of Nuclear Physics in Poland, almost indistinguishable in its structure from a purely mathematical multifractal.

“The absolute record in terms of multifractality turned out to be Finnegans Wake by James Joyce. The results of our analysis of this text are virtually indistinguishable from ideal, purely mathematical multifractals,” said Professor Stanisław Drożdż, another author of the paper, which has just been published in the computer science journal Information Sciences.

## The emperor was naked, and so is this.

*"Respected research math is dominated by men of a certain attitude. Even allowing for individual variation, there is still a tendency towards an oppressive atmosphere, which is carefully maintained and even championed by those who find it conducive to success."*Recent Princeton graduate Piper Harron's PhD thesis isn't written for these men. It is very cool number theory, and it is art.

## No cutesy adversaries

*“I think the post-war turn towards social responsibility in science and engineering was less a turn than a sideways glance. .. If researchers like us were actually supposed to know or care about this stuff in any operationally significant way, well, I think we didn't get the memo. So let me retransmit it.”*- Phillip Rogaway. The Moral Character of Cryptographic Work. [more inside]

## Internet quizzes are to Metafilter as...

## Statistical heaping, 20 yards, first down

What I've got: A spreadsheet containing every single play run in the NFL from 2000-2014 (500,000 in all)

What I'm going to do with it: Show that the referees subconsciously change the outcome of a play based on where the painted lines are on a field, and subsequently show that it doesn't matter.

What I'm going to do with it: Show that the referees subconsciously change the outcome of a play based on where the painted lines are on a field, and subsequently show that it doesn't matter.

## Where are all the women? The math said there would be more women!

One mathematician’s formula suggests that all-male lineups don’t “just happen,” despite what conference organizers might claim. "...in any conference with over 10 speakers, say, it would be extremely rare to have no female speakers at all—less than 5 percent chance, depending on one’s assumption about the percentage of women in mathematics as a whole."

## Can an iPad run Drug Wars? Oh... it can?

The TI-83 graphic calculator is still a standby for mathematics education in America. This Mic.com article looks at some of the causes and effects of that fact. [more inside]

## The likelihood that there's interesting or important math is pretty high

Shinichi Mochizuki and the impenetrable proof - "Fesenko has studied Mochizuki's work in detail over the past year, visited him at RIMS again in the autumn of 2014 and says that he has now verified the proof. (The other three mathematicians who say they have corroborated it have also spent considerable time working alongside Mochizuki in Japan.) The overarching theme of inter-universal geometry, as Fesenko describes it, is that one must look at whole numbers in a different light — leaving addition aside and seeing the multiplication structure as something malleable and deformable. Standard multiplication would then be just one particular case of a family of structures, just as a circle is a special case of an ellipse." (previously: 1,2; via) [more inside]

## Blowing the Whistle on the UC Berkeley Mathematics Department

*Given the success I am having with students, one might think that the Mathematics Department leadership would be expressing curiosity about how I am achieving that success. Instead, Craig Evans in early 2014 asked me "If you had a job at McDonalds and came along with all these new ideas, how long do you think you'd carry on working there?" The fact that the now Interim Chair of the UC Berkeley Mathematics Department should compare undergraduate education to fast food reveals everything you need to know about how students are regarded by the leading clique of men at the helm of the Mathematics Department of the number one public university in the world.*[more inside]

## Learning common core math with a check written by an upset father

When the father of a second grader got annoyed by common core math tools (namely, ten frame cards), his annoyance went viral when he wrote a check to his student's school using common core numbers. Then the Friendly Athiest on Patheos used that check to teach how common core math works at the second grade level.

## Fun math for kids

Unsolved problems with the common core. Computational biologist (and occasional curmudgeon) Lior Pachter pairs unsolved problems in mathematics to common core math standards.

## Steve Martin and Robin Williams Riffing on Mathematics

In 2002, Steve Martin sat down for a Q&A about his writing and his interest in mathematics. His friend Robin Williams was on hand to help out. Please pardon the video quality. Part 1 Part 2 Part 3 Part 4 Part 5

## You sank my battleship... with probability!

Battleship Probability Calculator by C. Liam Brown. Finds the best squares to try during the game.

## Inspired by mathematical theorems or open problems...

Conveyer Belt Font. More mathematical and puzzle fonts/typefaces you can play with in your browser. Read about them in the article Fun with Fonts: Algorithmic Typography. [PDF]

## a(n)=a(n−1)+gcd(n,a(n−1)).

Go ahead: Press the button.

*A number is printed on the tape. Press again and another number appears. Keep going. A few more. Notice anything special about those numbers? The sequence begins: 5, 3, 11, 3, 23, 3, 47, 3, 5, 3, 101, 3, 7, 11, 3, 13, 233, 3, 467, 3, 5, 3, . . .*## Can you add faster than a 5 year old

CMA is a "brain development program designed to develop higher learning capability and aims to promote mental arithmetic, enhance memory, boost creativity, and increase focus using the principle of Abacus". Watch some kids from The Philippines calculates in seconds, using their fingers. (SLYT)

## Cosmic Call

“In 1999, two Canadian astrophysicists, Stéphane Dumas and Yvan Dutil, composed and sent a message into space. The message was composed of twenty-three pages of bitmapped data, and was sent from the RT-70 radio telescope in Yevpatoria, Ukraine, as part of a set of messages called Cosmic Call.” [more inside]

## New Pentagons

Mathematicians discover a new type of pentagon that can cover the plane leaving no gaps and with no overlaps. It becomes only the 15th type of pentagon known that can do this, and the first discovered in 30 years. [more inside]

## One Way or Another

"In a patent dispute between two pharmaceutical giants arguing over who owns the royalty rights to a lucrative wound-dressing solution, their lordships sat in judgment over an issue that would have tested the mettle of the finest mathematical logicians; and in the process coined a new legal definition of “one”." [more inside]

## Famous Fluid Equations Are Incomplete

The Singular Mind of Terry Tao - "Imagine, he said, that someone awfully clever could construct a machine out of pure water. It would be built not of rods and gears but from a pattern of interacting currents." (via) [more inside]

## Loop - Pool on an elliptical table

Loop - Pool on an elliptical table.

*The ellipse has two significant points, called focuses, which have a remarkable geometrical property that is almost always explained using the example of an imaginary pool table. "If a pool table is the shape of an ellipse, then a ball shot from one focus will always rebound to the other focus no matter in which direction the ball is shot." That sounded interesting! Wouldn’t it be fun, I thought, if I could build one of these imaginary tables? So I did.*## "Their little heads are exploding"

Mrs. Nguyen’s Prestidigitation

*From a set of 1 through 9 playing cards, I draw five cards and get cards showing 8, 4, 2, 7, and 5. I ask my 6th graders to make a 3-digit number and a 2-digit number that would yield the greatest product...*and somehow we end up with lacing diagrams and Python. (The original post on Fawn Nguyen's blog)## Time with class! Let's Count!

I want to demonstrate how amazing combinatorial explosion is! Please don't stop me. An animation about numbers that get large. It has a happy ending and possibly even a moral. [more inside]

## HoTT Coq

Univalent Foundations Redefines Mathematics - "When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the century-old rules underlying all of mathematics." (previously) [more inside]

## Keeping It Fair

You're sitting down with your friends to play a boardgame, and you find yourself in a conundrum: how do you choose a first player? Sure, you could roll a standard die and take highest number, but what if there's a tie? That could take forever! Besides, wouldn't you rather be mathematically sure that everyone has a fair shot at each spot in the turn order?
Of course you would!

## 3Blue1Brown: Reminding the world that math makes sense

Understanding e to the pi i - "An intuitive explanation as to why e to the pi i equals -1 without a hint of calculus. This is not your usual Taylor series nonsense." (via via; reddit; previously) [more inside]