# Fabergé Fractals

Here's a mesmerizing gallery of "Fabrege Fractals" created by Tom Beddard, whose site also features a 2011 video of Fabrege-inspired fractal landscapes that must be seen to be believed. They're all made with Fractal Lab, a WebGL-based renderer Beddard created.

# Unknown mathematician makes historical breakthrough in prime theory

Yitang Zhang is a largely unknown mathematician who has struggled to find an academic job after he got his PhD, working at a Subway sandwich shop before getting a gig as a lecturer at the University of New Hampshire. He's just had a paper accepted for publication in Annals of Mathematics, which appears to make a breakthrough towards proving one of mathematics' oldest, most difficult, and most significant conjectures, concerning "twin" prime numbers. According to the Simons Science News article, Zhang is shy, but is a very good, clear writer and lecturer.

For hundreds of years, mathematicians have speculated that there are infinitely many twin prime pairs. In 1849, French mathematician Alphonse de Polignac extended this conjecture to the idea that there should be infinitely many prime pairs for any possible finite gap, not just 2.

Since that time, the intrinsic appeal of these conjectures has given them the status of a mathematical holy grail, even though they have no known applications. But despite many efforts at proving them, mathematicians weren’t able to rule out the possibility that the gaps between primes grow and grow, eventually exceeding any particular bound.

Now Zhang has broken through this barrier. His paper shows that there is some number N smaller than 70 million such that there are infinitely many pairs of primes that differ by N. No matter how far you go into the deserts of the truly gargantuan prime numbers — no matter how sparse the primes become — you will keep finding prime pairs that differ by less than 70 million.

The result is “astounding,” said Daniel Goldston, a number theorist at San Jose State University. “It’s one of those problems you weren’t sure people would ever be able to solve.”

Unknown Mathematician Proves Elusive Property of Prime Numbers [Erica Klarreich/Wired/Simons Science News]

(Photo: University of New Hampshire)

# Life of astronaut Sally Ride honored in Kennedy Center tribute

American astronaut Sally Ride monitors control panels from the pilot's chair on the flight deck in 1983. Photo by Apic/Getty Images, via PBS NewsHour.

Tonight, PBS NewsHour science correspondent Miles O'Brien will serve as master of ceremonies in a Kennedy Center gala honoring the life and legacy of astronaut Sally Ride. The tribute will highlight her impact on the space program and her lifelong commitment to promoting youth science literacy.

Her Sally Ride Science organization reached out to girls, encouraging them to pursue careers in the Science, Technology, Engineering and Math (STEM) fields, where a gender gap persists.

At the PBS NewsHour website, read the column Miles wrote immediately following Ride's death in July 2012, 17 months after she was diagnosed with pancreatic cancer.

## Death, be not infrequent —

The oldest person in the world died this year. But don't worry if you missed the event. The oldest person in the world will likely die next year, as well. In fact, according to mathematician Marc van Leeuwen, an "oldest person in the world" will die roughly every .65 years.

# Looking for mathematical perfection in all the wrong places

The Golden Ratio — that geometric expression of the Fibonacci sequence of numbers (1, 1, 2, 3, 5, etc.) — has influenced the way master painters created art and can be spotted occurring naturally in the seed arrangement on the face of a sunflower. But its serendipitous appearances aren't nearly as frequent as pop culture would have you believe, writes Samuel Arbesman at The Nautilus. In fact, one of the most common examples of mathematical perfection — the chambered nautilus shell — actually isn't. Even math can become part of the myths we tell ourselves as we try to create meaning in the universe.

Image: Golden Ratio, a Creative Commons Attribution (2.0) image from ernestduffoo's photostream

## The mathematics of tabloid news —

Leila Schneps and Coralie Colmez have an interesting piece at The New York Times about DNA evidence in murder trials, the mathematics of probability, and the highly publicized case of Amanda Knox. What good is remembering the math you learned in junior high? If you're a judge, it could be the difference between a guilty verdict and an acquittal.

# Weird probabilities of non-transitive "Grime Dice"

Michael de Podesta has been doing the math on "Grime Dice" -- six sided cubes whose sides average out to 3.5, but whose face values are all radically different:

The interesting thing about these is that the odds of one die beating another are simple to calculate, but shift radically once you start rolling dice in pairs. It's a beautiful piece of counterintuitive probability math:

The amazing property of these dice is discernible when you use them competitively – i.e. you roll one dice against another. If you roll each of them against a normal dice then as you might expect, each dice will win as often as it will lose. But if you roll them against each other something amazing happens.

• Dice A will systematically beat Dice B
• Dice B will systematically beat Dice C

and amazingly

• Dice C will systematically beat Dice A

So the fact that Dice A beats Dice B, and Dice B beats Dice C does not ensure that Dice A will beat Dice C. Wow!

And how about this: If you ‘double up’ and roll 2 Dice  A‘s against 2 Dice B‘s – the odds change around and now the B‘s will beat the A‘s ! Is that really possible? Well yes, and just to convince myself I wrote a Spreadsheet (.xlsx file) and generated the tables at the bottom of the article. If you download it you can change the numbers to try out other combinations.

## Celebrate "Pi Day" by throwing hot dogs down a hallway —

No, that's not a euphemism for anything. Buffon's Needle is an 18th-century experiment in probability mathematics and geometry that can be used as a way to calculate pi through random sampling. This WikiHow posting explains how you can recreate Buffon's Needle at home, by playing with your food.

# Calculus-performing mechanical calculator

A clip from the Discovery Channel's Dirty Jobs program on tanneries demonstrates the workings of a calculus-performing mechanical calculator that measures the surface-area of irregularly shaped hides with a fascinating and clever set of gears, calipers and ratchets.

Dirty Jobs - Tannery Mechanical Surface Integrator (Thanks, Dad!)

## Game theory and bad behavior on Wall Street —

An opinion piece by Chris Arnade on the asymmetry in pay (money for profits, flat for losses), which he describes "the engine behind many of Wall Street’s mistakes" That asymmetry "rewards short-term gains without regard to long-term consequences," Chris writes in a new guest blog at Scientific American. "The results? The over-reliance on excessive leverage, banks that are loaded with opaque financial products, and trading models that are flawed." [Scientific American Blog Network] Xeni

# The world's largest prime number — visualized

Philip Bump took the recently discovered 17-million-digit prime number and, six digits at a time, converted it into RGB colors. This is the result.

## Neil deGrasse Tyson on pi and other constants —

Both the Bible and the Indiana State Legislature have tried to redefine pi to equal something much more simple than 3.14159265358979323846264338327950 ...

## 86.54% liked this —

Science blogger Matt Springer analyzes the surprisingly fascinating math behind Reddit upvotes.

# Probability theory for programmers

Jeremy Kun, a mathematics PhD student at the University of Illinois in Chicago, has posted a wonderful primer on probability theory for programmers on his blog. It's a subject vital to machine learning and data-mining, and it's at the heart of much of the stuff going on with Big Data. His primer is lucid and easy to follow, even for math ignoramuses like me.

For instance, suppose our probability space is $\Omega = \left \{ 1, 2, 3, 4, 5, 6 \right \}$ and $f$ is defined by setting $f(x) = 1/6$ for all $x \in \Omega$ (here the “experiment” is rolling a single die). Then we are likely interested in more exquisite kinds of outcomes; instead of asking the probability that the outcome is 4, we might ask what is the probability that the outcome is even? This event would be the subset $\left \{ 2, 4, 6 \right \}$, and if any of these are the outcome of the experiment, the event is said to occur. In this case we would expect the probability of the die roll being even to be 1/2 (but we have not yet formalized why this is the case).

As a quick exercise, the reader should formulate a two-dice experiment in terms of sets. What would the probability space consist of as a set? What would the probability mass function look like? What are some interesting events one might consider (if playing a game of craps)?

(Image: Dice, a Creative Commons Attribution (2.0) image from artbystevejohnson's photostream)

# Math Fleet: command a space squadron and defend planet Earth with the power of math

Kevin Kelly told me about Phil Scale's new iOS application to teach kids arithmetic. It's called Math Fleet and it sounds great. (Phil created Kevin's Asia Grace photobook app, which is also wonderful.)

Phil says:

I've been an independent iOS app developer for four years, and my wife, Jennifer, and I work together from our home in Austin creating games and educational apps. Our newest app is called Math Fleet, an action game set in space where players must use quick math skills to save Earth from invasion, all while dodging asteroids and battling enemy star fighters.

The inspiration for the game came from our sons, Jack, Luke and Dylan (ages 7, 6 and 3) for whom I've downloaded and tried many educational apps and games. At the beginning of the summer we were all home together and I was brainstorming the next game, which I knew I wanted to set in space. I had my sons Jack and Luke playing a math game I had downloaded to earn playing time for the other games they really wanted to play. We all agreed though that the math game I had them playing, which cost me \$5, wasn't a very good game and there really wasn't very much math in it. I knew I could write a better game and we started talking about what we would do differently, and in that moment, we decided our mission was to create not just a better game, but the most awesome action math game out there, and that Jack and Luke would be in the driver's seat guiding how the game would take shape.

It became the ultimate geek dad summer for me as I fully committed myself to making their ideas a reality, and some of their ideas were pretty challenging to implement. Such as Luke's idea that the user pilot multiple ships, customizable and upgradable -- the eventual foundation of the game; Or the Patrol Sector concept drawn up by my 7-year-old, Jack.

Throughout the eight month journey, as I coded, they tested prototypes of controls, menus, action sequences, effects, space weapons, and ships. They told me what they liked and what they didn't like, what they'd do differently, and in many cases they would contribute key design concepts delivered as crayon drawings or Lego models. I learned more about game design by watching them, listening, and discussing ideas than I learned from writing my previous two games.

Finally, after eight months and 300,000 lines of code, Math Fleet is officially released, and is hopefully everything we set out to create to create an exciting math game that kids actually want to play, while also challenging their minds by combining fast problem solving with the stress and distraction of piloting a space fleet.

Math Fleet