**The first ever picture of the Mandelbrot set**, from this 1978 paper by Robert Brooks and J. Peter Matelski.

For comparison, here’s a more modern representation of this fractal wonder:

*(via Cliff Pickover)*

**The first ever picture of the Mandelbrot set**, from this 1978 paper by Robert Brooks and J. Peter Matelski.

For comparison, here’s a more modern representation of this fractal wonder:

*(via Cliff Pickover)*

**Multip-Line **

This is the coolest math trick I’ve seen in a while! Multiply large numbers by just drawing lines.

Most of us learned to multiply any two numbers based on sequentially multiplying from right to left, from ones to higher powers, while carrying over the extras from tens to hundreds to thousands and so on.

But what if you could multiply numbers just using lines? That’s what Vedic multiplication does! Give it a try, you’ll have a cool math trick to show your friends. It even works in non-base-ten!

This technique is often called Japanese multiplication, because it is (allegedly) taught to Japanese students, but from what I can tell it originated in India?

*(video by Chris Lusto)*

To celebrate the puzzle’s 40th anniversary, today’s Google Doodle is a fully-functional Rubik’s Cube! If you had a cube for every possible arrangement of the 54 colored squares, and you laid them end-to-end, those 43,252,003,274,489,856,000 cubes would extend 261 light years.

But no single Rubik’s cube can be configured to all of those Rubik’s universes.

If the traditional cube isn’t challenging enough for you, you can head over to the Chrome Cube Lab and try your digital hand at some other cubic puzzles.

The folks at Numberphile took an in-depth look at the math behind a Rubik’s Cube in a series of videos on YouTube. Here’s one of them:

Those who assert that the mathematical sciences say nothing of the beautiful or the good are in error. For these sciences say and prove a great deal about them; if they do not expressly mention them, but prove attributes which are their results or definitions, it is not true that they tell us nothing about them. The chief forms of beauty are order and symmetry and definiteness, which the mathematical sciences demonstrate in a special degree.

(via scienceisbeauty)

I would argue that in modern times we have expanded our ideas of beauty beyond symmetry and order, for math can describe chaos just as aptly, but I like the sentiment, A.

An excellent conversation with the mathematical physicist Freeman Dyson from Quanta Magazine, touching on everything from quantum electrodynamics to why getting kids into science might change the world.

Dyson is often contrarian, but always sharp and intelligent. From founding quantum electrodynamics alongside one of my heroes, Richard Feynman, to such science future fictions as the Dyson sphere, he has a particular way of approaching the known and unknown world that we’d all be well-served to consider.

On the value of math:

I was trained as a mathematician, and I remain a mathematician. That’s really my skill, just doing calculations and applying mathematics to all kinds of problems, and that led me into physics first and also other fields, such as engineering and even a bit of biology, sometimes a little bit of chemistry. Mathematics applies to all kinds of things. That’s one of the joys of being a mathematician.

I love that. No matter your field, you’ll do well to remember that you’re a problem-solver first and an applier-of-specific-skills second.

On the value (or not?) of the Ph.D.:

I’m very proud of not having a Ph.D. I think the Ph.D. system is an abomination. It was invented as a system for educating German professors in the 19th century, and it works well under those conditions. It’s good for a very small number of people who are going to spend their lives being professors. But it has become now a kind of union card that you have to have in order to have a job, whether it’s being a professor or other things, and it’s quite inappropriate for that. It forces people to waste years and years of their lives sort of pretending to do research for which they’re not at all well-suited. In the end, they have this piece of paper which says they’re qualified, but it really doesn’t mean anything. The Ph.D. takes far too long and discourages women from becoming scientists, which I consider a great tragedy.

I think he’s spot-on about many of the Ph.D.’s failings, but I think he simplifies the value of the “title” here, rather than the work one does to *get* the Ph.D. Therein lies the value, or lack thereof. The Ph.D. process (quite effectively) teaches a manner of thought and problem-solving that is tough (but not impossible) to replicate elsewhere. But a Ph.D. is most certainly *not* the only way (or even the best way?) to become a scientist, at least with respect to a scientist being not a vocation but being “someone with a generally scientific mindset”.

Finally, on why we need to get every child interested in science:

We should try to introduce our children to science today as a rebellion against poverty and ugliness and militarism and economic injustice.

Pixar: The math behind the moviesThe folks at Pixar are widely known as some of the world’s best storytellers and animators. They are perhaps less recognized as some of the most innovative math whizzes around. Pixar Research Lead Tony DeRose delves into the math behind the animations, explaining how arithmetic, trigonometry and geometry help bring Woody and the rest of your favorite characters to life.

View full lesson: http://ed.ted.com/lessons/pixar-the-math-behind-the-movies-tony-derose

Talk by Tony DeRose.

via TED Education.

It’s not exactly shocking that computer animation would involve a lot of math, but it’s so cool to see exactly *how* they apply it. Don’t ever say math isn’t worth it. Remember: you wouldn’t have your precious *Frozen* without it.

Strange attractors, take a look in full resolution at this page (byBrian Wissman, The University of Hawai‘i System).

According to Wikipedia, “an **attractor** is a set of physical properties toward which a system tends to evolve” … so what I’m taking from this is that if the world is a system, then it naturally evolves to look awesome.

Mathematical Object Minimalist Posters by Visualizingmath.(Yes, I actually attempted tomakesomething!)Thank you to Curiosamathematica for creating the Klein Bottle image!

These are

(via crookedindifference)

Source: visualizingmath

Eesh, I haven’t thought much about calculus since calculus class. Sorry your teacher can’t derive their way out of a paper bag.

Khan Academy, obvs, but I also recommend everyone check out Open Culture’s list of free online courses (scroll down for the math courses). It puts a cornucopia of learning at your fingertips. Bookmark that page. It’s glorious.

Got my mind on this money

And this money on my mind

THROUGH SCIENCE WE PROGRESS

Make the knowledge rain

Source: theuniverseandmore2.blogspot.it

Page 1 *of* 26

**I'm Joe Hanson, a Ph.D. biologist and science writer based in Austin, TX. I'm the creator/host/writer of PBS Digital Studios' It's Okay To Be Smart. Subscribe on YouTube by clicking below:**

**
**

**Check out my "Episode Extras" here. There's a lot of amazing science out there. Let's learn something together.**

**"Everyone's favorite Feynman of the Tumblr era"** - Maria Popova

**Joe's science book recommendations**, from brains to biology to space to art to physics.

Want more great sciencey goodness? Check out my favorite science links.

This is an indie blog that takes many hours a week to publish. If you'd like to support *It's Okay To Be Smart*, please consider even a small donation.

Or click here to shop on Amazon, and support *IOTBS* at the same time.

One of **Time Magazine's 30 Must-See Tumblrs - 2012**

My writing has also appeared at Wired, Scientific American, and in **The Best Science Writing Online - 2012**

loading tweets…