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Ishmael Ahmed
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We lost a beautiful mind today...
Maryam Mirzakhani won the Fields medal yesterday.

As a child in Tehran, she didn't intend to become a mathematician - she just wanted to read every book she could find!  She also watched television biographies of famous women like Marie Curie and Helen Keller.  She started wanting to do something great... maybe become a writer.

She finished elementary school while the Iran-Iraq war was ending, and took a test that got her into a special middle school for girls.  She did poorly in math her first year, and it undermined her confidence.  “I lost my interest in math," she said.

But the next year she had a better teacher, and she fell in love with the subject.  She and a friend became the first women on Iranian math Olympiad team.  She won a gold medal the first year, and got a perfect score the next year.

After getting finishing her undergraduate work at Sharif University in Tehran in 1999, she went on to grad school at Harvard.  There she met Curtis McMullen, a Fields medalist who works on hyperbolic geometry and related topics.

Hyperbolic geometry is about curved surfaces where the angles of a triangle add up to less than 180 degrees, like the surface of a saddle.  It's more interesting than Euclidean geometry, or the geometry of a sphere.  One reason is that if you have a doughnut-shaped thing with 2 or more holes, there are many ways to give it a hyperbolic geometry where its curvature is the same at each point.  These shapes stand at the meeting-point of many roads in math.  They are simple enough that we can understand them in amazing detail - yet complicated enough to provoke endless study.

Maryam Mirzakhani took a course from McMullen and started asking him lots of questions.  “She had a sort of daring imagination,” he later said.  “She would formulate in her mind an imaginary picture of what must be going on, then come to my office and describe it. At the end, she would turn to me and say, ‘Is it right?’ I was always very flattered that she thought I would know.”

Here's a question nobody knew the answer to.  If an ant walks on a flat Euclidean plane never turning right or left, it'll move along a straight line and never get back where it started.  If it does this on a sphere, it will get back where it started: it will go around a circle.  If it does this on a hyperbolic surface, it may or may not get back where it started.  If it gets back to where it started, facing the same direction, the curve it moves along is called a closed geodesic.  

The ant can go around a closed geodesic over and over.  But say we let it go around just once: then we call its path a simple closed geodesic.    We can measure the length of this curve.  And we can ask: how many simple closed geodesics are there with length less than some number L?

There are always only finitely many - unlike on the sphere, where the ant can march off in any direction and get back where it started after a certain distance.  But how many?

In her Ph.D. thesis, Mirzakhani figured out a formula for how many.  It's not an exact formula, just an 'asymptotic' one, an approximation that becomes good when L becomes large.  She showed the number of simple closed geodesics of length less than L is asymptotic to some number times L to the power 6g-6, where g is the number of holes in your doughnut. 

She boiled her proof down to a 29-page argument, which was published in one of the most prestigious math journals:

• Maryam Mirzakhani, Growth of the number of simple closed geodesics on hyperbolic surfaces, Annals of Mathematics 168 (2008), 97–125,

This is a classic piece of math: simple yet deep.  The statement is simple, but the proof uses many branches of math that meet at this crossroads. 

What matters is not just knowing that the statement is true: it's the new view of reality you gain by understanding why it's true.   I don't understand why this particular result is true, but I know that's how it works.  For example, her ideas also gave here a new proof of a conjecture by the physicist Edward Witten, which came up in his work on string theory!  

This is just one of the first things Mirzakhani did.  She's now a professor at Stanford.

"I don't have any particular recipe," she said.  "It is the reason why doing research is challenging as well as attractive. It is like being lost in a jungle and trying to use all the knowledge that you can gather to come up with some new tricks, and with some luck you might find a way out."

She has a lot left to think about.  There are problems she has been thinking about for more than a decade. "And still there’s not much I can do about them," she said.

"I can see that without being excited mathematics can look pointless and cold. The beauty of mathematics only shows itself to more patient followers."

I got some of my quotes from here:

and some from here:

They're both fun to read.

#spnetwork doi:10.4007/annals.2008.168.97 #geometry #mustread

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The second enstallment
You Don't Vote For Kings

Part 2 in the series. You've heard that 97% of scientists believe in global warming, but that isn't true.

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A Convenient Truth

The first post of a new series on that climate change book going around. What does it really say about climate change, and should we be skeptical of climate change.

Part one: emotional appeals. We are all susceptible to a good emotional appeal. Won't someone think of the children? But how do we separate an emotional argument from an evidence-based one?

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The Family room is a community of caring folks who live to see all families thrive. It is the village.

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Ah Javascript you had me at the prototype...

//Using class inheritance in JavaScript is like driving your new Tesla Model S to the dealer and trading it in for a rusted out 1983 Ford Pinto.

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I made a thing. Share the thing!

The first two installments are free through the end of summer, and the next two are 99 cents. After that, I'm going to try something different.

"A unique brand of justice, morality, and heroism."
"Gripping, immersive, entertaining."
Amazon: 4.7 Stars
Goodreads: 4.3 Stars

An enigmatic mastermind recruits four people with extraordinary abilities and offers them everything they want in exchange for the impossible. But after they uncover a plot to hack the human race, they're not sure which side they're on -- only that not all of them will survive.

THE MINUS FACTION is a super-powered speculative thriller in seven novella-length episodes.

In Episode One . . .

Beaten. Burned. Broken.

Capt. John Regent returns a paraplegic after escaping months of captivity and torture -- except no one knows who took him or what he disclosed.

When a government agent comes for answers, she discovers John's fantastical secret and sets him at war with his own country. But the veteran in the wheelchair has one last mission, and he'll fight off the powers-that-be long enough to save the life of a troubled soldier -- even if it costs John his own.

"Keeps you guessing, keeps you surprised."

In Episode Two . . .

Xana Jace keeps her head down, which isn't easy when you stand seven feet eight inches tall. She works the night shift and stays out of trouble, striving only to be reunited with her son.

But she's running out of time. The strange disease that compels her body to grow also threatens to choke her heart.

When a masked gangster terrorizes the small community that shelters her, Xana is left with a terrible choice and just twenty-four hours to discover the truth that everything she believes is a lie.

"A brutally honest sci-fi thriller."

You can also get the full set for free on my website. Just sign up for the new release mailing list:

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Does not quantum entanglement imply retro causality, and multi universes does not exclude retro causality either, does it?
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