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Sarawr Queen of Kings
Wife, Mother, Father's Rights Advocate, Systems Administrator, Geek, Writer, Dungeon Master, basically, all-around awesome
Wife, Mother, Father's Rights Advocate, Systems Administrator, Geek, Writer, Dungeon Master, basically, all-around awesome

Sarawr Queen of Kings's posts

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Maryam Mirzakhani, 1977 - 2017

She died yesterday, a mathematician who had not yet reached the height of her powers: the first Fields medalist from Iran, and also the first woman to win that honor. Here's what I wrote when she won:

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 good to read. For a mathematically informed obituary, see this by Terry Tao:

The animated gif is a clip from this video:


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Guys... we can teleport things? WE CAN TELEPORT THINGS !!

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Yeah, still being defended in the "so what" column...


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H/t +Sarah Rios 
It's not just about Russia. Bush stood up for the press, too.

"We need an independent media to hold people like me to account,” Bush said. “Power can be very addictive, and it can be corrosive. And it’s important for the media to call to account people who abuse their power, whether it be here or elsewhere.”

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🎶 Raking up is hard to do... 🎶 
2 Photos - View album

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A horrifying reminder that the political climate of our nation is not that of the world. And that our fellow Americans are not our only brothers and sisters.

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One of the things I have found recently is that I have been holding bias toward the parties. I often find myself trying to excuse the actions of the more left-leaning politicians. Because of Trump's presidency and what I expect from my fellow Americans, I have become more critical of both parties and elected officials. I will condemn the immoral, hateful, and harmful actions, no matter the party affiliation and or how often I have agreed with an action in the past. Weighing rights and wrongs is not a reason to overlook the wrongs when you feel there are more rights.

I also have found that while I disagree with many actions in the Trump presidency, I can't completely discredit every action, as some have been for the better. While I struggle with whatever reasoning is behind the decisions he makes, that I support, I will at least acknowledge when something is in agreement with my own ideas and opinions on the subject.

Either way, one thing this presidency has taught me, is that party doesn't matter. What matters to me, are the rights of the people, who this, and every administration is hired/elected to serve. And I will support or condemn the actions of any political leader who helps or hurts the rights, livelihood, and liberties of my fellow Americans, regardless of how many times I have agreed with actions in the past, and regardless of party affiliation.
So consider carefully what you think is meant by “honor the king” (1 Peter 2:17). Take as long as you need to work it out. But whatever you come up with, be prepared to apply your conclusions consistently, regardless of which party the current “king” comes from. If you feel that “honoring the king” means we should cut Donald Trump a lot of slack, give him the benefit of the doubt, and help him to succeed, then I hope you did that with Bill Clinton and Barack Obama. If, on the other hand, you feel that Bill Clinton and Barack Obama should have been held to a very strict moral standard, then you cannot apply a more lenient standard to Donald Trump without compromising your credibility.

This is a lot of fallout from some ugly controversy in my (very small) circles. +Gary Henry spoke straightforwardly, and was criticized. This is his reasoned defense.

I'm posting this publicly because it needs to be heard.

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It is hard to overstate the significance of this agreement between Trump and Putin. "Agreeing not to meddle in each other's domestic affairs" is a code-phrase used by Russia and China for decades - one that every US president has told them to go to hell about.

For those unfamiliar with the term: that includes executing journalists, persecuting people for sexual orientation, race, and religion, and of course, invading other countries, if that land has "historically been a part of (Russia, China, etc)." Putin considers Crimea and eastern Ukraine to be Russian domestic affairs, in much the same way that Xi considers Tibet, Hong Kong, and Taiwan to be Chinese domestic affairs.

For decades, Russia and China have been building their own international alliances, both using this as a key selling point. The basic pitch is "Come do business with us; unlike the Americans, we'll never interfere in your domestic affairs." This doesn't mean "domestic affairs" that might affect local markets, exports, or relations with the controlling country, of course; a country's currency policy is clearly an international matter. It means "you can engage in all the repression and corruption you want; we will in fact bribe you handsomely."

As a result, both countries have been building up "alliances" of dictatorships. Trump has just agreed to the #1 rule of being a member of the Russia Club.

And having joined that club, by implication, we are no longer running our own. Certainly anyone considering joining up with us will now know that we won't really act to protect them from Russian interference - and given that this interference is a major threat for a lot of countries (Russia has been quite expansionist lately, and has no trouble making demands of its clients), this makes the value proposition of an American alliance a lot less compelling. Basically, we have just moved from being a clear leader of the largest alliance of nations in the world, to being a tier-2 member of the dictators' club.

Let nobody say that Trump hasn't achieved anything. I think he just ended the Cold War - with a surrender. 
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