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Rebuttal to the recent Guardian article

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Nice atmospheric abstract puzzlers in Humble Weekly Sale. Recommended.

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**The network of mathematics**

Starting in the 1950s, Alexander Grothendieck revolutionized math by introducing many new concepts: schemes, stacks, motives, topoi and more. He wrote over 6000 pages! And then, after many quarrels with the mathematical establishment of France, he disappeared into the Pyrenees, where he now lives in seclusion.

The

**Stacks Project**is an open-source reference book with many authors which aims to explain a lot of the math Grothendieck and his collaborators created. It's currently 4000 pages long! You can download it as a single huge PDF file... but much better, you can read it on the web, and

*see how each result relies on previous ones!*

4 days ago, +Pieter Belmans made this a lot more fun. You can now see beautiful

*pictures*of this enormous network of mathematics! For example, the picture below is everything leading up to "result 01WC" which says that “a locally projective morphism is proper”.

I don't even know what this means... but never mind. What's cool is that you can go to a page with this picture:

http://stacks.math.columbia.edu/tag/01WC/graph/force

and however your mouse over any dot and see the different results leading up to this one!

Someday, if civilization doesn't collapse, all math will be linked up this way. There will be tools to help you explore it, starting with the easy stuff - and links to videos where people explain the ideas! There may even be online cafes where you can hang out and talk to other travelers who are visiting the same branch of math:

**"Well, I came here because I was learning about Coxeter groups and someone told me I had to learn about root systems of Lie algebras. I plan to spend a few days here and then go back - do you want come along?"**

But even right now, people are already using these networks to study

*statistical properties of the structure of mathematics!*For example, +Cathy O'Neil, aka "mathbabe", has gone through all 10,445 items in the Stacks Project. For each item, she looked at the graph like the one here. The nodes are the all the items on which the given item depends. The edges are the links between those items. Then she plotted the number of edges as a function of the number of nodes. You can see it here:

http://mathbabe.org/2013/07/31/analyzing-the-complexity-of-the-stacks-project-graphs/

What does it mean? Cathy has some ideas...

... but I think we're starting to see a new kind of metamathematics, where people use statistical methods to study the structure of mathematics itself. This is mathematics

*as actually done by people*, so it involves issues of taste and style. These are subjective things. But I suspect there are some features of math that are fairly independent of who is doing it. Maybe some theorems are 'important' in a fairly objective sense - important crossroads that most travelers tend to stop at. And someday we may understand why.

For more on the Stacks Project's new network visualization tools, read this blog article by Cathy O'Neil:

http://mathbabe.org/2013/07/30/the-stacks-project-gets-ever-awesomer-with-new-viz/

#networks

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"In a real historical piece, if they tried to make everything slavishly right any show would be unwatchable, because there would be too much that the audience couldn’t understand. The audience would be constantly distracted by details like un-filmably dark building interiors, ugly missing teeth, infants being given broken-winged songbirds as disposable toys to play with, crush, and throw away, and Marie Antoinette relieving herself on the floor at Versailles. Despite its hundreds of bathrooms, one of Versailles’ marks of luxury was that the staff removed human feces from the hallways regularly, sometimes as often as twice a day, and always more than once a week. We cannot make an accurate movie of this – it will please no one. The makers of the TV series Mad Men recognized how much an accurate depiction of the past freaks viewers out – the sexual politics, the lack of seat belts and eco-consciousness, the way grown-ups treat kids. They focused just enough on this discomfort to make it the heart of a powerful and successful show, but there even an accurate depiction of attitudes from a few decades ago makes all the characters feel like scary aliens. Go back further and you will have complete incomprehensibility."

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Apparrently money

(Thanks to +Mika Raento for the pointer.)

*does*make you happy, or so says a large data set.(Thanks to +Mika Raento for the pointer.)

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Ramadan on huomioitu: "Yhdysvaltain hallituksen mukaan paastoa kunnioitetaan pakkosyöttämällä vankeja vain öisin."

Vain lievästi makaaberia ottaa tuo seikka huomioon, kun sama hallinto jättää muun eettisen sikailun teoissaan huomioimatta.

Vain lievästi makaaberia ottaa tuo seikka huomioon, kun sama hallinto jättää muun eettisen sikailun teoissaan huomioimatta.

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The experiment cited in the article is pretty cool.

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