February 26, 2014 7:15 PM Subscribe

Each month, the Notices of the American Math Society runs a column called "What is...." which aims to explain an advanced mathematical concept in two pages, at a level accessible to a good undergrad math major. Armin Straub, a postdoc at Illinois, has collected them all in one place.

Some that I particularly like:

"What is ... data mining?" by Mauro Maggioni

"What is ... a sandpile?" by Lionel Levine and James Propp

"What is ... a random matrix?" by Persi Diaconis

If these are all too down-to-earth for you, feel free to head straight for Jacob Lurie's "What is ... an infinity-category?"
posted by escabeche (33 comments total)
145 users marked this as a favorite

Some that I particularly like:

"What is ... data mining?" by Mauro Maggioni

"What is ... a sandpile?" by Lionel Levine and James Propp

"What is ... a random matrix?" by Persi Diaconis

If these are all too down-to-earth for you, feel free to head straight for Jacob Lurie's "What is ... an infinity-category?"

I saw Mikhalkin give a six-hour seminar about amoebas at CUNY when I was a postdoc, about 10 years ago. What a wild, enriching, abrading, enlightening experience. It was before we had anything like the mechanisms of tropical geometry that have been built up since then but you could already see that something really great was happening. Awesome.

posted by escabeche at 7:37 PM on February 26 [1 favorite]

posted by escabeche at 7:37 PM on February 26 [1 favorite]

Wow! Thanks.

posted by benito.strauss at 7:46 PM on February 26

posted by benito.strauss at 7:46 PM on February 26

I am.....all at the same time.....impressed, depressed, regressed, and suppressed.

While flittering about reading, my concentration stream became restricted by, um, ennui and downright boredom.

I kept wondering why we as a nation are becoming evermore lagging in all things educational on this little orb we call home.

posted by chuckiebtoo at 8:10 PM on February 26 [1 favorite]

While flittering about reading, my concentration stream became restricted by, um, ennui and downright boredom.

I kept wondering why we as a nation are becoming evermore lagging in all things educational on this little orb we call home.

posted by chuckiebtoo at 8:10 PM on February 26 [1 favorite]

Some of them are more accessible than others. I clicked through to "What is ...a biholomorphic mapping" and the definition appeared to say that a function f: C^n -->C^n is holomorphic if each of the coordinate functions is holomorphic. Hmmm. Not a good place to start, since I don't remember what a holomorphic function is. (It got better, but still.)

I liked What is...a quasicrystal and What is...a tensegrity, though.

posted by leahwrenn at 8:30 PM on February 26

I liked What is...a quasicrystal and What is...a tensegrity, though.

posted by leahwrenn at 8:30 PM on February 26

Oh, this is wonderful! The world needs more math...

posted by Alexandra Kitty at 9:23 PM on February 26 [2 favorites]

posted by Alexandra Kitty at 9:23 PM on February 26 [2 favorites]

"... *which aims to explain an advanced mathematical concept in two pages, at a level accessible to a good ***undergrad math major.**"

Finally a post for me. Thank you. Favorited.

posted by triceryclops at 10:31 PM on February 26

Finally a post for me. Thank you. Favorited.

posted by triceryclops at 10:31 PM on February 26

I guess I was a mediocre undergraduate math major.

posted by scose at 10:31 PM on February 26 [1 favorite]

posted by scose at 10:31 PM on February 26 [1 favorite]

Well, so the first link I could find says that about 1% of college undergrads are math majors, so let's be generous and say that anyone better than the median is "good", so 0.5% of people who go to college. About 1/3 of Americans have college degrees, so the target audience I guess is roughly 0.16% of the general public. So, great, I guess, but I'll admit, I don't make it into that group.

posted by tylerkaraszewski at 10:33 PM on February 26 [3 favorites]

posted by tylerkaraszewski at 10:33 PM on February 26 [3 favorites]

Took maths in senior school. Did engineering mathematics at university. Okay, that was longer ago than I care to think about, but this stuff is over my head.

posted by YAMWAK at 11:39 PM on February 26

posted by YAMWAK at 11:39 PM on February 26

I looked at some of these for a friend. Inside "paraproduct" (hmm, that sounds interesting) there is an embedded add for the NSA. I'm not sure if that is a detriment or a strength of this collection.

posted by coolxcool=rad at 11:50 PM on February 26

posted by coolxcool=rad at 11:50 PM on February 26

To be fair, other institutions have ads in some of these of these as well.

posted by coolxcool=rad at 1:09 AM on February 27

posted by coolxcool=rad at 1:09 AM on February 27

I'm extremely interested in math but did terrible at it in high school. I'd like to retry it sometime in my life. Unfortunately I have no idea what any of these are talking about.

posted by gucci mane at 1:28 AM on February 27

posted by gucci mane at 1:28 AM on February 27

Two that I particularly like: Operads, because operads are very interesting things, though I doubt the article will convince you of that - like a lot of things in the area of algebraic topology and category theory, operads are an abstraction that's hard to appreciate until you've seen and wrestled with various specific instances and struggled with the mess and and then Papa Stasheff comes and shows you how to do it properly. And Quasicrystals, which are also interesting, but the first sentence of that one sums up its topic better than any of the other articles I've read.

posted by Wolfdog at 3:25 AM on February 27 [1 favorite]

posted by Wolfdog at 3:25 AM on February 27 [1 favorite]

And by the way, "accessible" is kind of a codeword. The phrase "at a level accessible to a good undergrad math major" means "even a good undergrad math major will not understand what this is all about after reading this article, but they might be intrigued enough to spend a couple of years figuring out what it's all about."

posted by Wolfdog at 3:40 AM on February 27 [7 favorites]

posted by Wolfdog at 3:40 AM on February 27 [7 favorites]

This is terrific–years of Math Club talks. I'm going to spend my afternoon implementing that sandpile algorithm in Mathematica. Thanks!

posted by Elementary Penguin at 3:44 AM on February 27 [1 favorite]

posted by Elementary Penguin at 3:44 AM on February 27 [1 favorite]

I'm extremely interested in math but did terrible at it in high school. I'd like to retry it sometime in my life. Unfortunately I have no idea what any of these are talking about.

Gucci, take a look at Khan Academy, it's a good starting point for re-learning math.

posted by KaizenSoze at 4:10 AM on February 27 [2 favorites]

Who wouldn't be curious about an infra-nilmanifold endomorphism? And like other math, can you combine the terms, like is there a monster horseshoe amoeba worm? (not linking four pdfs ;-) It does look like the article on data mining will be worth browsing, and the two on comohology will feed my quixotic efforts to grasp that topic. Hmm after looking at these there just must be a sub field in math with a quixotic function.

posted by sammyo at 4:34 AM on February 27 [1 favorite]

posted by sammyo at 4:34 AM on February 27 [1 favorite]

This rocks harder than actual rock music.

posted by Jpfed at 6:12 AM on February 27 [1 favorite]

posted by Jpfed at 6:12 AM on February 27 [1 favorite]

Some of us hate videos. :(

posted by Steely-eyed Missile Man at 6:30 AM on February 27 [1 favorite]

A lot of the jargon has to do with talking about how functions transform one set of mathematical objects to another-- that's what all the stuff about homomorphisms, etc, has to do with.

You can pick a lot of this up surprisingly easily if you look up some group theory and topology lectures on YouTube. You'll need linear algebra, also.

posted by empath at 6:49 AM on February 27

You can pick a lot of this up surprisingly easily if you look up some group theory and topology lectures on YouTube. You'll need linear algebra, also.

posted by empath at 6:49 AM on February 27

The weirdest thing about being a math major was that I did not know what most of my classes were about until about 1/3 of the way through the quarter. I can't think of another subject like that. Like in Spanish, I'd take a class called "The History of the Basque Country" and think, OK, that's like the part of Spain and France by the Pyrenees, and we'll learn about its history. In math, I'd sign up for Real Analysis and just think, whelp, they must have made this a required class for a reason. Then I took Algebra and Geometry again even though I was pretty sure we had covered all of those back in high school. Turned out there's a bit more to them.

In conclusion, math is a land of contrasts.

posted by Aizkolari at 7:14 AM on February 27 [9 favorites]

In conclusion, math is a land of contrasts.

posted by Aizkolari at 7:14 AM on February 27 [9 favorites]

that was always my problem with this column. "Why is..." is maybe more illuminating than "What" and you could probably answer with much less technical language. But, it would be a lot harder to write because you'd have to get some wizard to come down from their tower to explain it. I think you can get through an entire career in some fields of math without really getting why the problems you are having so much fun solving are actually important... (important at least to other mathematicians)

posted by ennui.bz at 7:46 AM on February 27 [2 favorites]

These are written for a particular audience. There is no point that I can conceive of in writing a "what is an operad" or "Why is an 'operad' even a thing?" article for an audience without a certain amount of background. There are lots of great articles that can be written about some of that background. And those articles get written, too, but the *Notices* is not where you find them.

posted by Wolfdog at 7:56 AM on February 27

posted by Wolfdog at 7:56 AM on February 27

Also, even among the intended audience, not every one of them is going to be an equally successful hit with every reader. Some of those articles perk up my curiosity and get me reading, doodling, programming, and so on. Others end with me saying "huh, I still really don't know what it is" or "Oh, so that's what that is. Er. OK, I guess!"

posted by Wolfdog at 7:58 AM on February 27

posted by Wolfdog at 7:58 AM on February 27

Welp, that paper was fun while it lasted...

posted by pwnguin at 8:06 AM on February 27

Before he was a mathematician he was a magician. Here's a profile for general audiences. (That's actual general, not mathematician general.)

posted by madcaptenor at 9:26 AM on February 27

Aww, pwnguin, that makes me sad. Because all they really wanted to say was that "we can now talk about 'adding' two stable sandpiles to make another sandpile", but the precise language that is the stock-in-trade of modern math turned you away. And I can't fault you, because it definitely is a barrier. Let's all take a moment and remember Martin Gardner.

posted by benito.strauss at 9:46 AM on February 27 [3 favorites]

posted by benito.strauss at 9:46 AM on February 27 [3 favorites]

One of my favorite AMS Notices articles of all time is "You Could Have Invented Spectral Sequences". It has the same basic principle as the articles in the links (to introduce a concept) although it's pitched at a higher level--if you don't know any algebraic topology, you are out of your depth immediately. But it takes something that's really quite scary (to me) and boils it down to recognizable ideas and motivations.

It also inspired You Could Have Invented Monads, which is a nice article if you've seen monads before, but the why still eludes you.

posted by TypographicalError at 10:52 AM on February 27 [1 favorite]

It also inspired You Could Have Invented Monads, which is a nice article if you've seen monads before, but the why still eludes you.

posted by TypographicalError at 10:52 AM on February 27 [1 favorite]

It's true, I could have invented spectral sequences. But I just couldn't live with the thought of that many future students cursing my name.

posted by Wolfdog at 11:04 AM on February 27 [2 favorites]

posted by Wolfdog at 11:04 AM on February 27 [2 favorites]

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me... for me, the titles didn't even make sense....

posted by HuronBob at 7:25 PM on February 26