There are a lot of online learning sites these days, including MIT/Harvard's EdX, Coursera, Codecademy, and Udacity, but Open CourseWare started it all. MIT decided to make all of its course materials, including syllabi, homework assignments, and lecture videos, available online, to the public, for free.

The Khan academy teaches a huge range of topics, from statistics to art history, from kindergarten level math to immunology. Recently, they even started offering test prep for standardized tests like the SAT, to level the playing field with students whose parents can afford private tutoring, and they have a college admissions section for some guidance.

I get periodic emails from them, and I recently received a link to this video, entitled, You Can Learn Anything:

For those who didn't bother to watch it, the video claims that no one is born smart, that learning requires struggle for everyone, and that this is a good thing. And ultimately, with enough effort, anyone can learn anything.

I applaud the notion that learning requires struggle. It casts frustration in a new light, and reminds people to persevere. But I don't believe that anyone can learn anything.

I studied math as an undergraduate, and for a miserable year in graduate school. And one of the few bits I've retained from all the math I learned and subsequently forgot is that math is HARD. Medical school was a lot of work, and what I do now requires intense effort and a certain kind of smarts. But nothing I've encountered comes close to the shear reasoning ability required for math.

Math beats everyone. Mathematicians, people who have chosen math for their professional lives, rarely produce new research past age 30.

One notable exception was the Hungarian mathematician, Paul Erdos (pronounced AIR DISH).

Paul Erdos |

He produced new material pretty much until his death in 1996 at age 83. Erdos never married or had any romantic relationship that anyone was aware of, gave away all his money in contests he devised for young mathematicians, lived with his mother until her death, and subsequently by hopping from the home of one mathematician to the next ("Another roof, another proof"), and used amphetamines most of his life so he could spend 19 hour days working on math ("Plenty of time for rest in the grave").

To give you a little more flavor, he once wrote a letter to a fellow mathematician that went something like this:

*Dear So and So,*

*Today I am in Australia. Tomorrow I leave for Hungary.*

*Let k be the smallest integer such that...*

Sure, Erdos never stopped learning. Math. But at what price? It's not clear that he was able to learn much of anything else. Certainly normal social interactions eluded him.

It's great that the Khan Academy has taken it upon itself to encourage people to learn. Learning is awesome! But I think there's a danger in encouraging the idea that anyone can learn anything, that the most difficult concepts are accessible to anyone with determination, regardless of innate talent or intellect. Because that isn't true. I will never be a Hall of Fame quarterback, or an Olympic sprinter, or even a mathematician like Erdos. And that's okay.

It all reminds me of a short story by Vonnegut, Harrison Bergeron (it was copyrighted in 1961, so I feel okay linking to it because it's been more than 50 years). The story takes place in 2081, when everyone is completely equal. Anyone who is exceptional in any way, be it dance, intellect, music, whatever, is subject to the Handicapper General, who plants noisemaking devices in people's heads to distract them from original thoughts, and attaches weights to anyone of physical prowess. All so no one will feel "less" then anyone else.

I presented a journal club on Erdos about 15 years ago based on the book "My Brain is Open" and the documentary "N is a Number." I have had a longstanding interest in the eccentricities of mathematicians and the idea that they only have a finite window to do their most creative work. When I was in the Peace Corps a good friend of mine and I taught on the same compound and he would tell me stories about Galois and Cantor. I studied the biographies of several others and was thinking of writing a paper on it - but you know how that goes.

ReplyDeleteI pulled my copy off the shelf and looked at some of the passages I had marked. One had to do with his amphetamine use. A friend bet him $500 he could not go a month without using amphetamines. He won the bet and resumed the pills stating (p 196):

"You showed me I'm not an addict, but I didn't get any work done. I'd get up in the morning and stare at a blank piece of paper all day. I have no ideas, just like an ordinary person. You set mathematics back a month!"

Wasn't he a character? I totally forgot about that anecdote. I read it in an Atlantic Monthly article years ago, when he was still alive. He used to call children, "Epsilons", too.

DeleteHe was unusual, even for a mathematician, because he wrote on multiple topics-math is usually very specialized. I read a couple of his papers, as an undergraduate. They were on a topic I was researching (Carmichael numbers), so I could follow his thinking, but man, he made leaps. I think it took me half an hour to figure out how to get from one line to the next. I'm sure it was instant, for him.

Fun fact: I don't know the exact figures, but a disproportionate number of mathematicians are left-handed.

I always feel sad thinking about Galois. He was only 19 when he died, in a duel, no less.

The point of my seminar was how eccentric you can be and yet be highly accomplished. Once you know the details of his life, it is hard to imagine that anyone else could live the way he did. Total disregard for material things. Borrowing money from his colleagues and always paying them back but no rational management of his finances. Giving money away to people who could solve problems. Incredibly intrusive and yet as far as I know - nobody ever turned him down. His elderly mother shipping out reprints of his papers all over the world from their apartment in Budapest to anyone who requested them. A fairly good table tennis player even as an old man. The list goes on......

ReplyDeleteAnd yet to his friends and collaborators he was a saint who according to his biographer was devoted to "the mathematical pursuit of pure beauty."

All of his relationships seem to be sustained by the discussion of abstract mathematical concepts and the recognition of his laudable personality characteristics. It is an incredible story.

It's certainly not true that anyone can learn anything, but it is true that measured IQ is not purely genetic and dependent on environmental factors.

ReplyDeleteThere is also a phenomenon of bright young things to whom intellectual endeavors come easily, and then, at some point, they don't. If they haven't had to struggle many of those I know just give up, because they assume that they're not meant for the particular field when it doesn't come easily. Many of them accomplish much less than people assumed they would based on their talent.