[sorry for the total lack of editing on this one – had an hard time stop today for work]
Last night I attended a talk about Gender Inclusivity in Mathematics at Harvard. This talk was the first of several talks planned for this year – more information on the series is here:
The speakers from last night were Cathy O’Neil and Moon Duchin. I’ve followed O’Neil for a long time online through her blog posts at mathbabe.org and her participation on the Slate Money podcast. Actually, I found out about the event last night through one of her posts:
I’d not come across Duchin, who is a math professor at Tufts, previously, but **holy crap** is that my loss. She had a fascinating perspective on how to approach your own math education as an undergraduate student and as a graduate student, too. It made me wish her talk had somehow been teleported back to the fall of 1989 when I started college.
As a funny (to me at least!) aside, Duchin mentioned that she has a book on the history of mathematics coming out soon. I forgot to ask for more info about that book at the end of the talk last night, but looking later for more information online I found out that she grew up on Stamford, CT. So, after completing our move from Stamford to Lexington just last week, my first bit of fun cultural activity in the Boston area was attending a talk given by folks who grew up in Lexington and Stamford. Some sort of weird birthday paradox happening there 🙂
Three things from the talk last night that are resonating with me today:
(1) The ideas from O’Neil and Duchin on advice they’d give to undergraduates.
Duchin started off by describing how she approached her undergraduate education. She said that she took many graduate level classes in various different departments, but that what really stuck with her 15 or so years later were the ideas that she came across in the more general undergraduate classes. One bit of advice from her was to resist the urge to accelerate as fast as possible in college. She mentioned that even today she’s taking an undergraduate class (in philosophy, I think) to continue to broaden her education.
O’Neil offered the idea that if you were planning on going to graduate school, taking some graduate courses in that field was probably a good idea. Duchin agreed and also mentioned that some research work she did in math as an undergrad helped her prepare for graduate school.
(2) O’Neil’s idea that math training helps you be better at admitting when you are wrong
This is a powerful idea that I’ve actually only heard from her. She’s also written about that idea here:
The passage that struck me reading this piece back in 2012 was:
Not every person gets trained in being wrong and admitting it. I’d wager that most people in the world, for most of their professional lives, are trained to do the opposite in the face of being wrong: namely, to wriggle out of it or deflect criticism. Most disciplines spend more time arguing they’re right, or at least not as wrong, or at least they have different mistakes, than other related fields. In math, you can at the most argue that what you’re doing is more interesting or somehow more important than some other field.
The idea of not bothered by being wrong has helped me tremendously in my job. It is funny how often in business people try to get a leg up – or just outright try to bully you – by telling anyone who will listen that you are wrong. But training in math teaches you to think about ideas from many, many different angles, and search and search for ways that ideas can be wrong. I think that O’Neil is right that this sort of training is unusual. But the more comfortable you are in searching for ways that you might be wrong, the more likely you’ll be to find the right (or at least a pretty goo) answer, I think.
The idea is pretty similar to the philosophy from this old article “Winning thee Loser’s Game” that success comes from avoiding mistakes rather than from successfully swinging for the fences:
I know that “growth mindset” probably long since crossed over into being a cliche, but that doesn’t mean it is a bad idea.
There was a fairly long discussion about the idea of what happens when you encounter a difficult problem. Two possible choices are:
(A) Hey, I can’t figure this out right now, but if I work hard I’ll be able to, and
(B) I can’t figure this out right now, so I must not be very smart.
The discussion last night, obviously, was that (A) is a better way to approach math (and the world of learning in general) than (B).
My first encounter with this idea was on Josh Waitzkin’s book The Art of Learning, though there’s plenty of other places to read about the idea. A suggestion from the audience was that girls are often taught that (B) and that boys are often taught (A). All I can say is that I certainly do try to teach my own kids (who are boys) that (A) is is a good way to approach learning.
Sort of on the same topic, O’Neil has written a lot about how math contests can lead to ideas about not being good in math, or about ranking. For example:
Jordan Ellenberg, who (among other things) was one of the top US math contest kids my year in high school, also writes about how he used to think that the top math contest kids would become the top mathematicians in his book How not to be Wrong and how he’s moved way past that idea now.
Some concern was expressed last night that Harvard’s undergrad math program can seem like a program where only the stars get attention. Having not been in Harvard’s math program, I don’t know, but I hope the ideas that O’Neil and Duchin talked about in relation to mindset help students a little with the ideas about approaching their own math education and also with the ideas that success in math is just for super stars. Hopefully Harvard’s math department is aware that people feel this way about their program and can take steps to change the source of those feelings.
Finally, one other thing that’s been on my mind that O’Neil and Duchin talked about is what they called the paradox of prizes for women. They gave a a pretty compelling argument that special prizes only for women can be damaging because when there is an open prize and a prize for women, men win the open prize and women win the other prize. Their argument extended beyond prizes, too, and applied to areas like hiring when special money in universities is set aside for hiring female faculty members.
It made me wonder if the two awards I’m sponsoring for ultimate could have unintended negative consequences:
I going to have to seek some more advice about this issue before the end of the year.
So, definitely a fun night last night. It was nice to see 100-ish people there for the talk. Hopefully this new series of talks will generate some good ideas both for the students in Harvard’s math department and hopefully some meaningful changes, too. Maybe some of those ideas and changes will extend beyond Harvard yard!