Knowledge is not the same as understanding

From tonight’s episode of On Point with Meghna Chakrabarti, “AI is steamrolling through math. Why does that matter?”:

Francis Su is a math professor at Harvey Mudd College in California and a former president of the Mathematics Association of America. He says math is more than just those numbers, equations, and variables. It is also a set of virtues.

SU: It's a set of character qualities, habits of mind, dispositions that enable you to live in the world with joy and wonder and awe and responsibility. If we lose sight of that, then of course people are going to have this idea that math is just calculation, and I don't want people to think of math that way, right? Math is more than that. Math is understanding. That's the whole reason anybody's ever been involved in the mathematical pursuits, to try to deeply understand things, and we can't cede that to AI.

Steven Strogatz: “What's going to be lost is, yes, human creativity, but what's also going to be lost is something like dignity. And what Francis Su is talking about is that struggle makes us better. We learn how to, we learn how to be better people in our lives.”

Chakrabarti, Su, and Strongatz are discussing the recent Open AI dump of hundreds of solutions to unsolvable mathematics problems, including a millenium question.And, yes, the math world is shook, and yes, it is sparking conversation of the point of problem solving, and what’s lost when we simply are given the answer, much like Icarus being simply given a set of working wings, without any real understanding of what he has. (This is why Daedalus is the example of hubris, not Icarus, but I digress.)

I remember when Big Blue played a chess match against Kasparov and won over 25 years ago. 

Back then, computers and the idea of artificial intelligence was wowing the socks off us, but this match left me sad. I didn’t think that there was a point to having “solved” chess, because the point of chess is to play a problem that is co-constructed by the two players. The solution isn’t the point, which is why it’s preposterous to conceive of a game-as-such between two wildly mismatched opponents. 

Yes, it was neat to watch the first match, and, in many ways, the computer scientists were taking thinking about—and playing—chess into new directions. But there is no mastery per se in a solution. What makes chess fun is the ways in which imagination of strategy plays out on a literal board, not the moment that a king is toppled. 

Chess is, at its heart, imagination at play, and not calculus of memorized moves. This is why, despite an updated Big Blue winning the rematch against Kasparov, people still play chess.