A Mathematician's Lament

Lockhart's critique of modern mathematics education deeply resonates with me. He exposes how the subject has been reduced to rote memorization and mechanical procedures, stripping it of its creativity and beauty. I fully agree with his approach of allowing students to derive their own solutions and discover mathematical rules and laws based on the problems they are solving. This method would be excellent for introductory courses or non-math majors, fostering deeper engagement and appreciation.

However, for mathematics majors, such a system would only work if introduced rigorously and at an early age. That said, I believe everyone's introduction to mathematics should mirror Lockhart's vision. Structured discovery through carefully chosen problems, paired with a Socratic method of questioning, can make learning mathematics both intuitive and amusing.

This book is epic. It fully represents what I wanted math to be, and has made me quite excited.

If the author didn't use so much darn vulgar terminology sporadically, this would be in my top 20 books. As it stands, still a “banger” as the kids say.

Very very very enjoyable. A passionate rant, written with enormous verve, about how everything we know about math is incorrect - and the way we teach it is just tortured. I loved it. I was already in the “maybe we should teach math different?” camp anyway. But this book took that little thread of thought I had, fed some pure electricity into it, and then shook it around like crazy. I was like WHOA.

Some notes:

I love, LOVE, how he not only compared math to a fine art, but SLAMMED THIS POINT INTO OUR HEAD OVER AND OVER AGAIN. It jibed with my recent feelings about teaching a kid to love math. Like, literacy is treated as a sacred part of our culture: we read books to our children at night. For many reasons: to build literacy skills, but also to cultivate just a pure love of story, to share culture, to give them a glimpse into this big wide world of ideas and books. We're not, like, drilling them on their letters. At least, not first thing.

Similarly, art class is about expressing ourselves - here are some tools, a general direction or prompt, and then students are set loose. We might share other artists' “solutions” or answers to that prompt, but we're not, like, trying to tell the students they are wrong and Jackson Pollock is right. We're just offering inspiration, and - again - welcoming them to the great human activity that is, in general, making art. Lockhart sees math in the same way. Like, the EXACT same way. He thinks it's just as absurd to memorize rules or get fussy over naming (rhombus, indeed!!!) as it would be to have art students memorize brush stroke patterns or get fussy over paintbrush types.

When I have had peak math moments - I remember a Calc I take-home final in college? - it feels like a game and, indeed, an act of creativity. A puzzle, but more open-ended. Of course, that was a blip in my life. The rest of the time, I just felt bad that I couldn't understand how to do a proof.

Anyway. I really loved this. Because it's like shockingly, clarifyingly TRUE. Like, he notes how most school math is almost COMPLETELY, ENTIRELY lost in adult minds - thus showing how both completely and utterly pointless a lot of it is, and how it ALSO misses the whole point. Two kinda distinct, related things. Like, not every adult is a great artist. But probably every adult understands what art IS (we can leave the caveat here about modern art and the whole “I could do that” bullshit critique - but that is for another review). But, Lockhart argues, we have many many many adults out there who have e.g. not only forgotten the quadratic formula (I know I have) but also entirely missed the point of WHY we were studying the quadratic formula in the first place (I definitely don't know why we learned it).

Going back to getting kids excited about math, I was reading through various cri de ceours by math teacher dads/moms with blogs talking about “math games” and “math books”. And these games and books were all about, basically: patterns. Symmetry. Bigness and smallness. Measurement. Like... THAT is the point of math. It's a creative, open-ended endeavor, like painting! There are many ways to paint the same tree. There are many ways to write the same Python program. There are many ways to math!! I remember when I told my co-parent this - “let's teach our kids to love math” - they were like, well, first we gotta them get to learn numbers. As Lockhart would say, AAAAAH. No!! Math is not about some Hindu-Arabic symbols!!!!

Anyway, v v v good. I loved it so much. It kinda reminded me of Rabbi Abraham Heschel's The Sabbath. Like, mind-expanding AND heart-expanding.

"If you want to build a boat, don't order people to gather wood and assign tasks and work, but instead teach people to long for the boundless immensity of the sea."

A Mathematician's Lament is more of an extended essay than a book - one man's problems with mathematics education without a viable solution. While I agree with him that the current state of mathematic in schools and unis is a travesty, the kind of “solution” he's recommending is not the real solution. We all know what most of us thought about the math (and many other fields) in ES and HS, and leaving it all to the student is not an excellent solution.

“Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity - to pose their own problems, to make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs - you deny them mathematics itself.”

This is a great essay/book. Says everything I've ever felt about mathematics in schools.
Every parent, teacher, student should read this one.

There are points where I have some disagreements but nevertheless those are with the processes not the concepts.