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Lockhart’s Lament

June 25th, 2009 (Visited 1739 times) Tags:

Mathematics is the music of reason. To do mathematics is to engage in an act of disvovery and conjecture, intuition and inspiration; to be in a state of confusion — not because it makes no sense to you, but because you gave it sense and you still don’t understand what your creation is up to; to have a breakthrough idea; to be frustrated as an artist; to be awed and overwhelmed by an almost painful beauty; to be alive, damn it. Remove this from mathematics and you can have all the conferences you like; it won’t matter. Operate all you want, doctors; your patient is already dead.

– A Mathematician’s Lament, by Paul Lockhart (PDF).

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18 Responses to “Lockhart’s Lament”

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Twitted by JesperBylund wrote on June 26th, 2009 at 7:23 am:

[...] This post was Twitted by JesperBylund [...]

Math and Art « Tish Tosh Tesh wrote on June 27th, 2009 at 9:38 am:

[...] Koster brought “Lockhart’s Lament” to my attention, and it resonates with my experience. I managed to find a deep fascination [...]

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Morgan Ramsay said on June 25th, 2009 at 6:40 pm:
I’ve never met a mathematician in touch with reality. I guess you have to be crazy to be that obsessed, er, “passionate” about counting. But I suppose my attitude is a consequence of the way mathematics is taught, which Lockhart laments.

I skipped to the ending section “The Standard School Mathematics Curriculum.” Sounds right. I actually skipped Algebra II through Calculus in high school though. But I, too, wondered why Geometry was inserted between Algebra I and II. ;p
Raph said on June 25th, 2009 at 6:44 pm:

From the same essay:

Then what should we do with young children in math class?

Play games! Teach them Chess and Go, Hex and Backgammon, Sprouts and Nim, whatever. Make up a game. Do puzzles. Expose them to situations where deductive reasoning is necessary…
Amaranthar said on June 25th, 2009 at 6:52 pm:
He was dead on with the “no duh” means of breaking a students curiosity towards math.

Puzzles would have gotten me a lot more interested back in my school days. I have to say, in all the aptitude tests I’ve taken, it was the math questions that I handled like puzzles of reasoning. I actually enjoyed those questions and had a feeling of real satisfaction when I took a known and reasoned out what had to be the right answer.

I think it’s fascinating how physicists use math to prove out theories, and how it’s led them to things like the Big Bang and the Atomic Nucleus. I wish I could do that, and be a part of it.
Eolirin said on June 25th, 2009 at 10:44 pm:
I dunno Morgan, I think if you’re going to be obsessed with something, the functional underpinning of the entire universe isn’t a bad choice.
Miraj said on June 25th, 2009 at 10:53 pm:
Thank you, Raph. This is the best thing I’ve read in months. It brilliantly articulates the frustrations I’ve felt about my formal education.
Peter S. said on June 25th, 2009 at 11:40 pm:
I loved learning math, and can certainly agree to the frustrations he has… and yet everything else in the article grates fiercely on my nerves. As though only math is so poorly treated! Surely, the subject of, oh, History was never drained of its color and reduced to pointless memorization.

Grr, and that’s but the least of my complaints. Math is not always interesting! Beauty is subective! It can be humiliating to discover the problem that took you all weekend to solve was figured out several centuries ago, as though the giving of it to you was a practical joke! Math is nothing BUT rules; discussing the creative aspect of it is like saying students have penultimate freedom with their coloring books provided it’s all kept inside the lines! (It IS creative, don’t get me wrong, but it’s not without qualifications.)

The whole “my [college] is the best of all of them” has gotten under my skin like crazy since before, well, college, regardless of which department it was coming from. That’s my bias, as I’m nearly irrational in how much it ticks me off. And sadly, I’m up too late as it is… no flamewar-esque ranting for me tonight. Grr.
Amaranthar said on June 26th, 2009 at 11:00 am:
Peter, I had a history teacher in High School (who was also my football coach) who would jump up on a desk top and act out images of what happened. Especially revolutionary folks rousing the rabble and other leaders giving speeches. It was quite entertaining and award winning, as he won national recognition for his history class and results.

He also happened to be a damn good coach, leading our small school to numerous victories over much larger schools. We even played in a “Game of the week” in a large city. But then they came out with computer rankings, and beating a small school like ours didn’t offer too many points, so we couldn’t get the big guys on our schedule anymore. It was our loss, the challenge was important to us.

But the point seems to be that a winner is a winner, no matter the field.
There’s too many “also-rans”.
Brad Vender said on June 26th, 2009 at 12:23 pm:
In defense of high school geometry, I thought that the application of arbitrary rules and structures in order to solve a problem was a wonderful introduction to computer programming.

As an argument that applied mathematics is more than just application of wrote rules, this Lament is quite interesting. From a practical standpoint, the basic wrote activities in math are still important to learn despite the calculator, just like spelling is still important to learn despite the spell checker. (And, gosh, I’m suddenly insecure about my spelling and grammar. (;_;) )
Yukon Sam said on June 26th, 2009 at 12:29 pm:
Math is the chalk marks we make on infinity.
Eolirin said on June 26th, 2009 at 2:49 pm:
Peter, Language is all about rules too, and any work of writing needs to follow them to be understandable, do we condemn writers as being “creative but with qualifications”? Hell, the writers we most praise are the ones that most closely follow the rules of the world they create as well, and we roughly condemn those that ignore internal consistency. I mean, what is a plot hole or an unbelievable event or character action that breaks suspension of disbelief except a violation of an unspoken rule? The only real difference is that in the authors case we recognize it merely as bad writing, and call it bad art. In the mathematician’s case it’s less ambiguously wrong. But the difference is only in the degree of play between correct and incorrect, not in the core principle. Both are modes of expression.

(As an aside, I find the process of figuring out the problem to be the point in and of itself, so the fact that it’s been solved already wouldn’t bother me in the slightest. The fact that it was hard would make it worth it. I can understand that lots of people don’t feel that way, but I doubt many of them become mathematicians either.)
Tesh said on June 27th, 2009 at 8:59 am:
Perhaps ironically, the best math class I have ever had was my Geometry class in 8th grade. The teacher let us take pretests on the chapters, and if we scored 90% or better, we could skip all of the homework for that chapter. We had to attend class, but we could play chess, read his puzzle books or tinker with origami.

I skipped probably 40% of the homework for that class, played a lot of chess, and fostered a lifelong obsession with origami. I spent a lot of time with puzzles. I even derived a way to trisect an angle, which was thought to be impossible. Of course, my method only worked on 90% angles, but still, it was a nice exercise in experimental thinking and challenging assumptions. (And I proved to myself why my method wouldn’t work on other angles, answering the questions that I put to myself.)

I got more out of that class than any other math class, college calculus included. I still love math.
Michael Chui said on June 27th, 2009 at 11:38 pm:
Hrm. In high school, I didn’t pass trigonometry, but my teacher let me go on to the next level anyways. I always figured it was because he had a soft spot for me.

But if it was just freaking two weeks’ worth of material, what the hell did I miss? Also, the whole thing was kinda awesome.

“Children are expected to master a complex set of algorithms for manipulating Hindi symbols, unrelated to any real desire or curiosity on their part, and regarded only a few centuries ago as too difficult for the average adult.” <3
Morgan Ramsay said on June 28th, 2009 at 6:15 pm:
the best math class I have ever had was my Geometry class

In my high school geometry course, all I had to do was tell the teacher’s assistant what grade I wanted. The instructor was too busy zoning out or sleeping off his hangover. He made all of his money from selling real estate anyway. That was definitely one of my favorite courses. Cautious me, I passed with a B+.
Peter S. said on June 29th, 2009 at 1:24 pm:
@Eolirin,

I’ve calmed down since last week, so I’m not going to be ranting like I initially wanted to. I did want to say, though, that I do feel that contrary to the author’s opinion, mathematics is much much MUCH more heavily qualified than other artistic media. Language has (post)modern freeform poetry, and other contexts where the rules have less application and going outside them isn’t wrong. Math, inasmuch as is learned by the end of high school, still has wrong answers. The student is still constricted, though I will note that (less than) a hundred years ago English as a subject was every bit as restrictive.

You do have to learn the rules to know the best ways to break them, that’s true for both as well. And now I’m thinkning of how one would compute an Anarchy Quotient for different modes of expression.
Sören said on June 30th, 2009 at 6:26 am:
@Eorilin: “Language is all about rules too” Right, logic derives from greek “logos” = word.

@Ralph: great article. As I’ve studied mathematics, I continue to tell people that it is not about numbers and formulas but about pattern finding. Numbers and formulas only are one single expression of some of those patterns. Other expressions are: paintings, music, poetry. I remember a recent discovery, that patterns in arabic architectural decorations match the penrose tilings.
Yukon Sam said on June 30th, 2009 at 8:58 am:
Math, inasmuch as is learned by the end of high school, still has wrong answers.

At the high school level, the art lies in convincing your teacher that your answer is right, but the assumptions of the question are wrong.

If you can pull it off, you’ve got a bright future in number theory.

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