Response to Lockhart's Lament

Mathematics is art. I do a lot of creative writing in my spare time and one of the most paralyzing roadblocks to actually getting writing done is not writing anything. To get to the stage of evaluation and reflection upon your own work, you have to do work to begin with. It's not until you've written a few scenes, developed a few characters, created some conflict, brought about resolution, that you can actually think about whether it works or not. Often times, you need someone else to look over your work as well because it can be difficult to see where I've made a bad decision or not included enough detail. The same is true for mathematics I think. You have to do mathematics to understand mathematics, and often times, you won't get it right the first time. You need to think, devise, strategize, implement, try again. The problem won't be solved by staring at the paper in the same way that a piece of music can't be composed by looking at an instrument. 

One thing that I disagree with is Lockhart's judgement of all mathematics classrooms as being these places where dreams go to die. It's very true that much of the joy is sucked out of mathematics by teachers overemphasizing procedure and not truly challenging students, however, I don't think what happens in math classrooms is actually that far off from what Lockhart wants. All that's really required is for teachers to say "now look what you can do with this" and "here's a problem, just try to come up with a solution". Of course, students need to be climatized to actually thinking mathematically, but with a bit of practice and time, I don't think Lockhart's vision for the mathematics classroom is that far off.