Mathematician's Lament by Paul Lockhart

#math #art

Lamentation

Lockhart set ups the problem of math education and how it is drawing comparisons to music and painting and how they would be taught if those subjects were treated how mathematics is. The highlighting idea of splitting students (or the population in general) into music people and non-music people is disturbing; students at that age are highly susceptible to ideas that form their identity and some carry it throughout their whole adult life. Its often meme'd in a self-degrading way that they don't gel well with mathematics and whether knowingly or unknowingly avoid anything that approaches any semblance of 'difficult' mathematics. The rough part highlighted at the end is that we all do know there is something deeply wrong about how we teach mathematics in schools and yet we infantilize the children who are affected the most about it and who voice their opinions out loud; when the same children avoid/fail/lose interest we act surprised and simply label them as not being 'smart' enough only causing a negative feedback loop.

Mathematics and Culture

When the artist is alive in any person, whatever his kind of work may be, he becomes inventive, searching, daring, self expressing creature. He becomes interesting to other people. He disturbs, enlightens, and he opens ways for a better understanding. Where those who are not artists are trying to close the book, he opens it, shows there are still more pages possible. -Robert Henri

Robert Henri's description above more effectively draws parallels between a mathematician and an artist compared to Lockhart's attempt. Its hard to argue against the cultural impact a great artist can have is no different to what a great mathematician can do. Its difficult and futile to try to describe what is and is not art, but its much more important to realize how mathematics can be and should be taught as an artform to allow more creative and flexible thinking, the myth of the 'objectivity' of math lends people to think that math is simply about following instructions and that things simply are due to some divine ruling rather than the more subjective nature of mathematics; we as humans get to decide which axioms are important, which fields to pursue and deem 'important' and what mathematical objects to define and study.

Lockhart argues that schools only care to teach 'what' is true and leaving out the 'why' when the 'why' is the core of what mathematics is. I would argue further that even if we teach the 'why' it would not be sufficient. An artist can learn the ins and outs of color theory and still find themselves struggling, its much more important to foster the mentality and curiosity to experiment and be bold; to not only know the why but to foster a love and fearlessness to dig deeper. To do math is not to simply sit down and study but to actually do mathematics;

The work of the art student is no light matter. Few have the courage and stamina to see it through. You have to make up your mind to be alone in many ways... alone one gets acquainted with himself, grows up and on, not stopping with the crowd. It costs to do this. If you succeed somewhat you may have to pay for it as well as enjoy it all your life -Robert Henri

To do math is a personal struggle, only you can figure out how these concepts fit together in your head; how they satisfyingly connect together and how you interpret them. The world can only bring us closer to this abstract 'truth' by our interactions with it but its our role as the mathematician to grasp the ideas from the aether and pull them into reality, no different to how an artist grasps and fights for their ideas to be embodied in some physical form. That is why mathematics is an art. The beauty in mathematics is not simply just the the whys and whats but the how and personal struggle behind it all, the human communicating and sharing their inner thoughts to the world.

To become a mathematician is like to become an artist; its performative, a struggle and to be human.