A Mathematician's Lament

http://www.maa.org/devlin/LockhartsLament.pdf

This is a great article on the failures of K-12 mathematics education. Descartes would be ashamed.

The thought process so essential to math has been all but eradicated in school. We are taught not to think philosophically (math is philosophical!); but to take in formula after formula, and find new way to spit them out through exercises and word problems. I especially enjoyed the section on proofs- the bane of all geometry students' existence! They create an illusion of the process that goes into thinking mathematically, but are really something else entirely. Geometry proofs once again involve the memorization of removed postulates, and finding inaccessible and uninteresting ways to "solve a problem".

What is sad is that we are all asked to wait eleven or twelve years to find out if we are ready to think mathematically. We can not be trusted with our innate ability to reason until we have taken in numerous rules and formulas that we have no understanding of.

Hume

Hume would find Descartes attempts to rationalize the world futile and pretentious. How can a person attempt to know more than what they themselves have experienced? Socrates himself said: "All I know is that I know nothing." Although Descartes claims that he can use his reason to realize that a puddle of wax is still wax, or that a mirage in the distance is just sensory deception, Hume does not think that is enough. Why is it wax in the first place? Can you ever really be certain that it is not something else?

This is why Hume champions empiricism. We interpret the world through our experiences and our reactions, not through the "facts" that scientists and mathematicians simply assume to be true.

Fear

On Thursday, we were asked to think of a time we experienced extreme paranoia. I couldn't come up with anything at first. When I was little, I was never scared of closets, white vans, or dark alleyways. They just never registered as something I should worry about.

But I did get scared a lot. Of absolutely nothing. When we were getting into line for recess, my heart would start pounding and I'd feel a hollowness in my stomach. I would be afraid to move, sure that something was about to go terribly wrong. And I got this random fear multiple times a week, so I knew that nothing was going to happen. No matter how many times I assured myself that everything was fine, I couldn't overcome the physical feeling of fear. For me, it was too strong a feeling for rationalization.

Descartes championed rationalism, while Hume believed in sensory experience. Neither philosophy seems perfectly accurate for me. All the rationalization couldn't make my emotions any less affecting, while accepting my fear never made it seem more real. All I could ever think was: This doesn't make any sense!