Assignment 22: Theodore

Scene: Dinner at my house, Friday night

My mother: “What do you think about this problem involving 

q-analogues?”

My father: “Isn’t that solvable using sign-reversing involutions?”

“Sure, but it can also be addressed directly.”

“Isn’t there an extra factor of 1+q?”

“Let me work it out. [She traces a diagram in the air.] No — it divides 

out.”

Obviously, I live with two mathematicians. As a result, not only am I 

interested in math, but my personality is affected as well.

Above all, mathematicians are playful. Despite the fact that math is closely

associated with numbers, mathematics is one of the least data-driven sciences.

Physicists know that the Higgs boson exists because of thousands of 

high-velocity experiments, but mathematicians don’t accept the Pythagorean 

Theorem based on examples of right triangles. Only a proof convinces us.

Therefore, mathematicians don’t carefully design experiments but rather

search for patterns and connections. The best way for us to stay open to new

ideas is to view math as fun. I use this philosophy for other subjects as well. 

It’s enjoyable to examine centuries-old politics, to learn another language, 

and to put my ideas on paper. Here, my perspective aligns with MIT’s:

learning should not be a chore.

If you’re not a scientist, you don’t care as much that mathematics relies 

less on data. But math is also distinctive for its age. Modern (read: correct)

physics did not exist before the Renaissance, and the first novel is only about

500 years old. By contrast, math, political science, and rhetoric date back to 

the Ancient Greeks. However, the latter two disciplines shift over time: Who

believes today that large-scale direct democracy is preferable to a republic? 

But mathematics is stability. Rumor has it that math began when Euclid 

noticed that the Egyptians were using incorrect formulas to calculate area.

To remedy this problem, he established the system that remains in place 

today: axioms support theorems through proof. To be clear, this system 

doesn’t hold imagination back, but rather frees it from the specter of faulty 

results built on shoddy reasoning.

But why does this matter? Does studying the inherent stability of math induce

a sense of emotional stability in me? No — that’s ridiculous. Do English 

teachers become murderous after reading Macbeth? Still, knowing that the 

theorems of the past will endure into the future encourages me to strive for the 

same permanence. If I blindly accept ideas, I am vulnerable to ephemeral 

falsehoods; if I reject all new ideas, I will lose the chance to learn. This mix of a

willingness to guess and a duty to check suits me for the academic environment 

of MIT. 

Note: If you want to see a real proof, look at this proof of the Pythagorean Theorem.

Strangely enough, President Garfield discovered this particular proof: 

www.maa.org/press/periodicals/convergence/mathematical-treasure-james-a-

garfields-proof-of-the-pythagorean-theorem