"Is Math Hard?" The answer - from Aquinas!

While I was working on my Ph.D., students and faculty at many schools were debating via electronic bulletin boards on the statement that "math is hard." (I think it was something said by some talking doll - and it started up a lot of chatter about math, women, education, and all kinds of things. But no one ever seemed to get to a definitive answer.)

Some time afterwards, I found the answer in a book called The Division and Methods of the Sciences which is a commentary by St. Thomas Aquinas on another book called De Trinitate by Boethius (the same guy who wrote The Consolation of Philosophy).

Aquinas answered that mathematics (considered as a subject) is easy: it is a simpler subject than "natural philosophy" (which includes physics), which in turn is simpler than "divine science" (or theology).

In fact, the subject is called "mathematics" which is Greek for "the learning" because it is learned - someone can teach it to you, and then you know it! And, though any given individual may find any given aspect of mathematics to be "easier" or "harder", it is still possible for a good teacher and a diligent student to work together - and for the student to acquire a COMPLETE understanding of that topic or principle.

However!

One must go to nature to learn something about it, and even then one might only know very little - or even be fully misled. For many many solid things, it is true that when they are warmed, they become liquid. Like ice, or lead, or glass - or even rocks. But when an egg is warmed, it becomes solid. And for iodine and "dry ice", there is NO liquid - these two materials "skip" the liquid and go right to gaseous form - which is called "sublimation"!

And that is just some simple physical materials. When one looks at living things, or when one gets very precise about measuring, one finds some very difficult questions. And one can sit and think for a very long time before proposing a solution, which may STILL not be correct.

And the matters of the supernatural - I mean in the sense of human beings, and angels, and God - these are even more difficult, for these do not admit of direct observation. One does not experiment on an angel. But this, perhaps, is where I will do best to direct you to Aquinas for more details.

(I would do a SWQR of the book, but do not have the time to do a good condensation. Maybe next week. Anyway, Nancy over at Flying Stars had been asking some interesting questions about math, so I found this above comments from a larger essay. Maybe I will post the whole thing later.)

One more note I must append, as I re-read this before posting. I used the word "diligent" to describe a student. This word (as a Latin verb) is used by Aquinas in his song Adoro Te devote, and it means "love". In order to succeed at aquiring knowledge, the student must LOVE that subject. And that means it would be best for the teacher to also love it, and communicate that love.

(You may laugh at my crazy uniting of topics, but this is why Chesterton says there is no such thing as a different subject!)