Last week we heard about Alcuin of York (also called Albinus, c. 735-804 AD), who came to the Emperor Charlemagne and promoted classical studies during his reign. Among the many other things that Alcuin did for the advancement of learning, he compiled a little book called Propositions for Sharpening the Youth. Alcuin’s Propositions are a series of math story problems. While today we could solve many of them rather quickly by using the right algebraic formula and a calculator, there’s something to be said for working through them unaided. If we’re simply looking to arrive quickly at an answer (say in an engineering job), then formulas and calculators are very useful. But what if there’s more to math than arriving at the answer as quickly as possible?
This line of inquiry leads us to ask even more fundamentally: what is the purpose of studying math? What is the fruit of it? I remember asking a math teacher from a classical school once, “What level of math is it necessary to attain?” and she answered, “How strong do you want your mind to be?” That answer has stuck with me, and it’s very telling. Math isn’t ultimately about being able to do a certain sort of problem (algebra, geometry, trigonometry, calculus, etc.), or even being able to do a problem quickly. Many students wonder, “When am I going to use this in the real world?” The answer (in many cases) is: they’re not. The study of math isn’t about acquiring the skill of solving certain problems, as if students were going to graph parabolas for a living. The study of math is about strengthening the mind. Certainly students will advance through various types of math problems and will learn to do them more quickly with practice. But the purpose of this is to exercise the mind and make it strong.
Formulas can be useful for shaping the way we think (e.g. solving for x). But they can also be harmful if we stop thinking about the numbers and simply follow a series of prescribed steps to arrive at an answer. As for calculators, their main use is for doing math that the mind can’t complete in any sort of timely fashion by itself. But then as soon as calculators become involved, the mind gets to rest, so students must use calculators with great care. A heavy reliance on a calculator may lead to finding an answer quickly, but it will not lead to the mind becoming strong. In order to enjoy the full benefits of math study, the student’s mind must be the primary calculator.
This understanding of math is in line with the purpose of Alcuin’s Propositions. He said his Propositions were ad acuendos, “for sharpening” (from that Latin verb acuo we get the English words “acuity” and “acumen,” both of which refer to “sharpness”). In order to understand how math sharpens the mind and gives us acumen, try one of Alcuin’s Propositions. Do not use a calculator or any formulas, but simply pencil and paper (or, for the really daring, do it all in your head). After you find the answer, notice that your mind feels the way your body would after a good workout. Here is Proposition 5:
“A certain buyer said: ‘I want to buy 100 pigs with 100 denarii in such a way that a mature boar is bought for 10 denarii; a sow for five denarii; and two small female pigs for one denarius.’ How many boars, sows, and small female pigs should there be so that there are neither too many nor too few of either [pigs or denarii]?”
In Christ,
Pastor Richard
