alice at the easel

My kid had math homework this weekend that she didn’t know how to do, and since she hadn’t brought her textbook home, she lacked instructions and definitions to help guide her back toward the path.  Unfortunately, while being a rational enough gal, I have no talent for numbers or numerical relationships.  Dad is good at math, but he happened not to be available at the height of the crisis.  The homework consisted of adding, subtracting, multiplying and dividing positive and negative numbers.  I vaguely recalled that rules exist, but couldn’t remember what they are.  So I suggested to my daughter that she experiment — perform some different approaches and see what results she got, and from those results have a guess at which rule is “it.”

She wouldn’t.  And so I pulled Music of the Primes off the shelf and started reading.  Music of the Primes is Math, the Movie — or an elegant, suspense-filled heart-tugging page turner of a math adventure book.  Yes, I know that’s hard to believe but tis true.  Math made thrilling for folks like me and thee.  Math the dream.  Math the you-should-have-been-there experience.

Unfortunately, Music of the Primes wasn’t working for her.  Too grown-uppy.  And by sixth grade a certain sense of, shall I call it, false reality sets in and a child gets mislead into supposing that “the answers” are out there sitting on a drab shelf ready to be innocently “learned” at the public school house.  I cannot blame my kid for having internalized this sensibility; it’s been drummed into her for years now.

Given the data available at the start of the nineteenth century, Legendre’s function was much better than Gauss’s formula as an approximation to the number of primes up to some number N, but the appearance of the rather ugly correction term 1.08366 made mathematicians believe that something better and more natural must exist to capture the behaviour of the prime numbers.

Such ugly numbers may be commonplace in other sciences, but it is remarkable how often the mathematical world favours the most aesthetic possible construction.  As we shall see, Riemann’s Hypothesis can be interpreted as an example of a general philosophy among mathematicians that, given a choice between an ugly world and an aesthetic one, Nature always chooses the latter.  [my emphasis] It is a constrant source of amazement for most mathematicians that mathematics should be like this, and explains why they so often get wound up about the beauty of their subject.

Imagine that: choosing a mathematical order — a beautiful one over the ugly alternatives — that in math one can sketch out ideas and test them, and even choose among them using an intuition that surprisingly sometimes matches the visible natural order.  In so many spheres of life we are offered chances to choose, to act, to inquire boldly, to investigate, to discover.  Oh would that we could instill even a nano-quantity of that free-spiritedness into the school house!

Above, Alice has boldy chosen to paint a dog leaping.  She has no qualms at all about portraying her Public Enemy Number One.  And she even makes him beautiful.

5 thoughts on “Learning Beauty

  1. A beautiful dog indeed – reminds me of a character out of ‘The lion, the witch and the wardrobe) – he was a wolf. I think many mathematicians are visual people and therefore aesthetes. Many great mathematicians were on the autism spectrum and have a great need for perfection (some types of beauty and simplicity can be perfection for them). I don’t think the converse is true – that visual people are necessarily good at maths.

  2. Gabrielle,

    Whew! I’m glad somebody FINALLY commented on this post. Alice can get so bent sometimes (“I’m not a toy, I’m a real cat ….”) I figure that there’s so many innumerates out there in the world that the topic is virtually a blog stat-repellent. I promised Alice (who’s usually great for generating stats) that I’d never use her on a math post again.

    Visual people not good at maths: oh boy, do I recognize myself! I sometimes transpose numbers, and it takes me a while to realize. Big differences too! — between say, 9,602 and 6,920 especially when it’s MONEY!

    I try always to remind myself that numbers have MEANING. (Got to try to respect the meaning.)

    Aletha

  3. Ok mom – good idea to suggest experimenting and thus thinking independently. When the school books are forgotten the internet is a fabulous source of math instruction. You can google for math rules, multiplying negative numbers, etc and get some really good clear information. It would have been another source of learning to go on the net with her to look for rules.

  4. Jones, Aren’t you an engineer or something? I forgot about that. And no fair. You and two or three other people can actually use both sides of their brain.

    My right brain is huge. And my left brain requires an electron microscope to be detected.

    Check the internet. Easy for you to say! I did look on the internet for math rules, but the rules require interpretation.

    So, you want to tutor me? If so, don’t forget bring chocolate.

    AK

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