In Mathematics, I Now Realize We’re Chasing Beauty
The idiom “chasing rabbits” generally means getting distracted, losing focus, and being unsuccessful in the end with these pursuits.
Mathematics has been a wonderful distraction in my life(so has music), pulling me in many directions, and caught up in an endless fascination with even its most minor details.
So truthfully, I don’t think I have missed out on anything. On the contrary. My life has been a blissful adventure — that still continues — chasing these rabbits, and getting lost in rabbits holes of mathematical awe and wonder.
But it only dawned on me recently that while the use of the rabbit in that idiom represents something much larger and eternal.
It represents beauty, and tying in Archimedes quote, it represents the surest path to uncovering any of the thousands of secrets that mathematics holds — and has held for thousands and thousands of years.
Sometimes these secrets are not so secret. The beauty is there for the taking by anyone of us.
Speaking of primes. You know, those “stubborn” numbers that don’t like anything but 1 and themselves to be factors. Well think of any prime number 5 or greater. Square it. Now subtract 1.
Did you know that this resulting number after these two innocuous operations will always have 24 as a factor! That’s right. Those peculiar primes, snooty with their factors, now are accepting a big one like 24 permanently as a factor with these consecutive operations.
Don’t tell me you won’t try it for a few primes greater than 5 right now!
There’s dozens more than I have come across just in the branch of number theory — a topic not taught in most K to 12 schools. A literal branch of mathematics that organically weaves in factual, procedural, conceptual, and historical fluencies.
It’s also beautiful as hell.
Chasing beauty involves our own imagination and curiosity. It works on overdrive when we are young children. The problem is we as math educators don’t give them the mathematics to begin this endless journey of chasing it.
We steal their curiosity early. We never give it back.
That’s why — with zero coincidence — the first pillar that I wanted to be foundational for The Global Math Summit was number theory.
Revitalizing number theory is just code for recapturing the journey of mathematics for its own beauty. To be filled by the beauty of anything has immense personal value in our lives — music, art, theatre, literature, etc.
We can only give society are best if we are fulfilled and nourished.
Current mathematics education is not nourishing our students — and teachers — with the most beautiful and inspiring mathematics.
As such, we are not getting the best out of them. We are not creating a culture of common curiosity of the mathematical universe.
We are closing the door on them to the secrets that make the universe hum and sing.
What if at school you had to take an ‘art class’ in which you were only taught how to paint a fence? What if you were never shown the paintings of Leonardo da Vinci and Picasso? Would that make you appreciate art? Would you want to learn more about it? I doubt it……….but this is how math is taught and so in the eyes of most of us it becomes the equivalent of watching paint dry. While the paintings of the great masters are readily available, the math of the great masters is locked away.
Ed Frenkel(Love and Math, 2013)
We are left with only two choices. Either we prioritize beauty and mathematics in school or we say that aesthetics are not important. The “beauty” road is not the easiest. Trails are not necessarily marked out. You will get wonderfully lost at times. Adventures could be different from one person to the next. It could be worse. It could be watching paint dry…
As always, actions will speak louder than words.
