My fascination with math started in January of 2013. Christie gave me a Barnes and Noble gift card for Christmas and I used it to purchase The Joy of X: A guided tour of Math from one to infinity by Steven Strogatz. It was the perfect re-introduction to a subject that I hadn’t really thought about since high school. As a business owner I used margins and percentages on a weekly basis. Other than that, math wasn’t on my radar. The author, a mathematics professor at Cornell University does a great job of introducing the concepts of certain mathematical ideas without having to actually work through a bunch of equations. When I finished the book I was hooked.
As much as I wanted to learn about different mathematical concepts and disciplines like topology, combinatorics and Non-Euclidean geometry, I also wanted to learn more about the history of math and the genesis of certain mathematical ideas. I poured over the biographies of mathematicians from Euclid to Gauss to Cantor. Each story was more interesting than the last. I easily spent 1000 hours in 2013 researching math and the history of math. You might say it became an obsession. At least it was a healthy one.
In the beginning of my research one particular story caught my attention. A rift between 2 academics. George Cantor and Leopold Kronecker. Kronecker criticized Cantors work on Set Theory. The details are not important. What’s important is that I quickly realized that all mathematicians don’t necessarily agree on all mathematical concepts.
By the end of the year I had an epiphany about math. The blame falls squarely on Professor Strogatz and his book, The Joy of X. I mean that in a good way. He opened my mind to the reality of mathematics. He doesn’t put it exactly like this. In fact I’m taking his writing out of context but here is my takeaway nonetheless.
These guys are making this stuff up as they go along. In his book he explains how the number one used to be considered a prime number. Now it’s not. If it were, the fundamental theorem of arithmetic would be incorrect. So instead of altering the definition, to say, excluding the number one. Mathematicians have decided one is not a prime number.
I’ve even read in other books that some professors don’t even use the word number when referring to the number one. They call it a unit. A unit!
To me, it’s like saying I’m not a person. I’m a human.
I imagine a global conference where the greatest mathematical minds converge to vote on whether to keep calling number one a prime number. All the countries raise their hands in agreement to exclude the number one from the list of primes. Except, the Russians. They’re having none of it. They’re coughing into their hands saying “bullshit” cough, cough “bullshit”.
Too funny. These math professors. They kill me.
So one is both a unit and a number. But it’s not Prime. Not anymore. Why? Because the greatest minds in math all agree.
Except it is Prime. At least for me. But I would never admit that in public.
I’m sure this kind of thinking doesn’t sit will at the university level math class. Lucky for me I’ve never taken a university level math class.
The real epiphany is that math is fluid. It’s as much an art as a science. If you follow me with this analogy I will take it a step further. Lets say that mathematical institutes and universities are the art museums of the world. Filled with Michelangelo’s, Titian’s, Renoir’s, Monet’s, Van Gogh’s and Warhol’s. I don’t have a ticket inside. I’m not invited inside. Not only that, I’m outside spray painting the walls. Nobody knows I’m spray painting the walls. Nobody even cares. I’m having fun and I can’t stop. I don’t want to stop.
What I’m trying to get at is that I have no credibility. None. I have no math degree of any kind. No formal training. It will be obvious in future posts. If it’s not already. No academic is going to pay attention to the things that I find interesting. Some of the ideas that I stumble across in my work have been known and proven for years. Others are of no interest to anyone but me. Others still may be interesting but unimportant. I ignore or disregard axioms if they get in the way. See. No credibility.
And that my friend is where the freedom lies.
The freedom of not having to meet anyone’s expectation. I have the luxury of making mistake after mistake with no one to tell me that I’m wasting time. I can play with numbers and equations all day long. It’s all spray painted rainbows and unicorns.
Until you get to proofs. Then things get more serious. And difficult.
And that’s why I need math professors. These guys are smarter than me. They see the world in a way that I don’t. Or can’t. Or haven’t learned. Some of these guys are what I like to call smart as f#ck. They get into math that is beyond me. Really deep math. I’m still playing in the shallow end. That’s cool though. Because the math pool appears to be infinitely wide. And these guys may have waded past a few gems. Lucky me.