As I reported elsewhere, I technically failed kindergarten. For example, one of the test we had to pass was the memorization of our home phone number. I refused to learn it. My mother, a teacher, was embarrassed. We also had to learn to count up to 10. I was 5 so I decided to it was more reasonable to learn to count up to 5. My mother was again embarrassed.
So it was decided that I must have had a learning disability. I was obviously bad at mathematics. (This last sentence is ironic: mathematicians will tell you that memorizing numbers is not mathematics. But I digress.)
For those who don’t know me… I have a three degrees in mathematics from some of the best schools in the world. I have also published some novel mathematical results. I am not a star mathematician or mathematical genius but I have credentials. Yet if my teachers had to make predictions based on my early schooling, they would have predicted nothing good for me. At least, nothing good in mathematics.
In retrospect, I am quite certain that I have never had a learning disability… except for the fact that I am an incorrigible contrarian. Still, my parents are not obviously good at mathematics. I see no evidence that I liked numbers. So how did I get good enough to outdo my peers?
Because I did not record my childhood, I can only speculate. Here is what I remember.
As a kid, I learned to read with Tintin. And my favorite character was professor Calculus (known in French as Tournesol). I also loved scifi. At the time, Star Wars was very popular. I remember dreaming of the year 2000 when I would get to fly in a starship.
As a parenthesis, I distinctly remember learning how to read for the purpose of reading Tintin. And Tintin was not part of the curriculum. Rather, my mother got me one album, and it was the most exciting thing I had in my room! I remember painfully deciphering Tintin, page by page.
In any case, I did not know much about Physics or Chemistry, but I knew that whatever Calculus did had to do with mathematics. I also knew that flying starships and building robots involved advanced mathematics.
So I was motivated to learn mathematics. That is probably the single most important factor. I simply wanted to be good at mathematics. When I got something wrong, I did not get discouraged, I tried to understand it better.
I also think that my contrarian nature helped me. It made me immune to the poor teaching of mathematics so prevalent in schools. For example, while my peers were memorizing multiplication tables, I tried to find algorithms to figure out the answer. I simply could not imagine professor Calculus memorizing tables. After all, professor Calculus is known to be forgetful!
Still, where did I learn mathematics? We did get some decent mathematics in the classroom from time to time, but on the whole I think it was mediocre. The manuals were simply not very inspired.
However, I discovered a magazine called Jeux et Strategie (Games and strategies) as a kid. It was an amazing magazine. Each month, it had pages and pages of fun mathematical puzzles. An ongoing theme was that of a race of aliens where some of them always told the truth, some of them lied all the time and some of them would just say anything. You could not tell them apart, except by analyzing what they said. This was my introduction to logic. Initially, the puzzles were way too hard for me. By the time the magazine stopped printing, I could do these logic puzzles in my head.
The magazine would discuss games like poker and monopoly. However, it would do so in a sophisticated manner. For example, I remember this article about monopoly from a top-rated player. He showed how the good players used probabilities to win. That is, you are not just supposed to buy any lot! Some are better than others, and you can easily figure out which ones are better.
I don’t play games a lot, but I really liked the idea that I could learn mathematics to beat people at games. It turns out that I never did become a better monopoly player, but I learned that if I used the right mathematics, I could!
As an aside, my grand-mother was a gambler. She would hold these poker games at her place every week-end. And they played for real money! She also brought me all the time to horse races (she had racing horses of her own). If you have never been to horse races, you should know that you get lots of statistics about the horses. It tells you exactly how often a given horse has won, and in what conditions. One of my early hobbies, as a kid, was to read these statistics and try to predict the winners. After all, I had nothing better to do (horse races are otherwise quite boring for kids). I even devised some algorithms that were fairly reliable. This taught me that you could actually use mathematics to get money!
The final step in my early mathematical education came when I got a computer. My parents gave me a TRS-80 color computer. I simply did not have much money to buy games. So I had to program it to stay entertained. Obviously, as a kid I decided to design my own games. I did not get nearly as far as I thought I would. I guess I was never very motivated in building a really good game since I had no way to share it. But I did build a few and this taught me a lot about discrete mathematics. I remember having to work out my own collision detection algorithms (how do you figure out whether a point has crossed a line?). I also got a lot out of magazines. At the time, magazines would regularly post the source code of simple games. This was just great! You could take an existing game and try to improve it, to see what would happen.
All along, what helped was that I had a friend who was a nerd too. He ended up becoming a software programmer too. I am sure that if all my friends had been into sports, it would have been much harder for me to stick with mathematical interests.
To sum it up, here are the factors that helped me become good at mathematics:
- Early on, I self-identified with scientists. I had a role model (professor Calculus).
- I have always been a contrarian: I refuse to accept things on faith. I am not sure where this came from. I doubt it is an innate trait, but I also do not know how to cultivate it in others. In any case, this plays an important role because I always refused to accept recipes. I think recipes are a terrible way to teach mathematics.
- I had access to decent and entertaining mathematical content, even if it wasn’t from the school I attended.
- I got my own (programmable) computer as kid!
- I hung around with nerds.
I am not claiming that this is some sort of recipe to turn kids into mathematicians. My real point is that I believe that mathematics is not innate. I also do not think that schools can teach mathematics. Not the kind of schools I attended.