# How I learned mathematics (as a kid)

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.

1. I have a very similar story to tell about my experience with math. The details of my story are slightly different, but the broad picture is almost identical.

Comment by Peter Turney — 14/1/2013 @ 11:40

2. Speaking of math education there’s some kind of minor revolution going on at Finland and Estonia. Teachers have been producing Creative Commons (BY-SA) licensed material. That could be a game changer or at least challenge the status quo.

I think these sort of moves are necessary for us to keep up with the progress. You definitely don’t want to fall behind as a nation when it comes to things like these.

Comment by Juho Vepsäläinen — 14/1/2013 @ 11:48

3. Seriously Daniel, I can always enjoy your articles and they help me start my day with an optimistic spirit. keep it up.

Comment by Abdullah — 14/1/2013 @ 12:13

4. I am undoubtedly much older than you are. When I was a small child I knew that my phone number was 54J. That is so small I couldn’t help learning it.

Your description of how you got turned on to math sounds like that of many mathematicians I know. The ingredients vary. I think I am less contrarian than you (probably to my detriment) and I did have one high school teacher who actually got me interested in solid geometry. Some mathematicians I know (not me) grew up in families that were interested in math and shared their interest. But what is in common with most of us a self-directed nature that makes us do what we want to do and not what people expect us to do, which is one aspect of being nerdy.

Comment by Charles Wells — 14/1/2013 @ 12:27

5. Do not rule out the possibility that you were contrarian by nature. My daughter certainly is – she is nearly 4 now, but I know for certain she was contrarian as early as she had language. She constantly experiments with consequences, and tests our assertions.

Comment by Dominic Amann — 15/1/2013 @ 10:02

6. @Dominic Amann

So there might be a contrarian gene?

Comment by Daniel Lemire — 15/1/2013 @ 10:15

7. For better or worse, I think there are natural factors that cause more or less contrariness. After all, there is a psychiatric disorder something like “oppositional defiant disorder”. Like most such things, it will probably turn out that this condition is a broad spectrum rather than an on-off switch.

I consider myself something of a “disruptor” rather than a contrarian (my wife might have a different view).

Comment by Dominic Amann — 15/1/2013 @ 10:24

8. Hi, I too learned math by playing monopoly. At some points I was tired of loosing everytime against so I went to the “bibliobus” (a mobile library we used to have in my birth town) and borrowed “Comment gagner au monopoly” (how to win at Monopoly) and then a discovery: the most frequent score you can do with two 6 dices is 7 (6+1, 5+2, ..) and so I started to try to learn basic probabilities (of course I failed but still, I started to win a bit more often)..

Good memory, thanks Daniel for that post

Comment by Djamé — 15/1/2013 @ 18:49

9. Unfortunately, my 9-year-old daughter is not very contrarian: she doesn’t object to busywork or mind that math in school is mainly easy stuff she already knows. Fortunately, she was apparently born with an interest in math — and she has her own Professor Calculus, in the form of Dick Feynman. I recently started reading her Feynman’s entertaining memoirs as her bedtime story. Whenever he mentions a math concept she wants to know all about it. First trigonometry, then e, now homotopy groups. So I try to give her a sense of the mathematical objects even though they’re far ahead of what she “ought” to be learning next. One question leads to another and we end up working back to more fundamental concepts. This curiosity-driven style of instruction might not work for all kids, or all parents, but she eats it up. It’s not very different from the way I teach grad students in my office: if they are missing some piece of math we need for a problem, I explain it on demand, working back as far as necessary. They are engaged because they need it RIGHT THEN. I am not sure whether this model of instruction can be scaled to larger classes.

Comment by eclecticos — 16/1/2013 @ 0:25

10. Well that is awesome, My dad was a teacher (and according to his students a good one), but he was always so tough on us that we did not want his help at all.

I don’t think being contrarian is entirely useful – in fact for some people it causes more trouble than good – Ashley Smith is an example. I am not contrarian in terms of tasks I will do, I just question arguments or beliefs.

I do see that contrarianism in a select few would be a darwinistic advantage for the species as a whole.

Comment by Dominic Amann — 16/1/2013 @ 10:30

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