In “ Chinese Myths,” Anne Birrell writes that the Coiled Antiquity myth, which belongs to “a minority ethnic group of south-western China,” describes “how numbers were created” and “provides the etiological myth of the science of mathematics,” but she does not give a source for this assertion, and I have not been able to find one, so I have to accept her word for it. They don’t typically appear in creation stories. The simplest one is where numbers come from. Mathematics, it turns out, is suffused with mysteries, and, though I could understand only simple ones, I was intrigued. How can things be there without actually being there?” The mathematician John Conway once said, “It’s quite astonishing, and I still don’t understand it, despite having been a mathematician all my life. This spectral quality is bewildering, even to mathematicians. Two people who do not share a language or understand a word the other is saying can do mathematics with each other, silently, like a meditation.Īn imaginary world’s being infallible is very strange. The known parts are ephemeral, but also concrete for being true, and more reliable and everlasting than any object in the physical world. Parts have been visited by only a few people, and parts are unknown, like the dark places on a medieval map. Parts of this world are densely inhabited, and parts are hardly settled.

No one’s version, so long as it is accurate, is more correct than someone else’s. Also, what is different for mathematicians is that all of them agree about the contents of that world, so far as they are acquainted with them, and all mathematicians see the same objects within it, even though the objects are notional. For mathematicians, though, this territory has more rules than it does for others. (Anna Karenina is no more actual than a thought about Anna Karenina.) Like other artists, mathematicians also have the run of a world that others hardly or only rarely visit. Like novelists and musicians, mathematicians produce thought objects that have no presence in the physical world. What else? That mathematics is both real and not real. A lifetime doesn’t seem sufficient to the task. Even those figures occupying the most exalted positions in regard to these speculations can’t settle them. What did I learn? Among other things, that, despite mathematics being the most explicit artifact that civilization has produced, it has also provoked many speculations that are not capable of being settled. I am done doing mathematics, so far as I was able to, but the thinking about it and the questions it raises are ongoing. While it was humbling to be made aware that what I know is nothing compared with what I don’t know, this was also enlivening for me. One channel involved trying to learn algebra, geometry, and calculus, and the other channel involved the things they introduced me to and led me to think about.

I know you.”Īfter a time, my studies began to occupy two channels. You failed the first time, and you will fail this time, too. When I would hit the shoals, I would hear a voice saying, “There is no point to this. I was returning to childhood not to recover something but to try to do things differently from the way I had done them, to try to do better and see where that led. It had always seemed less a subject than a destination, a private place where the bright girls and boys shared secrets.įor two years, I spent my days studying things that children study. I passed algebra and geometry in high school by cheating, which is not a good life lesson for an adolescent, but I had never taken calculus.

As a boy, I had been kicked off the math train at the algebra station, so I decided to start there and then learn geometry and calculus-three of the disciplines that the eighteenth century called pure mathematics. Hoping to make myself smarter and then write a book about it, I began studying mathematics when I was sixty-five, which was five years ago.

Calculus math for beginners