Mathematics is the big secret


As a boy in the first weeks of algebra class, I felt confused and then I got a little numb. Adolescents organize the world from fragments of information. In its way, adolescence is a kind of algebra. The unknowns can be determined, but this requires a special aptitude, not to mention the comfort of holding things back. Straightforward, logical thinking is required and a willingness to follow rules, which are not evenly distributed across adolescents’ capacities.

When I thought of math as a boy, it was to speculate about why I should learn it, because it seemed obvious that it wasn’t necessary in adult life. Balancing a checkbook or drawing up a budget was the answer we got to how math would be needed later, but you don’t need algebra or geometry or calculus to do any of those things.

But if I had understood how deeply entrenched math is in the world, how it plays a role in every gesture we make, whether it’s crossing a busy street or catching a ball, how it plays a role in painting and perspective and in architecture and in the natural world and so on, then maybe I would have seen it as the ancients had seen it, as a fundamental part of the design of the world, maybe even the design itself. If I had felt that the world was connected in its parts, I might have been stirred to a kind of wonder and enthusiasm. I may have wanted to learn.

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Five years ago, when I was 65, I decided to see if I could teach adolescent math—algebra, geometry, and calculus—because I had done poorly in algebra and geometry and hadn’t taken any calculus at all. I didn’t do well the second time either, but I’ve become kind of a math evangelist.

Mathematics, I see now, is important because it magnifies the world. It is a gateway to greater concerns. It teaches respect. It insists that you are receptive to wonder. It requires a person to play a lot of attention. Having to consider a problem carefully discourages distraction and sloppy thinking and encourages systematic thinking, an advantage, as far as I can see, in all endeavors. Abraham Lincoln said he spent a year reading Euclid to learn to think logically.

While studying mathematics for adolescents, a person traverses an area on which footprints have been left since ancient times. Some traces have been made by eminent figures, but most have been left by ordinary people like me. When I tried to follow a path in a fading light as a boy, I never saw the mysteries I moved between, but on my second pass I started to do so. Mathematics hadn’t changed, but I had. The person I had become was someone I could not have imagined as a teenager. Math was different because I was different.

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The math mystery for beginners, which is available to everyone, concerns the origin of numbers. It’s a simple speculation: where do numbers come from? Nobody knows. Were they invented by humans? Hard to say. They seem to be embedded in the world in ways we cannot fully comprehend. They started as measurements of quantities and grew into the means for the most accurate expressions of the physical world – for example e = mc².

The second mystery is that of primes, those numbers such as 2, 3, 5, 7, 11 and 13 that can only be neatly divided by one or by themselves. All numbers that are not primes are called composite numbers, and all composite numbers are the result of a unique arrangement of primes: 2 x 2 = 4. 2 x 3= 6. 2 x 2 x 2 = 8. 3 x 3= 9 2. x 3 x 3 x 37 = 666. 29 x 31 = 899.2 x 2 x 2 x 5 x 5 x 5 = 1,000. If people invented numbers and counting, how come there are numbers like primes that have properties that no one has given them? The great and all-encompassing mystery is whether mathematics was created by humans or exists independently of us in a region adjacent to the real world, whose location no one can specify. Plato called it the non-spatial-temporal realm. It is the timeless nowhere that never has and will never exist anywhere, yet is.

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Mathematics is one of the most efficient means of approaching the great secret, of considering all that is beyond what we can see or presently imagine. Mathematics does not describe the secret so much as implying that there is one.

On my second assignment, whenever I came across a definition of mathematics, I wrote it down. One of the things I liked the most was that math is a story that has been written for thousands of years, always being completed and may never be finished. Such a thought would have appealed to me as a boy and might not have made mathematics more inviting, but at least less daunting than it seemed.

The post Math Is The Big Secret appeared first on New York Times.


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