Learning about numbers brings us closer to the great mystery – 02/24/2024 – Seminars Folha

As a kid, the first few weeks of algebra class, I felt confused and then felt a bit numb. Teenagers order the world from fragments of information. In a way, adolescence is a kind of algebra. Unknowns can be determined, but doing so requires a special aptitude, not to mention a comfort with having things undefined. Logical and direct thinking and a willingness to follow rules are required, which are not well-distributed abilities among adolescents.

When I thought about math as a kid, it was to speculate about why I was being forced to learn it, since it seemed obvious that there was no need for it in adult life. Using a checkbook or creating a budget was the answer we were given about how mathematics would prove necessary, but you don’t need algebra, geometry, or calculus to do these things.

But if I had understood how deeply mathematics is embedded in the world, how it is present in every gesture we make, whether crossing a crowded street or catching a ball, how it is present in painting, perspective, architecture, in the natural world and so on, then perhaps I could have seen it the way the ancients saw it, as a fundamental part of the design of the world, perhaps even the design itself. If I had felt that the world was connected in its parts, I might have been provoked to a kind of wonder and enthusiasm. I might have wanted to learn.

Five years ago [este texto foi originalmente publicado em setembro de 2022], at age 65, I decided to see if I could learn the math taught to teenagers — algebra, geometry, and calculus — because I had done poorly in algebra and geometry and hadn’t taken calculus. I didn’t do well the second time, but I became something of a math evangelist.

It, I now see, is important because it expands the world. It’s an entry point to larger concerns. Teaches reverence. It requires one to be receptive to wonder. It requires a person to pay close attention. Being obliged to consider a problem carefully discourages scattered and careless thinking and encourages systematic thinking, an advantage, as far as I can tell, in all endeavors. Abraham Lincoln said he spent a year reading Euclid (a Greek mathematician celebrated as the father of geometry) to learn to think logically.

When studying mathematics, a person crosses a territory in which footprints have been left since ancient times. Some of the paths were made by illustrious figures, but most were left by people like me. As a boy, trying to follow a path in the dim light, I never saw the mysteries I was moving among, but on my second pass I began to see. Nothing had changed about math, but I had changed. The person I became was someone I could not have imagined as a teenager. Mathematics was different, because I was different.

The beginner’s mathematical mystery, available to anyone, concerns the origin of numbers. It’s simple speculation: where do they come from? Nobody knows. Were they invented by humans? Hard to say. They seem to be embedded in the world in ways we don’t fully understand. They began as measurements of quantities and became the means for the most precise expressions of the physical world —E=mc², for example.

The second mystery is that of prime numbers, such as 2, 3, 5, 7, 11 and 13, which can be precisely divided only by one or by themselves. All non-prime numbers 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 human beings invented numbers and counting, then how come there are numbers like primes that have attributes that no one gave them? The great and engrossing mystery is whether mathematics is created by humans or exists independently of us in a territory adjacent to the real world, the location of which no one can specify. Plato called this the non-spatiotemporal world. It is the timeless place that never was and never will be, but nevertheless exists.

Mathematics is one of the most efficient ways to get closer to the great secret, to consider what is beyond everything we can see or imagine. The mathematics does not describe the secret, but it implies that there is one.

In my second approach, whenever I came across a math definition, I wrote it down. Among the ones I liked most was that it is a story that has been written for thousands of years, is always being added to and may never be completed. Such a thought would have deeply appealed to me as a boy and might have made mathematics seem perhaps not welcoming, but at least less intimidating.