Infinite Ascent

In Infinite Ascent: A Short History of Mathematics, author David Berlinski gathers many basic concepts* and slowly reveals their coalescence, drawing the reader along with him as he tells the story of 2500 years of human intellectual exploration. It’s quite a ride**. He does it expressively with humor, many anecdotes, and writerly style.

And there is the Omar Khayyam of the Rubiyat, a Persian among Arabs, and so a songbird among sparrows, a mathematician of note, occupied with the solution of cubic equations, his lyrical intelligence finding in algebra the anodyne against time that time had long withheld.

His passion for mathematics is not singular. There is art in there and literature, a great deal of philosophy and science, and all of these built on one indefatigable premise, championed, he says, by Pythagoreans: “Number is the essence of all things.” Once you understand this, an entirely lucid world emerges—beautiful for its austere simplicity and elegant logic as well as for its chaotic dramas. As he coaxed into my mind the beginnings of the Cartesian map, the ghost of the third axis rising prematurely, I felt a rush similar to the first time I realized the truth of the Pythagoreans' doctrine. Numbers are every thing. They are inside everything, the bones from which we string our muscular hearts, trusting their existence, often completely unaware that they are there at all.

My uncle Marco is a doctor. I remember visiting my grandparents, once while he was there and hearing him talk about a biology lab. He looked at me (which was amazing, children were considered all but invisible when adults were talking) and asked what I wanted to be when I grew up intending, I’m sure, to make a point about staying in school. I said, “An environmental scientist or a marine biologist who saves sharks.”
I liked sharks, a lot.
He told me that I would have to study hard and learn chemistry and math. I must’ve pulled a face. He said, “You don’t like math?”

“I hate it! It doesn’t make any sense.”
“Don’t you like poetry?”
“I love poetry.”
“Math is poetry. The numbers are words. They speak—you just have to learn the language.”

I can still remember those words, clearly. It takes my breath away to think of the truth of them.

Ever since, even through struggling with a particularly horrible geometry class I had to repeat in high school, math has been a kind of poetry. I finally understood numbers, their reason and their potential… Variables, parabolas, and functions all moving sinuously together, hypnotic.

Infinite Ascent is more like watching a play than listening to a lecture. Berlinski paints a landscape of real people and their remarkable insights. They argue and create amazing things, fight and get things wrong; they live and die and breathe life into theorems and equations the beginnings of which many people see only in high school briefly and without interest. His enthusiasm and engaging writing style catch the reader’s attention and the way he builds on each concept, storytelling rather than simply throwing text on a whiteboard, draws comprehension in his wake.

If number is the essence of all things then mathematics is the language of everything, “an aspect of the mind’s conversation with itself.” A parent language, left to us to decipher ourselves and our lives, to make sense of our surroundings, and to convey our understandings, both fumbled and precise, to each other.

As the external world recedes, the mind returns to itself. I think, therefore I am. Engaged by and with itself, the mind is proof against doubt, the distinction between the way things seem and the way they are vanishing, seeming and being blessedly annealed…There is the world of matter and the world of mind. It is the individual, naked in his thoughts and alone, who must learn how to represent the external world.

This is math as poetry; as a meticulous, universal language; the history of math a prelude to its philosophy—and Infinite Ascent is a brief, beautiful introduction to all three.

Results:
Title: Infinite Ascent: A Short History of Mathematics
Author: David Berlinski
Page Count: 181
Time: I took my time and read a lot of it aloud. All day, about ten hours.


*Understanding some of the actual math requires at least a basic knowledge of advanced mathematical concepts.

**At one point I lay back, tented the book over my face and shouted, “God, I love math!” Let me know when it has the same effect on you and we’ll high five over tea and cookies.