Chris Dixon has written an excellent history of mathematics. When most of us think of math, we go “ugh” and call it boring and turn away, but really, it’s so fundamental that we should be far more excited about it. Most of the major turning points in my education involved math: it was geometry when I was in the 8th grade that sparked my first interest, and learning algebra and logarithms in high school chemistry got me focused on science. When I started teaching myself how to program computers (I was an inadequate teacher, and quickly signed up for courses in the CS department), I had to also teach myself basic Boolean logic, because in those ancient days when your only recourse was to learn assembly language, and ANDs, NANDs, NORs, and ORs were the name of the game. Transistors are just logic implemented in silicon.
I agree when Dixon writes,
Mathematical logic was initially considered a hopelessly abstract subject with no conceivable applications. As one computer scientist commented: “If, in 1901, a talented and sympathetic outsider had been called upon to survey the sciences and name the branch which would be least fruitful in [the] century ahead, his choice might well have settled upon mathematical logic.” And yet, it would provide the foundation for a field that would have more impact on the modern world than any other.
I would add that in the 1970s public education system, we wouldn’t have imagined that, either. I had teachers who thought math was stuff you only needed to know for business school — you know, accounting. You can still see that attitude when people wonder why they need to learn this algebra stuff, anyway — they’ll never use it. They’re wrong. You’ll just use it in unexpected ways, because what you’re being given is a creative toolbox for thinking about the world.
The historical context in this article is useful, though, for making a case that math isn’t just practical, it’s also a foundation for thought that belongs in the liberal arts canon. And also that it’s a significant part of philosophy, which too many scientific pragmatists also tend to dismiss.
“You can still see that attitude when people wonder why they need to learn this algebra stuff, anyway — they’ll never use it” and they go on to study economics and never do!
When most of us think of math, we go “ugh” and call it boring and turn away
Who is this strange “us” with such an appalling lack of appreciation for the finer things in life?
I’ve always found it strange when people say they’ll never use algebra and I wonder how they ever know if they’ve been given the right change.
Huge numbers of students I have to advise who are horrified to learn that biology has a math and stats requirement.
It’s a significant part of art and craft as well. In one way or another, it underlies most human endeavors.
This is one time when SMBC absolutely nailed it.
http://smbc-comics.com/comic/why-i-couldn39t-be-a-math-teacher
“[A] creative toolbox for thinking about the world” — Who needs that, when your phone can do it all for you?
The 1890 census was completed using Holorith’s punch cards. By the 1960’s IBM (which grew from a company founded by Holorith) was practically giving away the IBM 1620 with card readers and punches to colleges, and most peoples’ paychecks included the warning “Do not fold spindle or mutilate.” The value of reliably keeping track of “Yes” and “No” was becoming something that not just businesses, but ordinary people could see working in their own lives.
Then came paper tape, magnetic tape, floppy disks, hard disks, flash memory, and “the cloud.” Yes and No, true and false, have been hidden again, abstracted, and devalued. Math is numbers, and numbers used to be visible — long before they became holes in a paper card they started as clay marbles in a clay envelope, one marble for each sheep being sent off to market. Now we’re learning that numbers don’t matter and if you don’t like the truth you can just tweet some alternate facts. What use is math to a society that’s lost it’s marbles?
(Sorry. I work in environmental data management and preservation. I have been having nightmares in recent months.)
It’s a good history of mathematics and logic as far as it goes, but it’s very much a mathematician’s history rather than an historian’s. You can tell, because it says almost nothing about mathematics and logic in the Middle Ages – despite these subjects being at the heart of medieval university teaching and scholarship. Indeed, it is late antiquity and the Middle Ages that give us the concept of the “liberal arts” in the first place, with logic as one pillar of the Trivium and geometry and mathematics as two pillars of the quadrivium.
In fact, far from being a daring and unheard of risk, improving on the logic of Aristotle was what medieval Arts masters DID all day. Avicenna, Maimonides, Peter Abelard, Henry of Ghent, John Duns Scotus – the whole medieval scholastic tradition was all about modifying, improving and applying Aristotelian logic. As the article brushes against hinting at when it invokes the influence of Ramon Llull on Leibniz (Leibniz was heavily involved with editing the texts of medieval Franciscan thinkers, and drew a lot of his inspiration from all kinds of medieval thought).
The article also tends to ignore the cultural, political and economic influences on the “great men” of mathematics that it discusses. As if logic and mathematics have some kind of pure, extra-historical force all of their own, and their study was not affected by the vicissitudes of human foibles. Aristotle’s logic arose from a climate of 5th/4th century Athenian rationalism buoyed along by a conviction that Greek culture and values were pre-eminent, and that matters. As, very probably, does Frege’s extreme right-wing views and anti-semitic convictions.
Back when I studied economics, we had to learn linear algebra on a similar level with the Math students.
Business management on the other hand included statistics and accounting.
Don’t dismiss a field just because it is often misued.
Scientismist-
I have a science experiment. We erect two big granite monuments, one has the Ten Commandments carved on it, the other has 100 years worth of global temperature numbers. Let’s see which one is vandalized, defaced, or removed by government order first.
Kristjan Wager — When I took introductory econ as a senior undergrad, I was the only one in the class with any experience with calculus, and also seemingly the only one who could get their head around the notion of marginal value.
sigaba — The description of your protocol is incomplete. Erected by whom? Where? Are metadata also preserved in all cases? Do backups exist? Does the government in question operate under a constitution? Is the establishment of these Ten Commandments part of the government mandate? Are public safety and welfare?
I love the history of math. The Story of e, by Eli Maor, is good, for a history of calculus. I used to give my calc students a lecture on the history of numbers. starting with counting numbers and the invention of written numbers, up through the invention of complex numbers, in part to show why “imaginary” numbers were no less or no more real than any other kind of numbers.
I love to cook and bake. I often point out that knowing math is very important in the kitchen, too.
I was lucky to go to an elementary school where they taught us logic and sets and bases and matrices. When I saw it again in college I was like, this is kid stuff!
The underpinnings of math always seemed more exciting and intuitive than arithmetic. I only really learned the times tables when it was needed to do algebra. Math is fun!
“I would add that in the 1970s public education system, we wouldn’t have imagined that, either. I had teachers who thought math was stuff you only needed to know for business school.”
As a Dutchman who visited secondary school (12-18 years old) in the second half of the 1970’s I can only say one thing: wow. Wtf did you American students do in physics and chemistry class?!