This video and its responses have been going viral today, but as someone who has lightly studied the history & philosophy of math, I have to say, these are absolutely excellent questions, and the hate is completely undeserved. Thread time. https://twitter.com/aIeturner/status/1298372968838508546
First, just to get this out of the way, I fucking hate how people's first reactions to her video is to call her dumb, for questioning something we take for granted. She's thinking critically, unlike the folks who are just regurgitating what they've been told. Props to her!!
The first thing I'll start with is the question of whether math is real. This is argued about quite a bit in philosophy -- does math exist in a *real* sense independent of us & is it universal? Or is it just a human creation, a tool that we happen to use to describe the world?
A lot of older philosophers did think of math as something real, existing abstractly in the way that you and I exist. This is called Mathematical Platonism (tho not argued for by Plato himself), but there have also been many objections to this idea.
Now, one philosopher who did treat math as something that truly described reality was Pythagoras, who she mentions in the video. He's known for the belief that "everything is number," that our reality as we know it is governed/described/defined by numbers.
This helps address her question -- why did Pythagoras study math? One possible response is to say, he was concerned about existence/reality itself, and the way for him to understand our world was to understand math. (Much like why physicists today keep asking about the universe.)
Now this is where it gets a bit tricky! Pythagoras himself actually wasn't regarded that much as a mathematician, actually! His philosophies were influential (especially to Plato), but he didn't contribute to math the way others like Euclid did.
In fact, a lot of people question whether he himself was responsible for many of the contributions attributed to him, or if it was bundled with the contributions of his followers. What we take as "Pythagorean thought" might refer to a group of thinkers, not just one man.
Related to this, it's worth mentioning that she brings up his math as algebra, but the term algebra actually comes from the Arabic word al-jabr, and this field is typically credited to the work of the Persian mathematician, al-Khwarizmi (~800's AD).
What is notable about al-Khwarizmi, Pythagoras, and so many early others is that they were all concerned with things like astronomy, music, geography, etc. that they used math to help describe and understand. It's likely that these grand things also motivated their work.
One example I love is the connection of math, music, and astronomy. Pythagoras observed that there was a relationship between pitch of a musical note and length of a medium (like the string), and he connected this to how the sun, moon, and earth might also have their own pitches.
This is an idea known as the "music of the spheres," and later astronomers like Kepler (known for laws on planetary motion) were *obsessed* with linking planetary motion to music, seeing it as part of a grander truth (and Design) to the universe.
Today, we might take what Pythagoras and others believed in to be numerology (mystical or divine relationship of numbers to reality), but to them, math was a way to understand (the secrets of) the universe & there was beauty in how it worked out.
Also, she mentions y=mx+b, which comes more from Cartesian geometry. Remember the "Cartesian plane" that we use? This was a unification of Euclid's geometry and algebra, in a way where algebraic equations could be used to describe geometric shapes (like lines).
Decartes himself was a philosopher, and it's important that his interest in how the world worked (like, physically) as well as his interest in logic / rationality also played roles in his mathematics. (I could go on a whole different rant about logic & math & rationality...)
Of course, it wasn't just all for fun and games and music. With these systems they all developed, there were practical uses. Use astronomy for navigation or agriculture. Use Cartesian coordinates to estimate trajectories (to win a war, anyone?). And they saw/knew this.
Extended: Newton was interesting as hell because he was working on physics problems, but couldn't seem to address certain calculations with existing math... so what did he do? He invented calculus. Calculus didn't come first, the need for it with his physics did.
But notably, at the *exact* same time, Leibniz was dealing with his own questions about (meta)physics, and totally independently of Newton, he also came up with calculus. Could math just be made-up if two people, totally separately, could come up with the same system?
(The systems weren't *exactly* the same, but they did very similar things. Calculus meant slightly different things for Newton and Leibniz, too, though it helped us understand concepts of change, esp. at an infinitessmally small level. Math informs how we think about the world!)
Final note: A lot of this math is based off particular classical systems of logic (remember needing proofs?). But what if I told you classical logic doesn't work for everything? In fact, in 1936, to describe quantum mechanical phenomena, we realized we needed a quantum logic.
This led to things like the 1968 paper, "Is Logic Empirical?" which asked, if we've come up with a different logic to describe quantum mechanics, did we only come up with classical logic due to our experimentation under classical mechanics? Lots to think about.
To wrap up, she mentions how Pythagoras could come up with math, even without the technology we have today, and I think that's the beauty of it. His questions about the universe and reality influenced others' beliefs and understanding, which influenced others, which influenced o-
From starting with the most basic questions, we have generations of people building off of it, to get to where we are today. The things we have -- computers, phones, etc. -- came from a whole history of human investigation and invention, and it was a collective effort.
The questions we ask today could set us on paths to discover much grander and more incredible things in the future, even if each of us can only contribute a tiny, tiny amount to it. But add up all of these tiny contributions and together, we make these tremendous things possible.
Anyways, thank you for reading! There's a lot I missed and generalized (& not to mention this is a *Western* history of math), but this is roughly the scope of what I had to say. I encourage folks to find your own readings as well, a good place to start:
I don't ever like to ask, but pandemic is kicking my unemployed butt, so if you enjoyed the read, it would help me a ton if you sent something my way! Anything and everything helps.
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