What is Math? Part 2
DISCLAIMER. The content of this article is different than the podcast episode that this is supposed to represent. Apologies.
The next philosophy of mathematics we are going to discuss is known as formalism. This perspective holds that math is just a set of symbols with no inherent meaning, and solving problems is very mechanical. The only way that mathematics gains meaning is from applying it to something like physics or engineering.
The pinnacle of this movement comes from the philosopher and mathematician Bertrand Russell who wrote the book Mathematica Principia.
By the end of this book, they were able to prove that 1+1=2. Now, this does seem absurd but it seems less absurd in context. During this time there was a fear brewing in the mathematical community that mathematics had no foundation and without one it would crumble away. So part of formalism, which had logicism as a shoot off, was to give arithmetic a foundation in logic. Arithmetic was thought of as a foundational aspect of mathematics next to geometry, but it was accepted that geometry was built into our intuition, so its foundation was a priori. Russell and his associates failed however in securing this foundation and instead made mathematical logic a subject within mathematics.
So back to our thought experiment of recreating the education system and arguing for the return of mathematics. If an educator held this perspective, where mathematics was purely mechanical, then how do they help the student who doesn’t understand that process. This isn’t some sort of hypothetical, this is a real one. Students are told to just keep practicing the method, just repeat the process and they will understand it. Sometimes it does work, but that is rare. The student that is being taught from this perspective repeats the process and simply reaffirms that they can’t do the math. This also harms the student that is good at math though. If math is purely mechanical then the amount of creative thinking that has to go into solving a problem drops to zero. Eventually, they will need some creativity to solve a problem and it will shatter their self-esteem that they can’t understand the process.
So what is our other option? Does math exist outside of us? Is it just a mechanical process where no matter what students get the shorter end of the stick? The next article will be on the social-humanist perspective, and it will include a bit of a rant on education reform.
