yego.me
💡 Stop wasting time. Read Youtube instead of watch. Download Chrome Extension

The Methods of Mathematics Are Fallible


2m read
·Nov 3, 2024

If I quickly compare it to physics, we have this domain called particle physics. The deepest theory we have in particle physics is called the Standard Model, which describes all of the different fundamental particles that there are and the interactions between these fundamental particles, the forces that exist between them, and the gauge bosons which mediate the force between particles like electrons, protons, and neutrons.

Now, what is matter made of? We would say matter is made of these particles, the particles described by the Standard Model of physics. But does that rule out the fact that these fundamental particles might themselves consist of even smaller particles? We have this idea of string theory. So our knowledge of what the most fundamental particles are and what, in reality, the most fundamental particles are is different.

So too in mathematics, Deutsche explains that mathematics is a field where what we're trying to uncover is necessary truth. The subject matter of mathematics is necessary truth in the same way that the subject matter of particle physics are the fundamental particles. But because the subject matter of fundamental particle physics are the fundamental particles, that doesn't mean you actually find the fundamental particles. All it means is that you have found the smallest particles that your biggest particle accelerators are able to resolve.

But if you had an even bigger particle accelerator, you might find particles within those particles. This has been the history of particle physics, by the way. We used to think that atoms were fundamental. Then, of course, we found that they contain nuclei and electrons. In the nuclei, we found out there were protons and neutrons. Inside the protons and neutrons, we found out they were made up of quarks.

And that's where we're at right now. We're at the point where we say that the quarks are fundamental and the electrons are fundamental, but that doesn't mean that we're going to end particle physics right now. What we need are further theories about what might be inside of those really small particles.

Comparing that to mathematics, if necessary truth is the subject matter of mathematics, our knowledge of that necessary truth is what mathematicians are engaged in. They're engaged in creating knowledge about necessary truth. Because a mathematician has a brain, which is a physical object, and all physical objects are subject to making errors of degradation via the second law of thermodynamics or simply just the usual mental mistakes and errors that any human being makes, a mathematician is just as fallible as anyone else.

Then what they end up proving could be an error. So if I understand this point, even mathematics is capable of error. Because mathematics is a creative act, we're never quite done; there could have been a mistake in your axiom somewhere. Ultimately, even mathematics, the creative act, can have error within it.

More Articles

View All
Something Strange Happens When You Keep Squaring
Take the number 5 and square it, you get 25. Now take 25 and square it, you get 625. Square 625, and you get 390,625. Do you see the pattern? 5 squared ends in a 5, 25 squared ends in 25, and 625 squared ends in 625. So does this pattern continue? Well,…
Exoplanets 101 | National Geographic
(Dramatic music) [Narrator] They are nestled in the final frontier, countless worlds scattered throughout countless galaxies, challenging the notion that we are alone in the universe. Exoplanets are worlds that exist outside of our solar system. Also kno…
Is Humanity Inherently Evil? | The Story of God
I’ve come to meet Baptist Reverend and theologian Cutter Calloway to find out whether original sin means we are all evil at heart. “Pleasure to meet you.” “Thank you, have a seat.” “Thank you. Which book were you reading?” “The first few chapters of G…
Hydrodynamic Levitation!
Check this out! Hahaha, isn’t that awesome? That is hydrodynamic levitation. Check it out! This styrofoam ball is levitating on this stream of water, and it’s doing so in a very stable way. The set up is so stable you can play Frisbee through it, which is…
I watched the Eclipse in Argentina - Smarter Every Day 221
Hey, it’s me, Destin. Welcome back to Smarter Every Day. I am in the globe museum in Vienna, Austria, and going to show you something really neat. This is called a Lunarium. A Lunarium is a really interesting device used to calculate the position of solar…
A Warning For The 2023 Stock Market
What’s up, Graham? It’s guys here! So, 2023 is already off to an interesting start because, in just the last week alone, we’ve seen a woman go viral for buying a 1998 Ford Escort for 289 dollars a month for the next 84 months. A teacher was charged for ru…