4 ms·

> many people thinking mathematics is anything other than a language. I disagree with the claim that mathematics is only language, if by language you mean term

> many people thinking mathematics is anything other than a language. I disagree with the claim that mathematics is only language, if by language you mean terms and definitions. The EASY part of mathematics is the language. There are deep truths, too, and they are not just language. For a (kind of) popular example, the question of "Where do the zeros of the Riemann zeta function lie?" is way way more than just vocabulary. There is a 20 minute video by 3Blue1Brown on the subject. [1] [1]: https://www.youtube.com/watch?v=sD0NjbwqlYw https://www.youtube.com/watch?v=sD0NjbwqlYw

godelski 3y ago
> The EASY part of mathematics is the language. This is where I highly disagree. Doing the math is doing the language. I'm not sure which part is "easy". Even setting up problems is often incredibly difficult. This is where many physics students often struggle, despite having strong math skills there's a challenge to describe the problem to be solved. Even strong mathematicians often struggle to translate between mathematics and their native spoken language. Though 3B1B is quite good at doing this, though there is quite a lot of simplification to goes on due to the target audience. Like I said to the sibling comment, do not mistake how powerful and impressive language is. It created our modern world and there's a reason it is more important to us than even our phones. But all languages, including math, are never complete. They cannot describe everything, unfortunately. But I thought my name would have indicated that I was well aware of this notion. > "Where do the zeros of the Riemann zeta function lie?" is way way more than just vocabulary And a language isn't just vocabulary. That's like saying a programming language (which remember has a direct correspondence. They're equivalent) is just tokens. Idk if you want to look into CH Correspondence, Lambda Calculus, Abstract Algebra, Category Theory, or if I should just quote Poincare about mathematics being the study of relationships.
- Koshkin 3y ago
  A language is invented; mathematics is discovered.
  - godelski 3y ago
    Nice claim there, got anything to back it up with?
    - Koshkin 3y ago
      Mathematics and Its History by Stillwell might give one a good idea.
      - godelski 3y ago
        That's not a real answer. But since mine is easier, I'll just lay some stuff out. Which is real? Finite ZF? ZF? ZFC? Are you calling one of these math and the others not? What distinguishes them? Are infinities real? Are they not? No matter your choice we're going to lead to a decision where math isn't simply due to our ability to have mathematical systems in either form. Similarly I can mathematically describe geometries that cannot exist in our universe or create algebras which are not in fact useful. I lay out a lot more in the other comments. But I really don't appreciate the "trust me bro" responses. They are intellectually lazy and I have no reason to actually trust you.
        Koshkin 3y ago
        Trust has little if anything to do with knowledge. I know calculus not because I trust my professor. Trust no one, only yourself - after you have read the book, of course. What we are talking about here is a rather deep (and obviously confusing) philosophical topic, and HN is not the place to be discussing it in full, but the gist of it is this. Mathematical reality is somewhat different from the physical reality ("our universe"). The focus of mathematics is on abstractions and generalization. But abstractions are direct reflections of the objective (i.e. what is outside our mind). You are asking about ZF, ZFC, etc. Try asking yourself about XYZQJJX (it's language, after all, which you are free to invent, right?) and you won't be getting anywhere. You better trust me on this one.
        godelski 3y ago

godelski 3y ago

> The EASY part of mathematics is the language. This is where I highly disagree. Doing the math is doing the language. I'm not sure which part is "easy". Even setting up problems is often incredibly difficult. This is where many physics students often struggle, despite having strong math skills there's a challenge to describe the problem to be solved. Even strong mathematicians often struggle to translate between mathematics and their native spoken language. Though 3B1B is quite good at doing this, though there is quite a lot of simplification to goes on due to the target audience. Like I said to the sibling comment, do not mistake how powerful and impressive language is. It created our modern world and there's a reason it is more important to us than even our phones. But all languages, including math, are never complete. They cannot describe everything, unfortunately. But I thought my name would have indicated that I was well aware of this notion. > "Where do the zeros of the Riemann zeta function lie?" is way way more than just vocabulary And a language isn't just vocabulary. That's like saying a programming language (which remember has a direct correspondence. They're equivalent) is just tokens. Idk if you want to look into CH Correspondence, Lambda Calculus, Abstract Algebra, Category Theory, or if I should just quote Poincare about mathematics being the study of relationships.

Koshkin 3y ago
A language is invented; mathematics is discovered.
- godelski 3y ago
  Nice claim there, got anything to back it up with?
  - Koshkin 3y ago
    Mathematics and Its History by Stillwell might give one a good idea.
    - godelski 3y ago
      That's not a real answer. But since mine is easier, I'll just lay some stuff out. Which is real? Finite ZF? ZF? ZFC? Are you calling one of these math and the others not? What distinguishes them? Are infinities real? Are they not? No matter your choice we're going to lead to a decision where math isn't simply due to our ability to have mathematical systems in either form. Similarly I can mathematically describe geometries that cannot exist in our universe or create algebras which are not in fact useful. I lay out a lot more in the other comments. But I really don't appreciate the "trust me bro" responses. They are intellectually lazy and I have no reason to actually trust you.
      - Koshkin 3y ago
        Trust has little if anything to do with knowledge. I know calculus not because I trust my professor. Trust no one, only yourself - after you have read the book, of course. What we are talking about here is a rather deep (and obviously confusing) philosophical topic, and HN is not the place to be discussing it in full, but the gist of it is this. Mathematical reality is somewhat different from the physical reality ("our universe"). The focus of mathematics is on abstractions and generalization. But abstractions are direct reflections of the objective (i.e. what is outside our mind). You are asking about ZF, ZFC, etc. Try asking yourself about XYZQJJX (it's language, after all, which you are free to invent, right?) and you won't be getting anywhere. You better trust me on this one.
        godelski 3y ago