5 ms·

I'm sorry, but if you don't know how to solve x+1=7, you don't actually understand maths.

by Tainnor 2y ago

chris_wot 2y ago
I agree, but how far do you take this? Do you say if you don't know the Peano axioms you don't understand maths?
- Tainnor 2y ago
  No.
  - chris_wot 2y ago
    Why?
    - Tainnor 2y ago
      Because knowing how you derive arithmetic from axioms isn't necessary for mathematical modeling. Mostly only logicians, theoretical computer scientists etc . need to know about PA. Euler and Gauss didn't know about PA (it hadn't been invented yet), clearly they were still great mathematicians.
WheelsAtLarge 2y ago
I made it an easy equation to make a point. Pick your favorite multivariable set of equations. Depending on the situation a computer can solve it in a fraction of the time and with better accuracy than a human with pencil and paper. And it can create thousands of variations in a matter of minutes.
- Tainnor 2y ago
  > I made it an easy equation to make a point It was a bad example then. Obviously there are equations that are difficult to solve by hand and you don't need to remember all tricks in order to do successful modeling, but if you're not able to solve x+1=7, it means you don't even understand what an equation is, so you won't be able to use it for modeling anything.
kqr 2y ago
Maybe that's fine? I mean I'm sure a lot of people who fix stuff up in their homes know very little of the physics behind their hammers, but they can still use them just fine. Maybe a good tool does not need to be understood on a deeper level to be used. If we gave students more exposure to maths as a tool to be used, rather than arcane formulae and symbolic manipulations, they could build an intuition and appreciation for it that allow them to use it even if they cannot perform the mechanical transformations of equations on their own. I'm not saying x+1=7 is a good example of that -- my son, who is not even literate, could answer that in the blink of an eye. But recently I needed to get the implied marginal probability out of a partition of conditional probabilities, i.e. solve for p in something like e = ap + b(1-p). Could I have done it manually? Sure. Did I plug it into a symbolic solver? Absolutely. For me the insight lay in (a) knowing that was the shape of the equation I knew, and (b) that I needed to rearrange it to get p as a dependent variable. Actually going through the motions is not that important, in my mind.
- Tainnor 2y ago
  > I'm not saying x+1=7 is a good example of that. Exactly, it's not. I'm not arguing with what you're saying, I'm arguing with what GP wrote.

I'm sorry, but if you don't know how to solve x+1=7, you don't actually understand maths.

chris_wot 2y ago

I agree, but how far do you take this? Do you say if you don't know the Peano axioms you don't understand maths?

Tainnor 2y ago
No.
- chris_wot 2y ago
  Why?
  - Tainnor 2y ago
    Because knowing how you derive arithmetic from axioms isn't necessary for mathematical modeling. Mostly only logicians, theoretical computer scientists etc . need to know about PA. Euler and Gauss didn't know about PA (it hadn't been invented yet), clearly they were still great mathematicians.

WheelsAtLarge 2y ago

I made it an easy equation to make a point. Pick your favorite multivariable set of equations. Depending on the situation a computer can solve it in a fraction of the time and with better accuracy than a human with pencil and paper. And it can create thousands of variations in a matter of minutes.

Tainnor 2y ago
> I made it an easy equation to make a point It was a bad example then. Obviously there are equations that are difficult to solve by hand and you don't need to remember all tricks in order to do successful modeling, but if you're not able to solve x+1=7, it means you don't even understand what an equation is, so you won't be able to use it for modeling anything.

kqr 2y ago

Maybe that's fine? I mean I'm sure a lot of people who fix stuff up in their homes know very little of the physics behind their hammers, but they can still use them just fine. Maybe a good tool does not need to be understood on a deeper level to be used. If we gave students more exposure to maths as a tool to be used, rather than arcane formulae and symbolic manipulations, they could build an intuition and appreciation for it that allow them to use it even if they cannot perform the mechanical transformations of equations on their own. I'm not saying x+1=7 is a good example of that -- my son, who is not even literate, could answer that in the blink of an eye. But recently I needed to get the implied marginal probability out of a partition of conditional probabilities, i.e. solve for p in something like e = ap + b(1-p). Could I have done it manually? Sure. Did I plug it into a symbolic solver? Absolutely. For me the insight lay in (a) knowing that was the shape of the equation I knew, and (b) that I needed to rearrange it to get p as a dependent variable. Actually going through the motions is not that important, in my mind.

Tainnor 2y ago
> I'm not saying x+1=7 is a good example of that. Exactly, it's not. I'm not arguing with what you're saying, I'm arguing with what GP wrote.