Let's discuss Mathematics

I thought that you were initially suggesting that having many "uninteresting" object is the flaw of the "true false" logic. Then again being "interesting" is subjective.

 

No, I never said they are a flaw (ironically, you can even form this in the P--->Q fashion). How can something that produces stuff be itself responsible for a flaw when it is a mental construction? Mental constructions don't have unintended byproducts like physical constructions do (again from the hypothetical point of view of the construction itself ) and this because in a mental construction the observer (you) is very linked to the construct (your mental world).

Anyway, the first to create a formal logic system was Aristotle, and his included more than true/false (also had "indistinct"). The dynamics of that system were different due to using a larger grammar (basically that of the greek language). But it should be noted that the first to present a formal system where stuff like that in the current one are true, was Philon of Megara, who famously argued that a false conditional will always bring about a true statement.

 

A very general question.
What kind (ie relatively more tied to which current) of "future math" do you think Erdos had in mind, when he spoke of those possibly being needed to prove the Collatz Conjecture?

 

Linear: y = ax + b
Quadratic: y = ax^2 + bx + c
Cubic: y = ax^3 + bx^2 + cx + d

Why is quadratic called quadratic, rather than planar? Should not quadratic have x^4 in it?

 

Quadratic's root is the same as square. So 4 sides, but literally x^2

 

Here periphrasis is used, and they are called "first degree", "second degree" etc

 

I think it is also worth noting that virtually no highschool student is actually aware of why the formulae for third-degree equations work. Even second degree are learned mainly as formulae leading to two roots for real numbers. It would help if students actually relied less on memorizing some formulae, cause no one is going to examine something new by just parroting those.
Then again, what do you expect when almost all of the math "problems" to be solved in exams merely ask you to turn the equation into a difference or addition of squares? You don't need insight on how lego are created, if all you want to do is model the same hut 1000 times.

 

I'm not sure how my colleagues do it but I guarantee that I prove all the second degree formulas to my students every year (those who are on the year where they get taught how to solve them of course), showing them how you find the roots (if they exist) and why in other cases they don't.

 

What about the third degree?
Also, it is a gimmick to have a problem which just needs you to memorize the third degree formulaes or you are stuck, when you don't even know why they work. Rewarding isolated memory isn't a good idea, non?

 

Third degree isn't really a subject we study (except if there's an obvious root, which means it's just the study of a second degree equation), although sometimes when we start talking about complex numbers it's mentioned that "i" was first invented for third degree equations.