Myuncle

It seems any intelligent animal or alien, would agree on math, it's always a win-win situation, any primate or parrot would agree with us on the same math. If in a distant galaxy there are aliens with only three fingers per hand, I bet they would have a base 6 numeral system, if we met each other we would agree on math, but we would have to compromise, change even the symbols, change our base 10 system, or learn their 6 base system, or compromise, agree, and create something in the middle, like a base 8 system...

Since we are part of the universe, is both. Math allows us to have an approximation of reality, without math we wouldn't have that approximation either.

I am an amateur ajb, but just by googling for the word "math", the definition looks always poor and vague, and when a definition is vague, it means that it can be manipulated and used as a weapon to boost your ego. There are so many things to say. Math is an agreement, it can be easily accepted by everyone, as long as we agree that in theory a unity is identical to another unity, 1=1 (all theory, but in practice it might not even exist, since an orange is not exactly identical to an other orange, an atom or quark might not be exactly identical to an other atom or quark). Everything is a consequence of that agreement. That's a very useful agreement between humans, very convenient, that allows us to measure and quantify everything, and to agree on measurements and quantities. Mammals and birds, particularly parrots, can understand various numerical concepts. Everything can be calculated very slowly with additions and subtractions, and everything else is a shortcut of additions and subtractions. The origin of multiplication was the need to create a shortcut for long tedious additions, and the origin of division was to create a shortcut for long tedious subtractions, and so on. These shortcuts are very useful, they make our life more comfortable. My new question is: when should we say "stop" to these shortcuts, are they really useful? Do they make our life simpler and more comfortable? How many of these shortcuts are really necessary? How many of them are only created to win a science award or to sell books? How many of them are used, and how many of them are never used? I hope math prodigies and experts on this website can share a honest answer. Math was born to make our life simpler (just like burocracy and banks...yes...), but if not used porperly it will just make our schools more complicated than needed, discouraging students, and demotivating them.