Math: Real or Created By Humans?

[saminator910]

is math "real", or created by humans, and other questions about the nature of math.

These questions have disturbed me for the past month. If I define a certain mathematical structure, say a function, is it real? what makes it real, when a class of students ponders a function are they all just imagining this same hypothetical object, or does it exist? Do we humans create math by assigning symbols, or values to objects? Does all of math exist beyond what we humans know, is it all present but undiscovered, or have we been building on axioms to create more math. Have the primes placed in our number system been distributed at the beginning of time, or have we humans created them by defining operations such as division on a number system that we have made up? Can anyone give me any insight on these questions?

 

[LCKurtz]

Perhaps not a direct answer to your question, but you might like to ponder what Professor C.R. Wylie was talking about in his sonnett "Paradox":

Paradox
by C. R. Wylie

Not truth, nor certainty. These I forswore
In my novitiate, as young men called
To holy orders must abjure the world.
'If . . . , then . . . ,' this only I assert;
And my successes are but pretty chains
Linking twin doubts, for it is vain to ask
If what I postulate be justified,
Or what I prove possesses the stamp of fact.

Yet bridges stand, and men no longer crawl
In two dimensions. And such triumphs stem
In no small measure from the power this game,
Played with the thrice-attenuated shades
Of things, has over their originals.
How frail the wand, but how profound the spell!

 

[haruspex]

The questions we ask, and hence the branches of mathematics that are developed, are to some extent cultural, but the answers we get are not. These follow from logic which is quite independent of any physical facts about the universe in general or us in particular (though some philosophers may disagree).
Any sufficiently advanced civilisation will develop counting and arithmetic, completely equivalent to ours. They may go on to ask questions about numbers, leading them to invent the concept of a prime number, and discover many of the same facts about them.

 

[TGlad]

If I define a certain mathematical structure, say a function, is it real?

It is a real concept

 

[Curious3141]

It is a real concept

“Of course it is happening inside your head, Harry, but why on Earth should that mean that it is not real?”

Dumbledore always says it best.

 

[micromass]

This thread does not meet the guidelines of the math forums. The math forums are for technical math questions only.

 

[HallsofIvy]

This is a question on the philosophy of mathematics, not mathematics.