[imok20]

Ah, don't we wish. There's this thing called an "Axiom" that is, ruefully, generally, arbitrary. Definitions, too.

e.g. Some say the set of natural numbers contain 0, some say it doesn't.

Granted, the kind of math being discussed here isn't open to much interpretation, but I thought I'd note it.

[camccann]

Definitions have nothing to do with truth, they serve only to clarify communication by establishing a common language; and mathematics as a whole makes no claim regarding the truth of axioms, only what a set of axioms do and do not entail.

There may be disagreements in matters of taste as to what Choice of axioms (har har, little joke there) one makes, but given a basis of axioms to work from--rarely more than a handful--the rest is, for most purposes, not at all open to interpretation.

[hexis]

Rarely is a person screwed by a controversial axiom.

[thomaspaine]

You'd be surprised. The first thing that comes to mind is modern macro-economic forecasting, which is built on a host of controversial axioms. These forecasts are little better than Roman augury, and one could argue they are actually a net negative because they give us the false pretense of knowledge.

Using game theory to make predictions, expected utility theory, etc the list goes on and on (sorry to pick on economics, I'm sure there are plenty of other fields that suffer the same problems).

Just look at some of the assumptions made by the financial engineers who caused the recent financial crisis if want your head to explode: http://en.wikipedia.org/wiki/Black–Scholes#Model_assumptions

[roundsquare]

Applied math != math.

In fact, the problem with the axioms your talking about isn't that the math is wrong, its that the axioms aren't "true" of the real world.

Not that what you are saying isn't important, but you are talking about two completely different things. I mean, compare the axiom of choice to "people maximize expected utility." One of them is about the pillars of mathematics/logic, one is about how people act.

[hexis]

You and I might be using the word "axiom" differently.

[thomaspaine]

All right, in the black-scholes example I admit that those are not axioms in the traditional sense. Maybe the expected utility axioms would be a better example: http://en.wikipedia.org/wiki/Expected_utility_hypothesis#von...