Is math built on assumptions? I just came across this statement when I was lecturing a student on math and strictly speaking I used: 

Assuming that the value of $x$ equals <something>, ...

One of my students just rose and asked me:

Why do we assume so much in math? Is math really built on assumptions?

I couldn't answer him, for, as far as I know, a lot of things are just assumptions. For example:


*

*$1/\infty$ equals zero,

*$\sqrt{-1}$ is $i$, etc.


So would you guys mind telling whether math is built on assumptions?

Mathematical and ordinary language and reasoning are the same in this respect. 
If there is a general question of whether and how human thought relies on hypotheticals, that's an interesting subject to explore, but the only reason it appears to be happening more often in mathematics is that the rules of mathematical speech are more exacting and force the assumptions to be brought out explicitly.  In everyday communication there is a larger collection of assumptions, most of which are not articulated, or are assumed (often wrongly) to be carried by context or shared background.
