# 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?