Is mathematics perfectly flawless?

How do we know that our mathematics is right? Can we really say with complete certainty that our mathematics is correct? That it is totally flawless and able to explain all the phenomenon of the natural world perfectly? If say a superior race of life forms from the far reaches of the galaxy came to us and demanded that we show them what we know, threatened to enslave us if we refused to show them, and wipe us out completely if our math turned out to be flawed, would the chance be worth taking?