If one is talking about paying the bill at the groceries, filing income tax returns, or making a transaction at the bank, one may be right in saying that advanced mathematics has no application in these and similar everyday contexts.
But if one is an actuary, an aircraft designer, a submarine builder, or an astrophysicist one knows all too well that advanced mathematics is not only useful, but indispensable.
Then again, it depends on which branch of mathematics one is talking about. Number theory is as useless a branch of mathematics as you can get. But even neuroscientists find Fourier transforms to be useful.
When one has not been involved in such matters it is difficult to understand this, and one tends to become eloquent on the uselessness of mathematics!
Spurts of Thought 