Many things you learn as impossible in math are possible, just not possible with the current level of understanding. Calculus isn't an end. It is the start of everything. Compared to what comes after Calculus, learning Calculus is the equivalent of learning to count to 10.

Told, you can't divide things by zero. Did this for multiple years in engineering and calculus. We divide by zero all the time.

Told there is no square root of a negative, there is. We called it imaginary, its not imaginary. it exists. We could have called them extradimensional numbers, because that's what they are. Numbers on a different dimensional line than the normal real number dimensional lines. In early school, there is no need to understand this yes as its not something you use in day to day life. Its physics math tool offering a new dimension just like, x, y, z. Now you got xi, yi, zi. That's 3 new dimensions on top of the existing 3 that can used for more detailed information about a point.

Told there is nothing bigger than infinity. There is. 2*infinity is bigger in that is grows faster. Power sets which are infinite sets of infinite sets are bigger as well. You find there is an entire new number line just for the infinite numbers, often called the non-ordinals.

There are lots of solutions for those things learned in the past that had no solutions. The math just wasn't known yet.