The maths of today has very little to do with the maths of 500 years ago, let alone 2500 years ago. Sure, we still have the Pythagorean theorem, but in today's modern formulation it's trivial. We still have numbers, but they are no longer something that can be totally ordered. With numbers we even turned things upside down, because we used to first try to define single numbers and only then collections of numbers. These days we say that "a number is an element of a number field", "a vector is an element of a vector space" etc. and we define the structures first. But the biggest departure probably is the widespread reliance on proof. In XVI century you could call yourself a mathematician without proving things, as long as the ideas you came up with worked in practice.

I'm sure that in the programming world we'll still have "if"s and variables/aliases 200 years from now. And that's right about how much commonalities modern mathematics has with the mathematics of the age of Euclid.

Disclaimer: I took a course in history of mathematics and I have to say, if I was born as little as 200 years earlier I wouldn't be able to stand mathematics. These days, it's actually interesting to me. Similarly to how mathematics in primary through high school is really boring.