But since the advent of computers, empirical math has come back into vogue. Computations that you'd never tackle with pencil and paper are calculated numerically, and much of the deductive work has moved over to studying the properties of numerical algorithms, rather than the actual problems those algos are solving.

The honest fact of the matter is that most math problems can't be solved analytically. Higher-order roots, most differential equations, and many integration problems are intractable in principle. And even if some of them happen to be exactly solvable, it's a moot point; we can solve them numerically without a problem, so there's no need to waste time using deduction. Some people lament the lack of theoretical rigor, but I think we should embrace a wider view of mathematics. Deduction is a hammer, and numerical methods are a screwdriver; you use them both to build a house. Mathematics is not limited to what's theoretically tractable; it's just that, until recently, *mathematicians* were so limited. When you're calculating the strange attractor of a dynamical system, or inverting a large matrix, you aren't quibbling about which axioms are satisfied; you're hacking out approximate truths, just like the Egyptians did long ago.