Quantitative math might be the wrong word, maybe applied math? In quantitative finance, you make quantitative models about the world, and build math that realize those assumptions and understanding. A simple example: options are a great financial trading instrument that you can model mathematically, the simplest being the Black-Scholes model. You can imply things like volatility of the stock price based on the price of the option to get a better understanding of what a risk neutral market is thinking, and compare that to the actual market distribution.
>And what were the equivalents of DL/ML for physics before calculus?
This is a good question. Before Newtonian calculus, and the laws of gravitation, people were building very complicated conic models (ie. eclipses, parabolas etc.) to get better and better prediction of planetary motion. A lot of parametric math came out of this, with many sophisticated models getting better and better, giving these astronomers an illusion of progress. However, Newton's insight was that motion is connected to mass, and this insight was the basis of how to derive the laws of motion, which gave us the laws of gravitation (F = (Gm1m2/r^2)). This insight eliminated the previous Keplarian models of motion, because you were now able to predict the motion of arbitrary rigid bodies using very simple math (we teach this in highschool). Ofcourse, Newtonian motion has its limitations that's why we have quantum physics and Einstien's relativity theory. But for practical technological applications, Newtonian physics on its own gets you incredibly far.
Where is ML/DL? It would be akin to Keplarian elliptical motion. More realistically however, it's closer to aether theory of light, and will go the way of GOFAI. This stuff isn't grounded in modelling any scientific observation. Moreover, they are mathematically useless. Back propagation doesn't converge, and why should you fit your data to an arbitrary mathematical structure? In practise, DL/ML doesn't work at all, you will be much more successful by modelling your problem mathematically. For example, consider an automobile manufacturer, which has all kinds of moving parts in their planes. They typically model each part mathematically (ie. gear x under goes exponential time decay), and imply their parameters using rigours test data. Then you use some sort of an empirical statistical model to predict the failure.
I've seen deep learning companies come and fall flat on their face trying to beat the accuracy of these deterministic systems. Those guys needed a lot of data, and GPUs. I'm not even criticizing the fact that DL is a black box. It's worse, it's inferior to everything out there on every metric imaginable. These mathematical models in contrast have been in production for decades, with yearly updates, and they run in real time with little historical data, they are fully understandable and they beat every method we know of.
This isn't the first time multi layer perceptrons gained hype. They didn't work in the 80s, or 90s or the 2000s, they don't work now. The math behind DL is the same that we had in the 80s, they just called it multi layer perceptron. None of the ideas in modern ML/DL are new, all these ideas like reinforcement learning, GANs etc.