I am mathematician by training. The algorithms relied mostly on undergrad level mathematics when I took some courses six years ago, not easy, but I think there

I am mathematician by training. The algorithms relied mostly on undergrad level mathematics when I took some courses six years ago, not easy, but I think there are harder algorithms. I think it is qualitatively different from programming, because you try to find a reasonable good fit for data you know to guess new future data. Classical programming relies on rules and decisions. ML is closer to numerics, statistics, simulations. Guess the function from the data vs define a function and programm it.