I'd love to know a few of those decisions that you've to take on a day-to-day basis (even once every month) as a software developer, which needs calculus and probability.

Since much of my work involves audio and video, practically everything I do can be thought of in mathematical terms. I'm not explicitly writing a function that says "integrate this" or "differentiate that" (except for the Accumulator and Differentiator plugins in my automation logic system[0]). I do write things, both for fun and profit, that have patterns similar to integration and differentiation.

Related to what I said in another comment[1], there's rarely a binary influence from my (admittedly very limited) mathematical and theoretical background, where a decision would go one way with it and another without. Rather, my understanding of calculus and probability shapes the way I think about and approach problems.

For example, when I see a problem that looks like one of gathering data and accumulating a result, I can recognize that it looks similar to a numeric integral, and apply what I know about integration to solving the problem. Integrals and derivatives are also constantly in my mind when I think about the physics of the world around me.

Probability, especially Bayesian reasoning, also influence the way I perceive and approach problems, both in software and in reality. Consciously thinking about prior expectation combined with prior confidence, even if I'm not thinking in numeric terms, helps me to understand how my mind works, know how to communicate new, unintuitive ideas to others, and form more concrete thoughts about my environment.

In summary, a very rudimentary understanding of calculus and probability theory are necessary to understand and reason about (i.e. predict) the physical world. Moreover, I have a general desire to learn all that I can and integrate it into a web of concepts, which I reason about as a combination of directed and undirected graphs, where concepts are vertices, relations between concepts are undirected edges, and influencing concepts and prerequisite knowledge are directed edges.

[0] http://www.nitrogenlogic.com/docs/palace/ [1] https://news.ycombinator.com/item?id=4630006

> I'd love to know a few of those decisions that you've to take on a day-to-day basis (even once every month) as a software developer, which needs calculus and probability.

Machine learning needs an understanding of basic statistics and probability.

I struggled mightily with calulus reuirements when I was getting my CS. I've never really used "pure" calculus more than a handful of times. I'm still glad I took it, though, because the process of learning how to solve complex probelms has been, I believe, very valuable.