At my previous job ( https://www.rsa.com/ ), where I worked for 7 years, I've often had to use various mathematical techniques to do my work as a software engineer.

Here are some concrete examples from my career.

* Combinatorics and probability theory - Entropy analysis of authentication schemes, algorithms for enumeration and analysis of related combinations and permutations, etc.

* Calculus and probability theory - Implementation of bloom filter for space-efficient indexing, tests and analysis of false-positive rates, etc.

* Statistics - Adaptive authentication schemes, performance measurements and predictions, network event correlation, etc.

* Discrete mathematics and algorithms - Tree traversals, graph search algorithms, etc. were useful in a variety of situations, e.g. data retrieval in tree-based distributed databases.

* Asymptotic analysis, Big O notation, etc. - Data deduplication in distributed databases.

* Modular arithmetic - I didn't really implement any cryptography algorithms; I only used them. But the understanding of modular arithmetic was essential to understanding some of the limitations of cryptographic algorithms based on modular arithmetic, e.g. why the message size cannot exceed the size of the modulus, as well as for software engineering tasks like decoding certificates found in network traffic.

* Formal language theory, DFAs, etc. - Parser generators for network event parsing, SQL engine development and related query optimizations, etc.

So these are 7 examples from 7 years. There may be more examples but I cannot remember them right now.

I have felt from my personal experience that although most of the work does not involve mathematics, once in a while an interesting problem comes up that can be solved efficiently with the knowledge of mathematics. It is not easy to predict when such a problem would come and it is not always easy to recognize whether the problem at hand can be solved or analyzed efficiently by known mathematical techniques. So it is good to have someone in the team or be the person who has a good breadth of knowledge in mathematics, so that when such problems do come up, they are addressed efficiently. Fortunately for me, I love mathematics and there were people around me who also loved mathematics, so we got a lot of interesting work done.