Back in university, I had many friends who would ask, "We already use libraries, so why should we know differential equations?" Whenever I hear that question, I always think the same thing: we aren't taught mathematics to memorise formulas; we're taught it to gain the ability to break a problem into pieces and reassemble them.
The Source of Analytical Thinking
Being able to judge whether an algorithm's complexity is O(n log n) or O(n²) requires a background discipline of logical reasoning—and that discipline comes straight from mathematics. Someone who has wrestled with calculus, linear algebra, or probability theory approaches a problem with the reflex of "first clarify the assumptions, then prove it." The same reflex kicks in when writing code: first consider the edge cases, then build the solution.
Personally, when I'm solving a complex bug, I often reach for a pen and paper rather than the debugger. I write out the system's state like an equation and search for the step where an unexpected transformation occurred. That habit is a leftover reflex from my mathematics classes, but it has saved my life in software more times than I can count.
Going Beyond Programming
What I really want to emphasise is this: software isn't just "programming." Learning syntax takes a few weeks at most; but modelling a system correctly, choosing the right data structure, understanding the mathematics behind a machine learning model, grasping why a cryptographic protocol is secure—all of these demand a mathematical foundation.
If you stay someone who only "writes code," your toolkit will eventually hit a wall. But if you have a mathematical thinking habit, even when you encounter a completely unfamiliar problem class, you can still produce an answer to the question "How do I model this?" Tackling a network optimisation problem without knowing graph theory, or designing a recommendation system without understanding probability, eventually confines you to a copy-paste level of engineering.
Instead of a Conclusion
For me, mathematics isn't a "requirements checklist"—it's a way of thinking. I think my interest in philosophy actually stems from the same root: both force you to "question what you see." If you want to be a good engineer, you first need to be someone who can ask a good question—and that's exactly what mathematics teaches you.