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I studied mathematics for my undergraduate degree, but today I work in IT. A friend of mine from my university days is on course to earn a doctorate in statistics, and he is preparing to take an actuarial sciences exam this summer.
While we were discussing his research today, he sent me a picture of the virtual setup he uses to do work while mobile: OneDrive to store documents, a symbolic calculator app to perform basic calculations, and OneNote to take notes and compile data. In response, I sent him a picture of some of the items lying around my desk: my Concise circular slide rule, a Charvos drafting tool set dating to 1947, and an "advanced mathematics" book published in 1959, complete with a table of mantissas of logarithms.
The moment, while humorous, was an interesting moment of reflection. His tools were those of abstraction: a textbook meant to examine theorems and provide the reader with logical exercises, a symbolic calculator meant to manipulate unknowns and indeterminates, and a space for contemplating the reasoning behind the conclusions being studied. My tools, on the other hand, were those of computation: a mechanical device meant to quickly perform calculations with a few decimal places of accuracy, drawing implements to create approximate representations of theoretically-perfect figures, and a reference book focused on producing numerical answers instead of logical constructs.
The study of mathematics is, essentially, the study of logic. Logic is first applied to the manipulation of set quantities--this is called arithmetic. Certain properties of those manipulations are pointed out and examined, at which point they are applied to unknown quantities--this is called algebra. The same process is applied: unknown quantities are manipulated, properties are pointed out and examined, theorems and equations are built. This continues through geometry, calculus, linear algebra, topology, Galois theory, and so on. At each level, logical tools are applied to objects, and we study the ripple effect caused by using one logical rule or another.
This is what I was being trained to do in my university studies, but it is not what most of the world, especially industry, uses mathematical processes for. People and businesses are faced with problems, and all they want are solutions, regardless of how one arrives at such solutions. The mathematical underpinnings of the traveling salesman problem are not important to a logistics company, as long as they can develop an algorithm that handles the most common base cases. Banks are not interested in why prime factorization is hard--RSA is difficult to break, and if it can be used to encrypt financial transactions, it's good enough. And even if the solution presented is crude, or perhaps not even mathematically correct in all cases, what matter is if it works for what the user needs it to do.
The solution-oriented approach to mathematics, and indeed all problem-solving, is exactly what is expected of me in my current job as an IT professional. It's also the hardest part of my job. I still find it a little unnatural. But today's conversation with my friend was another reminder of how my interactions with mathematics have changed since I left university.
I don't focus on the process anymore. Now I have to focus only on the answer. I no longer show my work.
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[Last updated: 2021-10-28]