I'm a 73-year-old Canadian programmer with no formal education in computing.
After completing a PhD in pure Mathematics, I started working the next day writing scheduling algorithms in Fortran on an IBM 4341 (my supervisor played poker with the company President, so that helped).
Although I picked up Fortran quickly, I had to study scheduling algorithms because my specialty was mathematical logic.
Then I became a university Statistical consultant, but I knew nothing about that either (my boss wanted to learn logic).
Five years later, when Prolog became a popular AI language, I quit my job and began writing expert systems as an independent.
Prolog (PROgramming in LOGic) is based on the first-order predicate calculus, so my formal training was exactly what I needed to understand logic programming.
After that I branched into databases, which I'm still doing as an independent.
So, I didn't need to know anything about computing to become a programmer.
But my domain knowledge (math) gave me a powerful tool to solve some computing problems.
Mathematics isn't just another toolbox - it also represents an attitude. Well-structured code, modularization, and generality are natural by-products of theorem proving. So interest in any area of mathematics will make you a better programmer.
Presumably you mean Justin. His father, Pierre, was supremely confident and for good reason. He was in a class by himself as an intellectual and politician.
I did a PhD in pure mathematics decades ago, simply because it was so interesting. None of it seemed practical at the time (eg. category theory, topology, Horn logic) but that changed when computing began to embrace these ideas. In fact, one of my profs suggested that I study whatever I want until I reach 30, when the concrete begins to settle. That was really good advice for me.
After completing a PhD in pure Mathematics, I started working the next day writing scheduling algorithms in Fortran on an IBM 4341 (my supervisor played poker with the company President, so that helped).
Although I picked up Fortran quickly, I had to study scheduling algorithms because my specialty was mathematical logic.
Then I became a university Statistical consultant, but I knew nothing about that either (my boss wanted to learn logic).
Five years later, when Prolog became a popular AI language, I quit my job and began writing expert systems as an independent.
Prolog (PROgramming in LOGic) is based on the first-order predicate calculus, so my formal training was exactly what I needed to understand logic programming.
After that I branched into databases, which I'm still doing as an independent.
So, I didn't need to know anything about computing to become a programmer.
But my domain knowledge (math) gave me a powerful tool to solve some computing problems.