DiBeos

What does it really mean to be a mathematician? Is it a title you earn with a degree or is it something deeper?

The definition might seem simple at first, we want to say that a mathematician is someone who does mathematics. But as soon as you start asking what that means, things get complicated. Some people say you need formal credentials. Say at least a bachelor’s, maybe a master’s, and ideally, a PhD. In that view, you’re not a real mathematician unless you’ve studied the subject at a high academic level, or maybe even contributed original research to the field.

From a different perspective though, the title shouldn’t depend on a piece of paper. Take mathematicians like Ramanujan, someone who is largely self-taught but who made significant contributions in number theory, or Ada Lovelace, with computing, or George and Mary Boole, or Oliver Heaviside, or Benjamin Banneker, and the list can go on. 

So, if your mind works mathematically, and you’re working with mathematical ideas, even if it’s on your own, aren’t you then a mathematician?

There’s also the more practical, and sort of work-based definition: maybe a mathematician is simply someone who uses math professionally. People like data scientists, statisticians, financial analysts, and engineers. So the people whose daily work involves applying mathematical thinking.

But this definition can be both too broad and too narrow. Too broad, because someone using Excel formulas every day isn’t necessarily thinking about mathematical theory and expanding mathematics in general. But also too narrow because someone might be deeply exploring mathematical ideas in their spare time, but they’re not being paid for it. Does being a mathematician require money? A job? Or just the mindset?

Okay well, let’s assume it’s the mindset. But, in that case, do you also then have to make original contributions to the field? Because in academia, that’s pretty much the standard.

By including that in our definition, we then have to exclude a huge number of passionate math teachers, communicators, and enthusiasts who aren’t publishing in journals but are doing the essential work of spreading and deepening the love for the subject. Take someone who spends their life tutoring high school students in algebra. Or someone who makes explainer math videos online. Are they, then, not mathematicians?

Because of all of these nuances, maybe the question isn’t about credentials or career paths, but identity. Maybe before answering whether you’re a mathematician or not, you should ask yourself: do you approach the world with a mathematical lens, asking questions, seeking patterns, and exploring structure? Do you find joy in solving problems, in playing with numbers, in pondering about the abstract? Do you try to expand your knowledge? Then maybe that in itself is enough. 

Nobody owns the title of mathematician, and there’s no central authority that makes you one. Mathematicians are able to peer review each other’s work without having to have any kind of title assigned to them, just out of pure love for the subject. 

Let’s take Ramanujan for example. He had almost no formal training in mathematics, but because of his obsession and intuitive brilliance, he developed results in number theory that were so deep and surprising that they still fascinate mathematicians even today. 

And he wasn’t “validated” by academia until much later, when G.H. Hardy recognized his genius and brought him to Cambridge. Imagine if Hardy hadn’t taken him seriously. Would history have remembered Ramanujan at all? Does that mean he wouldn’t have been a mathematician?

Or take George Green. He was almost entirely self taught, and received 1 year of formal schooling between the ages of 8 and 9. He wrote a paper in 1828 that introduced what we now call “Green’s Theorem”, which is a foundational result in vector calculus that physicists and engineers still use to this day. He published it privately and was mostly ignored in his lifetime. But nowadays his name is found in nearly every undergraduate math curriculum. No formal training. No academic title. Just ideas.

There’s also George and Mary Boole, a married couple, both of whom were self taught mathematicians. George ended up actually becoming the first math professor of Queen’s College, Cork, in Ireland, again despite being self taught, and Mary wanted to change math education by making it more accessible in her writings (like The Philosophy and Fun of Algebra, Lectures on the Logic of Arithmetic, Logic Taught by Love, among others).

There are many others like them, but the point stays the same. 

Now, take some people who don’t formally contribute to the field. Math YouTubers (like me haha) or independent bloggers who explain abstract algebra, topology, or cryptography with incredible clarity, sometimes, and dare I say often times, they do it better than a university lecture. They’re doing the hard work of understanding and communicating complex ideas, and in doing so, they’re actively participating in the mathematical community.

And then there are the modern examples, the amateur mathematicians on the internet, the kind of people who spend hours on math.stackexchange or Reddit’s r/math, writing up full proofs, finding typos in published work, or solving problems for fun. Some of these users have no formal degree. Others have degrees in entirely different fields. But their posts are often so precise, so rigorous, so insightful, that they could pass for something like graduate-level lecture notes. If someone dedicates their evenings to solving abstract problems and sharing their reasoning with the world, how is that person not a mathematician?

These are people who might never publish papers, never go viral, never speak at a conference. But they return to math day after day, not for recognition, but because there’s an itch in their brain they just want to scratch. They are, in every meaningful sense, doing math. And if doing math is what makes someone a mathematician, how can we possibly exclude them?

So I’ll ask you: are you a mathematician? And do you think defines a mathematician? Let us know what you guys think.