One of the strangest questions I have asked myself as I have studied mathematics is “When can I call myself a mathematician?”. There does not seem to be a satisfactory answer. It is perhaps ironic that in a field renowned for the rigor of its definitions, basic terms like “mathematician”, “mathematical maturity”, and even “math” itself go undefined. Sure, these words are commonly used, and many people have some sense of what they refer to and what they do not, but explicitly spelling out that meaning is tricky. Rather than just being a pedantic exercise, thinking about one’s self identity with regards to math is an important part of learning mathematics.
This topic comes up a lot nowadays in relation to k-12 math education. Educators argue (convincingly) that getting students to see themselves as someone who can succeed in math is a crucial part of the process for those students to learn, retain, and utilize mathematical concepts. While math anxiety runs rampant amongst the lower levels of mathematics education, the upper levels of mathematics are rife with imposter syndrome and insecurity. I often question whether I am ‘good enough’ or if I really ‘belong’, and I know many of my peers (and even my professors!) feel similarly. That question, “when can I call myself a mathematician?” is really a stand in question for deeper concerns about belonging and achievement. There is no universal, agreed-upon moment of acceptance in the mathematical community, and so the individual must substitute their own.
Below I consider some possible ways of defining when is appropriate for someone to call themselves a mathematician. I have seen people argue for each of these viewpoints, online and in person. I point out some advantages and flaws of each.
Self-Identification
I want to call myself a mathematician. I feel like a mathematician, and that is how I think of myself. As an undergraduate preparing to (hopefully) enter graduate school to pursue a PhD in math, I am certainly more knowledgeable about mathematics than an average person off of the street even though I am also much less knowledgeable than my professors or current grad students. The self-identification view says that my skills and relative knowledge do not really matter so much as it matters how I view myself. If I feel like a mathematician and identify with the label and the group, then that is enough. This is by far the most broadly inclusive viewpoint (including students of all levels, self-learners, and professionals in math heavy fields), but it is also guilty of kicking the can down the road, so to speak. Allowing people to self-identify avoids answering the titular question by saying, essentially, “you can call yourself a mathematician when you feel ready to call yourself a mathematician.” Liberating, but devoid of guidance.
Recognition by Others
Here we flip the previous view on its head: instead of thinking about when a person feels ready to call themselves a mathematician, we focus on when others (like the person’s peers) feel comfortable calling them a mathematician. I do not particularly like this viewpoint. Just like the previous viewpoint outsources the question to the individual, this viewpoint appeals to some sort of ‘wisdom of the crowd’ without any indication of what that wisdom might be. This viewpoint makes math feel like an exclusive club where you need to know someone in order to be invited in. And we should not forget how recently it was that the ‘crowd’ felt that women and minority groups should be excluded from the club.
Professional and/or Student
This viewpoint is based around your occupation and how you spend your time. If you are paid to do math, then you are a mathematician. Continuing off of that, if you are a student who is primarily studying mathematics then you are a mathematician. Some people like to add the requirement that the student is in a formal program of study, such as enrolled in a university, but personally I think that if you are studying on your own then you still count as a student. This viewpoint captures the idea that a mathematician is someone who ‘does’ math, and for that reason I feel this is the best general description of what it means to be a mathematician. It is broad and inclusive enough to capture most cases I feel embody the term “mathematician” but still provides guidance about when you can and cannot be considered a mathematician.
There are still questions about what it means to ‘do math’, but that is a discussion for another day.
Expert in the Field or Contribution of Original Work
I see these two viewpoints brought up occasionally, but they can generally be lumped together. They tie the title of mathematician to achievement. The advantage of thinking like this is that there is no doubt that someone who meets this definition is deserving of the title. If someone has made an original contribution to the field of mathematics or are recognized as an expert in the field, then what can they be called other than a mathematician? This may be a roundabout way of appealing to the ‘recognition by others’ viewpoint, but at least here there are specific factors listed. The downside here is that it is restrictive. Depending on how tightly or loosely one defines ‘expert’ and ‘original work’, some math professors might not fit the definition which seems like a serious oversight.
Obtaining a Degree (Such as PhD)
If you were to pick a single moment to delineate between ‘not being a mathematician’ and ‘being a mathematician’, the moment of earning a PhD is about the best you can do. The moment encompasses elements of all the other viewpoints: The person earning the degree has chosen to spend years studying and doing mathematics, so surely they identify with math in some form. They are being recognized by their peers, faculty, and an institution as being worthy of receiving the degree. They will have essentially been a professional student for several years leading up to the degree. And in order to receive the degree they must have demonstrated some level of expertise or original work. This viewpoint also has the advantage of providing guidance: either you have a PhD and can call yourself a mathematician or you do not and therefore cannot. Everything just comes together so neatly. And yet ….
Is there really a significant difference between some a week before getting their PhD and that same person a week after getting it? Is that difference enough that the latter deserves to be considered a mathematician and the former does not? I do not think so. And this view excludes all of the people who get a master’s degree, which shares many features with a PhD, or a bachelor’s degree, or who self-study and learn math on their own. This view also casts the PhD as some sort of destination in and of itself on the journey of learning mathematics which, so I am told, is not the case.
Conclusion
There is no straight-forward answer to the question of when you can call yourself a mathematician. That may be annoying to people like me (I would love to just refer to myself as a mathematician all over this website, but I would feel guilty doing so since I am still a student), but overall the lack of a formal definition is likely a good thing. Mathematics is broad and diverse, and so are the people who do math. To draw a line in the sand is to define an in group and an out group, and that does not help anyone.