If mathematics were a game of Dungeons and Dragons, the character classes that would be most highly venerated are the wizards and sorcerors. Wizards are figures like Grothendieck and Noether, people who built huge towering edifices of theory and were masters of the formal. Sorcerors are people like Von Neumann and Ramanujan, mathematicians whose incredible intuitive facilities led them to make massive leaps at which others could only boggle.
Of course, mathematicians don’t fall so cleanly into categories, and most famous mathematicians are both wizardly and sorcerous. But I think the distinction is interesting. And it also opens up the question, what about the other classes?
There are fighter mathematicians, whose up-to-date and specialized knowledge of a specific field allows them to steadily make progress. I would maybe say that Judea Pearl has fighter-like aspects; it seems like he’s been working away at causality for a long time, steadily building and integrating with other fields. For some reason, I also think of Emily Riehl in this way; it seems like she has a strong goal (i.e., making a language for infinity category theory) and is systematically attacking it piece by piece, though I am not tuned in enough to know whether this is an accurate description.
Cleric mathematicians, I could interpret this in two ways. The first way is that maybe a cleric mathematician is one who refactors knowledge. In this sense, I’d say that Bill Lawvere is cleric-y. Another interpretation is that a cleric mathematician is a very good teacher, one who heals their students’ misunderstandings. As I haven’t been taught by many famous mathematicians, I can’t give a terribly famous example, but I would say that Melody Chan is pretty cleric-y, among the teachers that I have had.
What would a rogue mathematician be? I think a rogue mathematician would be someone who steals lots of ideas from other fields and integrates them into new fields. I think the whole field of applied category theory is rather rogue-ish. I don’t know though, I could think about this in different ways.
A bard mathematician, on the other hand, I have a very firm grasp on. These are the mathematicians who know a bit of everything, and spread their knowledge widely through collaboration, writings, and song. There are two bard mathematicians that immediately jump to my mind: John Baez and Paul Erdos. In my mind, the bards are the mathematicians that glue mathematics together, giving it tradition and forging bonds between theories and people. Another strain of bardy-ness are the mathematicians who spend a lot of time illustrating things, like Robert Ghrist or Grant Sanderson of 3Blue1Brown fame.
I think that there is a growing appreciation that wizards and sorcerors are not the be all and end all of what the ideal mathematician should look like, and I think this is a good thing! I don’t really have anything more profound to say in terms of the implications of this, I mainly just thought the classification was interesting.
There are more D&D classes, but their correspondence with mathematical archetypes is left to the reader!