Traits of the Greats


What are the traits of great philosophers? Matthew Hammerton, a PhD student at Australian National University, came across a passage by Cambridge University mathematician Timothy Gowers about how genius is neither necessary nor sufficient for success as a research mathematician, asking whether philosophers thought something similar about those who produce high quality work as academic philosophers.

The passage is from Gowers’ Mathematics: A Very Short Introduction. He says:

Here is a rough and ready definition of a genius: somebody who can do easily, and at a young age, something that almost nobody else can do except after years of practice, if at all. The achievements of geniuses have a sort of magical quality about them – as if their brains work in a completely different way. Every year or two a mathematics undergraduate arrives at Cambridge who regularly manages to solve in a few minutes problems that take most people, including those who are supposed to be teaching them, several hours or more. When faced with such a person, all one can do is stand back and admire.

And yet, these extraordinary people are not always the most successful research mathematicians. If you want to solve a problem that other professional mathematicians have tried and failed to solve before you, then, of the many qualities you will need, genius as I have defined it is neither necessary nor sufficient. To illustrate with an extreme example, Andrew Wiles, who (at the age of just over 40) proved Fermat’s last theorem and thereby solved the world’s most famous unsolved mathematics problem, is undoubtedly very clever, but he is not a genius in my sense.

How, you might ask, could he possibly have done what he did without some sort of mysterious extra brainpower? The answer is that, remarkable though his achievement was, it is not so remarkable as to defy explanation. I do not know precisely what enabled him to succeed, but he would have needed great courage, determination, and patience, a wide knowledge of some very difficult work done by others, the good fortune to be in the right mathematical area at the right time, and an exceptional strategic ability.

This last quality is, ultimately, more important than freakish mental speed: the most profound contributions to mathematics are often made by tortoises rather than hares. As mathematicians develop, they learn various tricks of the trade, partly from the work of other mathematicians and partly as a result of many hours spent thinking about mathematics. What determines whether they use their expertise to solve notorious problems is, in a large measure, a matter of careful planning: attempting problems that are likely to be fruitful, knowing when to give up a line of thought (a difficult judgment to make), being able to sketch broad outlines of arguments before, just occasionally, managing to fill in the details. This demands a level of maturity which is by no means incompatible with genius but which does not always accompany it.

As we’ve discussed before, more than those in any other discipline, philosophers place a greater emphasis on brilliance, or innate, intellectual talent in their assessment of what is required for success at philosophy. Does such emphasis withstand scrutiny, or should we take a page from Gowers and give a lot of credit to other traits? Which ones? More generally, which traits make one more likely to produce high quality philosophy?

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Urstoff
Urstoff
4 years ago

I think there’s a difference between high-quality philosophy and philosophical work that will get you noticed and read. The former is often very boring, whereas the latter seems to always have a combination of novelty and polemicism. The philosophers we remember aren’t the ones that hedge and play it safe. Stake out a novel (and hopefully counterintuitive) position, and if you’re clever enough to rigorously defend it, then you’re more likely to be remembered than not. Report

Boring quality?
Boring quality?
4 years ago

If something is philosophically boring, how is it high quality?Report

upstate
upstate
Reply to  Boring quality?
4 years ago

Urstoff never said that high-quality philosophy is philosophically boring, just that it’s sometimes boring — which it is.

To contribute something myself: I was struck by Gower’s claim about “attempting problems that are likely to be fruitful.” I wonder how this relates to what seems to be a more prominent approach in philosophy, namely, attempting to be right. I often find myself getting worked up over someone somewhere saying something false. I wish I could care less about that and instead get worked up over someone somewhere saying something worth discussing — whether or not what they said is true or false.Report

Richard Yetter Chappell
4 years ago

There’s a big difference between “genius” and intelligence / intellectual talent, right? Gowers himself writes that Wiles is “undoubtedly very clever”. I do think that high intelligence is likely to be a crucial trait for any serious academic discipline. (Which is not to deny that other traits matter in addition, of course.)Report

Matthew Hammerton
Matthew Hammerton
Reply to  Richard Yetter Chappell
4 years ago

I agree that high intelligence is one important trait for an academic researcher to have. However, there are narrower and broader interpretations of what ‘high intelligence’ amounts to. When Gowers discusses mathematical geniuses he emphasises mental speed as one of their defining characteristics. I suspect that many people’s judgments of innate intellectual talent in philosophy are based, in part, on quickness of thought. The student who can instantly follow the logic of a complex argument, or is quick in the seminar room to respond with a good counterargument, is often judged as possessing raw intellectual talent more than the student who takes her time to digest a complex argument and think up a good reply. However, perhaps (along the lines of what Gowers says about mathematics) quickness of thought is not very important for research success in philosophy, and it is other aspects of intelligence, as well as other traits beyond intelligence that matter. Report

Richard Yetter Chappell
Reply to  Matthew Hammerton
4 years ago

Hi Matthew, yes I’d agree with you there! Being quick on one’s feet is a very different (and less important) philosophical talent than (say) insight and creativity.Report

Tom
Tom
4 years ago

I find discussions of ‘conditions for greatness’ to be pretty pointless- as if we could achieve greatness if only we followed the right guidelines. I think ‘great’ people, if anyone, will make their own way. Report

Matthew Hammerton
Matthew Hammerton
Reply to  Tom
4 years ago

I tend to agree. I think the more useful question is: which traits are generally needed to achieve moderate success? This question matters because, in various ways, judgements about whether someone has the right kind of traits to succeed in philosophy influence decisions about who gets hired, or offered a scholarship, or recommended as someone with potential. Report

Daniel
Daniel
4 years ago

I’m pretty sure spending all day on DN is the only trait shared by great philosophers.Report

YAAGS
YAAGS
4 years ago

Well the odd thing here is that what philosophers think of as brilliance and innate talent are precisely those traits that Gowers treats as banal: the insight to see ahead of time where a line of argument will go and the various lines of objection that can be raised against it, and the ability to make connections between diverse fields of thought. No one in philosophy cares about how quickly you can take a complex integral in your head. Why would they? Report

Headcase
Headcase
4 years ago

Solving complex mathematical problems at a young age while your mind dwells into multi-tasking is no value to anyone unless used in the correct pretext. One of the most interesting phenomenon’s I find is that people that have this terrific trait of problem solving maths equations struggle in other areas of life. Mathematical equations can be taught, but I have forever though that knowledge unless used to aid in someone’s life is clearly just pointless.Report

Matthew Hammerton
Matthew Hammerton
4 years ago

One skill not present in Gowers’ list that I think is very important in philosophy is the ability to write well. I take it that the formal methods of proof in mathematics mean that excellent writing skills are not particularly important. However, I think they play a significant role in philosophical success. Having a good argument that is original is often not enough. To get that argument published in a good place where people will read it, presentation matters a lot. Report

Tom
Tom
Reply to  Matthew Hammerton
4 years ago

This is a completely incorrect thought about mathematics. It comes about because most philosophers’ understanding of mathematics comes exclusively via their exposure to logic. But most math is *very* different from logic. Importantly, essentially no mathematics at all is formal in the sense you are suggesting. None. At all.

Writing, and in particular being able to write engagingly and clearly, is as crucial in mathematics as in philosophy. Report

Matthew Hammerton
Matthew Hammerton
Reply to  Tom
4 years ago

Fair enough, I stand corrected. Report

Tristan Haze
Reply to  Tom
4 years ago

I’m not convinced by this, and I think Matthew is trying too hard to be undogmatic and has conceded too readily.

Tom: you seem to be attributing to Matthew an understanding of ‘formal’ such that a proof is formal iff its correctness can be shown on well-defined purely syntactic grounds, or something like that. I.e. the understanding introduced in proof theory in logic. But charity suggests another reading. Namely, something a bit fuzzier, like ‘uses symbols and precise definitions’.

Now I don’t doubt that writing clearly and engagingly is important in mathematical research, but I do doubt that it is quite as important as in philosophy, on the whole. And you haven’t given any argument that it is.

It’s tempting to make a crack about the dogmatic, uncompelling style of your comment being characteristic of mathematicians!Report

Tom
Tom
Reply to  Tristan Haze
4 years ago

It’s also tempting to make a crack about the incessant demand for argumentation in your comment being characteristic of philosophers.

This is a situation where an argument seems unneeded. The claim being made is descriptive: mathematical proof is mostly a matter of the formalism present. Normally, we check descriptive claims (when possible) by comparing the description they provide to the described object and seeing if they match.

So, here’s my recommendation: go read some real mathematics. See if the description provided fits it. If you come away genuinely believing it to be as Matthew describes, then we can have an interesting debate. And arguments will be needed to support non-descriptive claims of the sort `this passage ought to be read this way and not that way’.Report

Tristan Haze
Reply to  Tom
4 years ago

You’ve shifted to a different sort of claim about what ‘is mostly a matter of’ what, and that does sound more descriptive, but the original disagreement was about whether or not good writing is equally important in mathematics and philosophy. And that doesn’t seem, as you want to make out, to be a straightforward descriptive question which can be settled by simple observations.Report

some person or other
some person or other
Reply to  Matthew Hammerton
4 years ago

Just to add to this response: one of my very best friends who is a mathematician (but with a background in philosophy) once told me that he thought the mark of a good math paper (we were discussing how this extends to philosophy!) was that one could skip over all of the formalism and still know exactly what was being said, and confessed to me that he rarely read the formalism unless someone seemed to be proving something in a way that would be useful to his own work. So, writing definitely matters in math! (I have another friend who wrote an entire dissertation in math that only included three mathematical formulas and was otherwise written entirely in English, but I think that is… fairly unusual.) Report

Adam Omelianchuk
Adam Omelianchuk
4 years ago

I find Philippa Foot’s remarks on this subject to be illuminating. She once said, “I’m not very clever at all. I’m a dreadfully slow thinker, really. But I do have a good nose for what is important. And even though the best philosophers combine cleverness and depth, I’d prefer a good nose over cleverness any day!” Report

Michel X.
Michel X.
4 years ago

I suppose this isn’t a very helpful comment, since I’m offering it in a skeptical vein, but I’ll say it anyway.

Since the publication of Linda Nochlin’s “Why have there been no great women artists?” art historians (I’m idealizing somewhat) have been sensitive to the fact that “greatness” doesn’t have all that much to do with ability, talent, or skill, and has a whole lot more to do with one’s social and professional context. So, for example, it’s not really true that Marie-Denise Villers was a less-skilled painter than Jacques-Louis David (some of her work was attributed to him, in fact, and lauded as his greatest!), but she’s almost entirely unknown because… well, because she was a woman and women’s painting was an “amateur” pursuit, and because she painted portraits rather than historical or Biblical scenes and portraits weren’t as prized as the latter two kinds of pictures, and because her work was attributed to others (like David). Similarly, Rachel Ruysch isn’t really any less skilled a painter than, say, Rembrandt: her still lifes are really, really well done, and her technical abilities are indisputable. In fact, she enjoyed a fairly successful career because her work coincided with the lingering effects of Tulipmania in the Netherlands (viz., increased interest in flowers and gardening). She was almost immediately forgotten, however, because still lifes were among the lowest-status kinds of pictures one could paint at the time.

Anyway, the point is just that “greatness” seems largely independent of skill, at least past a certain point. Past that point, it seems to have a lot more to do with timeliness, with working on the kinds of things or problems that people around you value (or will soon come to value) most (along with having access to that world, being lucky enough to attract notice, etc.). Intuitively, that seems to me like a point that also applies to philosophy. A great many philosophers (historical and contemporary) are very good, very clever, highly intelligent, whatever. (Probably most, since the gauntlet of a PhD is no small feat.) Whether they get counted as ‘great,’ however, usually seems to have more to do with what we care about than it does the brute quality of their work. Those who work mostly in subfields at the bottom of the totem pole are much less likely to ever get counted as ‘great’ than those working in subfields at the top, even if their contributions are of similar weight and quality. That’s not to say there’s no room for “genius,” whatever that really means, but rather that we tend to overestimate its contribution(s).

To be clear, I don’t think any of this is necessarily bad. But I do think that we ought to be aware that them’s the apples.Report