my thoughts on this topic were sparked by 3 separate incidents that happened to me last night. but first, let me define these terms for the unfamiliar :P
(1) polymathy and monomathy
taken directly from wiktionary, a polymath is "a person with extraordinarily broad and comprehensive knowledge" while a monomath is "a person with an extensive knowledge of a single subject or field, but little knowledge of others." in other words, a polymath has expertise in a variety of subjects, while a monomath specialises deeply in just one.
well-known polymaths include
- da vinci (artist, scientist, engineer, anatomist, inventor)
- aristotle (philosopher, biologist, physicist, logician)
- newton (mathematician, physicist, astronomer, theologian)
- leibniz (mathematician, philosopher, historian, diplomat)
while well-known monomaths include
- van gogh (painter)
- beethoven (composer)
- marie-sophie germain (mathematician)
(2) "bUt lEiA wHy aRe yOu eVeN tHinKiNg aBouT tHiS wHeN u hAvE sChOoL wOrK u sHd bE dOinG?! 🙄☝🏻"
first of all SHADDAP bcs this is way more interesting and important than school work, but here are the 3 incidents i mentioned earlier
incident 1:
yesterday marked the end of bimo 2 (well actually not yet, but the lectures at least), and so megavan (our head coach) left us with a few of messages. one of the things he mentioned was to stop the hate for math oly subjects. comments like "geom sucks" or "i hate combi" constantly flood our server chats, and although ik ppl are usually half-joking, i agree with megavan when he said that it's not a good culture to have, especially for newcomers who are likely to be influenced to adopt that kind of mindset. megavan talked abt the "main" culture in math oly (it's basically like ppl will call themselves "geom mains" meaning that theyre deeply devoted to geometry, and often times hv little appreciation for the other topics, tho this is definitely not true for everyone who labels themselves as a "main"), and said we shd instead learn to appreciate all subjects, tho it's not wrong to have a favourite. then, to sorta strengthen his point, he brought up zs (very orz ex-imo representative), and said that zs hated geom, which costed him SIX years of non-gold at imo rip (but he fortunately ended up winning a gold in his final year). megavan even dared to say that zs's skill level in other topics were better than wjr's (msia's most orz ex-imo representative who got double gold), but zs performed less consistently simply bcs he refused to like geom.
let me point out the obvious moral of the story here: if u want to be consistently good at math oly, u hv to be versatile across all topics. in fact, i'd say that's the exact reason wjr (who actively preaches against the "main" culture) is so good and can perform insanely well in every test/mock - it's bcs he has never "main-ed" anything, and is roughly equally good in every topic.
i realised this a while back, and for that reason, i spent months in 2024 grinding each topic (algebra, combi, geom, number theory) accordingly in attempt to balance out my skills (tho i can say i still hv more confidence in my geom skills despite rarely ever practicing it hfdshfdjs). ultimately, i think it was a good choice bcs i seem to perform more consistently across topics now (at least at the p1/4 level), but honestly sometimes i can't help but get jealous of geom mains who are able to crack a p3/6 lol xD
incident 2:
i was scrolling thru substack and this post popped up in my home feed. the part that really struck me was what they said abt the learning curve. if u're too lazy to read it, basically the writer says that as ur expertise grows, ur learning curve flattens, which i think is 100% true. like think back to the times u've studied using a textbook. ur first read is the most crucial one, accounting for maybe 50-70% of ur knowledge. every read after that just fills in the gaps, but the more and more u read, the less and less gaps there are to fill - same goes for everything else, even skills (e.g. it might take only a few months to get ur running pace from an 8 to a 5, but then it could take u forever to get that down to 4.30). u could argue that knowledge in a certain field is infinite and therefore there are infinitely many gaps to fill, but "not all knowledge is equal" and so the significance of that "fill" begins to decrease as ur expertise grows, tho yes i agree that's debatable haha
BUT point is, the way one could work towards being a polymath is to dive into a certain discipline, and stop as soon as they hit a plateau OR if their studies start getting too niche (i would argue that hitting a plateau/nicheness implies a very decent level of knowledge already) to move on to the next thinggg. this way, they build a strong foundation across multiple fields and are constantly learning A LOTT bcs they're always riding on the steep slope of the learning curve + tackling the most valuable knowledge there is - so essentially they're like hyperproductive all the time
incident 3:
well this one didnt reaaaallly happen by chance, but i noticed a while back that some guy in the bengkel imo server set his discord status to "day XX | polymath push challenge." after those back-to-back incidents that got me thinking abt polymathy, i got curious and so i dmed him asking abt this "polymath push challenge" thing. he explained that some random indonesian youtuber started a community where ppl would actively work towards becoming a polymath. he told me he learnt/studied from youtube, and every day he'd make sure to be consistent and track his goals. i rlly admired his efforts, and this intrigued me abt polymathy even more
(3) the darkside of monomathy
in today's world, we're generally expected to specialise in certain disciplines, and i dont think that's all that bad. (specialisation is also what unis look for!) realistically, it's near impossible to contribute to a field if we only ever skim the surface of it, and so specialisation is necessary. but i think bcs of this, we tend to be ignorant in other disciplines - like a kind of intellectual tunnel vision - and we start missing the bigger picture.
as for myself, i consider myself decently knowledgeable in stem fields, but history? geography? politics? finance? yea no im like embarrassingly STUPID and clueless in those disciplines SO DONT EVEN ASK. i can get good grades if asked to study it like in school, but i study it just for school and forget everything right after the exam oops. but it sucks bcs i know i SHOULD learn it, and learn to enjoy it even. and ngl not knowing the bare minimum of those fields makes me feel like rlly dumb and stupid. even in math, sometimes i think ive specialised too much in math oly. like i still know nothing abt things like multivariate calculus, real/complex analysis, etc.
(4) polymathy vs monomathy + conclusion
as with many open-ended questions, u can probably guess the cliche thing im about to say: neither is superior to the other, the key is striking a balance. yea, disappointing conclusion, huh? but here's my perhaps more interesting take: both are essential, but i still think we shd prioritise monomathy more than polymathy.
see, polymathy helps u connect the dots between things. one field can often provide insights to another. like how maths and physics are closely tied. so are physics and chem, chem and bio, bio and psychology, psychology and the arts... the chain goes on and on. but revisiting my previous point, i think in a time where most fields have already reached such a niche point, it's very difficult to contribute much without specialising in smth ykwim. in earlier times, i think polymathy was more feasible, bcs neither the fields nor the distinction between the fields were as well-defined/developed as they are today. like think abt it, we credit newton as a major contributor in physics, but in some way... he "invented" it? as in, he defined what physics even was, if that makes any sense. not to mention, bro invented calculus. point is, the foundational principles weren't fully developed yet, and so in some sense it was easier to be a polymath while contributing to the field bcs everything was rather shallow at the time. but now, like i said, specialisation is generally seen as superior, bcs everything has exploded in complexity so u would need to know smth deep enough in order to actually DO smth with it.
also, i generally think specialisation is much more impressive than polymathy (at a surface level). FOR EXAMPLE, my younger bro used to play lots of games. basically, he'd install a game and play it... but after a couple weeks in, as soon as he got stuck on a level for too long or smth, he'd give up, delete the game, and install a new one. so yea hes played a lot of games in his lifetime, and has achieved a decent skill-level for many of them. but wouldnt u agree it's much more impressive to meet someone who has... say, completed all levels in all candy crush games? (i would also like the point out here that i completed all the levels in plants vs zombies 1 when i was like 9 - yes im soooo cool i know.) like, i think we can agree that being extremeeely good in one thing is much harder than being decently good in a whole bunch of things. it's also the reason unis favour students with a spike ig, bcs it shows the student rlly dedicated a lot of effort to master that ONE THING, instead of just scattering their effort here and there to win mediocre awards in a bunch of things (jack of all trades, master of none).
AND SO. that's why i think monomathy should be a higher priority, but i still rlly think polymathy is very very essential bcs otherwise u'll be stupid LIKE MEEEEEEEEE!!! also, it'll cost u like zs lmao. (more abt why i think we shd work towards being a polymath later.) i did some fancy googling and found this thing called "T-shape person" which is basically what im tryna sayyyy. like i think we shd practice polymathy, but we also need one area of expertise.
despite everything i said abt monomathy being slightly superior, I STILL THINK POLYMATHY IS SEVERELY UNDERRATED, and that we all need to start practicing it. why? okay let's revisit what i said 2 paragraphs ago: "like, i think we can agree that being extremeeely good in one thing is much harder than being decently good in a whole bunch of things." i said that as a reason that monomathy is more impressive than polymathy, but we shd realise that that's also the beauty of (surface-level) polymathy - it's "relatively "EASY." rmbr we discussed "not all knowledge is equal"? by practicing surface-level polymathy, u get to gain VALUABLE knowledge with minimal effort (in comparison to having to spend lots of effort on some niche thing, which is arguably less valuable). now im no genius BUT THAT SOUNDS LIKE A PRETTY GOOD DEAL TO ME. and so that's exactly why... i've decided im gonna start briefly venturing into OTHER FIELDS as well, WOAWWWW. not as a serious pursuit (bcs im still busy wt school), but i wanna dedicate some time every week learning about stuff im not good at (especially the stuff i shd already know) thru online resources, just for the fun of it.
SO YUPPP TO CONCLUDEE, guess im gonna start looking into polymathy now. U SHOULD TOO.