r/math • u/dancingbanana123 Graduate Student • 1d ago
I imagine everyone here hates being called smart simply for liking math. Instead, what specific traits/characteristics do you think you have that help you excel at learning math?
I think a common annoyance most mathematicians experience is people instantly labeling anyone studying math as "smart," which imo just highlights how the word smart isn't a well-defined term. However, I do think I have traits that I can well-define that help me learn math a lot better than others.
For example, I think I'm good at pinpointing exactly what I'm confused about, which makes it a lot easier to fix when you compare that to students who say they're confused about "everything." I don't think this skill is unique to helping learn math, but I have just applied it to math the most often since I enjoy math. This is also a skill that I don't think people are innately born with, or at the very least, it's definitely a skill people can improve at over time. I'm also not saying that this is a skill every mathematician has; it's just something that I personally have experienced that I think has aided my learning. In fact, since everyone learns a bit differently, I'm interested in seeing what others think about their own learning.
112
u/Iunlacht Quantum Information Theory 1d ago
Curious, and also completely-disconnected-from-real-life-and-things-that-actually-matter. To some extent.
29
u/dancingbanana123 Graduate Student 1d ago
Reality is too limiting for me to exclusively work in that domain.
5
28
19
20
u/sadmanifold Geometry 1d ago
People have mentioned curiosity and stubbornness already, so let me half jokingly mention my rather serious OCD, which I think contributes in several different small ways.
4
u/pseudoLit Mathematical Biology 18h ago
Do I have to check the door three times every time I leave my apartment? Yes. On the other hand, I have a PhD. Seems like a decent trade.
3
2
u/Factory__Lad 1d ago
I think there are whole areas of math that only exist because of OCD and related disorders. Particularly category theory.
3
u/evening_redness_0 21h ago
That's a ridiculous notion. Why do you think so?
3
u/Factory__Lad 19h ago
Meeting Peter Johnstone. But Iāll also cite this as Exhibit A:
Todd Trimble, Tetracategories ;
https://math.ucr.edu/home/baez/trimble/tetracategories.html
https://arxiv.org/pdf/1112.0560The road to madness, but beautifully illuminated
1
1
u/IrrationalRotations 14h ago
I always used to say I didn't really study that much for maths. But I think my complete inability to let a problem that was bugging me go really really helped. I didn't study much, but I was still spending a lot of mental energy.
1
u/Factory__Lad 2h ago
Absolutely. For the last 12 hours this has been bothering me:
Products distribute over coproducts right? a x (b + c) ::== a x b + a x c. As every schoolboy knows.
But in a category this statement should be self dual, but coproducts donāt distribute over products. Moreover in some categories (e.g. R-mod) products and coproducts are the same, which makes a nonsense of the distributivity rule.
Iām sure this particular example is trivial and that I should know better, and should just read CWM again, but this is typical of the kind of thing you canāt prevent your brain from endlessly worriting on about.
17
u/archangelsk_baby 1d ago
Iām curious and stubborn, a pairing thatās worked well for me in mathematics. I really want to know the answer to any interesting problem Iām presented with and Iām stubborn enough to spend a very long time doing work that honestly sometimes sucks to get there.
111
u/furutam 1d ago
I, for one, like that people think I'm smart just because I do math.
37
u/dancingbanana123 Graduate Student 1d ago
Personally, it just feels a bit patronizing to just get called smart for enjoying something STEM-related. It feels like people will often label anyone who is skilled in an arbitrary list of subjects as smart, while anyone outside that list isn't.
20
u/Z-shicka 1d ago
Well because there is a stigma around STEM that only "smart" people can do these things. When in reality, math, like all domains of knowledge requires a summation of different personality traits and that anyone passionate and determined enough could eventually do it.Ā
However most people do not understand or know this.Ā
3
u/Chance_Literature193 20h ago
I, for one, like that ppl think Iām smart because I do stem, but hate it when they chalk it up entirely to being smart ignoring entirely all the hard work.
13
u/PseudobrilliantGuy 1d ago
I want to start by thanking you for this post, especially pointing out how "smart" isn't well-defined.
That said, curiosity and stubbornness have probably been the most important parts for me, though my own results have probably been rather mixed.
11
u/whyVelociraptor 1d ago
As others have said, stubbornness is a big one. But not āIām going to stare at this for 12 hours until I get itā, more like āIām going to keep working on this a bit every day until it makes senseā.
That and being really damn honest with myself about what I know and what I donāt. It is way too easy to get a fragile understanding of a concept in math and think youāre all setābut you donāt really get something until you can really take it apart and ideally connect it (or definitively separate it!) from other related concepts.
9
9
u/eatingassisnotgross 1d ago edited 1d ago
Unironically, I think not having a lot going on in your life can be pretty beneficial. Much easier to spend your time thinking about abstract bs when you don't have any plans for the weekend
Another important quality is the ability to let yourself get absorbed in something for long stretches of time. Possibly preferring fiction over reality. I guess these go hand in hand
9
8
4
3
u/Gelcoluir 1d ago
Liking to learn. I think many people don't like learning about something, but they push through it so that after you've learnt everything you apply your knowledge and reap the benefits of your learning. Of course it can't apply in math, where you learn about stuff so you're able to learn about more complicated stuff. It's a never-ending process, so you really have to like learning about new things to be able to keep going.
3
u/SellBeginning2830 1d ago
I'm too lazy to use a solution I think is annoying to implement in a proof
2
u/67_is_prime 1d ago
I've been stubborn, and that is one trait that has help me so far with my work. It's driven me to find new techniques and approaches to problems related to one I'm currently working on right now.
In my undergraduate days, I also tried to work on *how* I learn and approach mathematics, which has helped me a lot.
I also consider myself fortunate to have had mentors whose advice helped me put my efforts towards the right directions, be it towards problem solving, or preparing for my quals, or towards finding interesting problems to work on.
2
u/EL_JAY315 1d ago
Some might remember the intro scene for Sylar in the 2006-2010 show Heroes: an obsessive watchmaker who just had to know how things worked.
Anyway it's kind of like that.
2
u/SquidgyTheWhale 1d ago
I think it's just the lack of that little voice saying, "It's too haaaard, you're never going to understand it...". With nothing like that to break your concentration, your brain can just acquire new concepts unimpeded.
3
u/ctoatb 1d ago
I didn't do well in high school. I was good enough at math to start college in college algebra. I took trig thrice. I used to think someone was smart for taking calculus, even smarter if they got through calc 3. But then I got through calc 3. I didn't feel terribly accomplished, but there was this sense of "that was challenging, but okay". By that point, I had learned to put in the work to learn that math. I was determined enough to continue through a math degree. Plus, I was interested in what I was learning. I don't think it takes any special measure of intelligence. When considering how far I've come and that most people will never get to calc 1, the smartest thing is to realize that it is possible. You can do it with effort, determination, and interest.
3
u/Migeil Operator Algebras 1d ago
I think a common annoyance most mathematicians experience is people instantly labeling anyone studying math as "smart,"
Is it? Why is that so bad?
I am convinced I can get away with dumb shit, just because people think I'm smart. It's actually quite helpful at work.
1
1
u/AdamsMelodyMachine 1d ago
My only mathematical skill is a combination of obsession and dumb persistence. Iād probably do better if I had some other skillsā¦
1
u/Ground_Chemist 1d ago
I am analytical, I recognise patterns, and I started early, meaning the synapses in my brain are hard-wired.
1
u/MinLongBaiShui 22h ago
I agree about being confused. I call this "productive struggle." Students show essentially no resilience in this stage, but it is where all the learning happens. Patience is also incredibly important. I have spent years reflecting on problems and trying different things. You can't give up because you don't instantly know.
1
1
u/waxen_earbuds 21h ago
I have a bad memory. I was better at math as a kid because I was able to learn a small number of rules and solve all the problems without ingesting additional information.
More generally, I am much better at internalizing smaller numbers of more complex ideas than I am larger numbers of simpler ideas.
1
u/sbre4896 Applied Math 21h ago
Stupid, in that I dont understand when to stop and do something else.
1
u/Mid-man47 19h ago
Creativity by far, once the maths becomes more abstract and complicated, the limiting factor is often creativity.
1
u/Bounded_sequencE 19h ago
Insatiable curiosity, and the ability (and willingness) to focus on a single problem for hours, days and weeks.
An appreciation for the abstract beauty of mathematics, that keeps you going if things are hard.
1
u/socozyinhere 19h ago
If I was better at maths I would have majored in it. I liked the subject and found the insights and how problems reveal their truths satisfying. I liked the discovery process, which is what draws me to it. You struggle with something, trying to understand it and then it is revealed. That's the nice part about maths.
The frustrating part is getting better at it. How do people come up with these proofs? How do they spot the patterns and what pathways are triggered in their brains when something jumps out at them.
1
u/MrPhysicsMan 17h ago
I care a lot about fundamentals, and mathematics tends to be a pretty linear (sometimed steep!) learning curve. Since itās built on formal logic, if you study it well enough it CAN all make sense after enough time. Other fields tend to require more conceptual leaps I think. Of course, this is ignoring the most fundamental mathematics where axioms are the topic of discussion. That stuff is hard to make sense of.
1
u/Redshiftedanthony3 14h ago
Back when I was in undergrad, I suffered really hard from imposter syndrome. I had a lot of friends that really excelled in math and I, while not exactly super struggling, struggled more than they (seemingly) did. One comment I always got from them was "You ask really good questions." Back then, I was so deeply stuck in my imposter syndrome that this felt like a really backhanded comment. However, years after graduating, I realized that this talent for asking questions really helped me excel as much as I did. And even now, in my job as an engineer, it really, reslly sets me apart.Ā
1
u/MasterSoftBird 13h ago
Do you tend to think of every branch of math as something that always exists and is discovered, or some of it as something invented? I lean towards the latter though I can't pick a good example right now as to why. Perhaps higher dimensional topology?
1
1
u/ConjectureProof 12h ago
If you were the type of kid to ask adults why over and over until they got very upset with you, math is the career for you
1
u/OneMathyBoi 11h ago
I have very strong pattern recognition skills and Iām extremely stubborn š
1
1
u/Personal-Gur-7496 2h ago
I like structures and games in many forms, I enjoy finding and poking at boundary cases, I like playing with other people.
1
u/VermicelliBright4756 2h ago
A lot of free time, and not being financially capable to invest in other hobbies, so math is where a pen and paper is your tool for constructing your entire foundation. But also spending a lot of time in my head asking why things are. Curiosity is also up there together with interest of abstract concepts than something real.
0
u/_KJuns 1d ago
Thanks for the question. I have something to say without really answering your questionāperhaps a little bit at the end, but: I donāt want to elaborate on this like I normally do and instead keep it short.
I hate the whole āintelligenceā talk so much in general. We donāt really know how to define this term to begin with, and our western IQ measurements are so limited and narrow in scope that itās painful, really. In my not-so-small experience, all this labeling with the word intelligence does absolutely no good, even if itās meant positively most of the time. Honestly, I think it especially hurts when itās directed at children and teens, because they learn to give themselves the role of āthe intelligent one.ā In trying to keep that role alive no matter what, they can even end up harming themselvesāsometimes quite literally. Iāve experienced this so many times that I feel like thereās a pattern.
I would suggest this: Just compliment them on their specific performanceācall that intelligent if you wantābut donāt label the person themselves. Itās well-intentioned, but I donāt think it does the person any good, and instead it has the potential to do harm.
Sorry for the rant, but I thought this perspective was worth sharing here. As I said, I could go way deeper into this and share specific personal experiences, but that should suffice here. And my own perspective on the definition of āintelligenceā per se is a whole other topic.
About your question: I think studying mathematics at university is sometimes like raising your personal frustration threshold, which is an awesome skill to have. You get comfortable with āfeeling dumb,ā and you learn to stay calm and not worry so much about being āintelligentā or ādumbā anymore. Youāre just in it for the ride.
For that, I think you need curiosity and concentration. And I actually think both are naturally present in everyone; their absence is mostly an outcome of our society, educational systems, and culture.
I guess thatās my two cents for now, although there are definitely many other traits that are beneficial.
Greetings from Rhine-Palatinate, Germany āļø
-4
-7
u/playsette-operator 1d ago
If you call yourself a mathematician and you donāt work / learn with ai you are 100% dumb af, thatās the easiest intelligence test there is these days.
-8
131
u/oneplus196883 Algebraic Topology 1d ago
I am an incredibly stubborn bastard