Out of curiosity, what does it look like to not-suck at math?
Do you wake up in the morning and are reminded of constants and theorems in everyday things and laugh empathetically with donuts as you recognize your shared absurd topological homology, or go to the office and automatically recognize what's possible and not from its implied complexity class in office conversations? Are you checking Bayesian priors in your interpretation of the news or other risk?
This is only half kidding, as I also identify as useless at math, but I think its words and concepts can be very funny, and I wondered what someone who actually knew this stuff might think about. It begs the question of what one is actually doing when they are doing math as well. Are you reasoning with abstract and quantitative models, are you writing papers and proofs of new ideas, or are you encoding a narrative dynamic into a symbolically defined logical relationship? Maybe you're just being recognized as a peer by the community of people who recognize each other as good at it?
When I learned music again later in life, I found I appreciated the same things, but with better intuition and words for articulating and reproducing them. Working musicians have a trade where it's expected they can show up and perform in a group based on sight reading of the notation, same as a programmer.
All this is to say, I see a lot of these "I can't math / how do I math" threads and am always interested in them, but maybe we should start with, "how does anyone math" first. So, how do you math?
I'm no mathematics savant, but math has always been easy for me. I never recall struggling to understand concepts, even through my university degree.
What I vividly recall is my fascination with algebra and geometry as a child. While on hikes I would imagine the equations necessary to approximate the flora around me, to calculate the parts of the rays of light, and so forth.
And while I never applied myself strongly to homework, I did pay with math as I've would pay an instrument.
That is to say, this should sound like how musicians describe hearing the music of nature, and their fascination with sounds and musical theory.
Math is an instrument that one can play to make beautiful music.
> Out of curiosity, what does it look like to not-suck at math?
To me, it looks like the rest of your comment, wherein you casually mention constants, theorems, topological homology and other concepts that don't even come to mind for many people who self-identify as being bad at maths (as I do).
Thank you, but I am mathematically illiterate. I can't identify greek letters after sigma without looking them up, I ignore equations in papers and other texts unless they are supporting something that offends me, I don't have a working understanding of why certain operations are meaningful or their uses other than knowing there is probably a python library that does anything I could need.
However, things have shapes and relationships, most of which we can't physically see, but we can reason about and compare them, and that's about as deep as I get. e.g. do things at a certain level of abstraction have a similar shape, and what are the words that describe that? Does this tell us more about the thing itself, or the limits of our ability to percieve it, and it's just an artifact of our lens? It's like having an ear for music, where you hear fragments of other pieces in everything, and interpret forms and symmetries and respond to intuitions, expectations, and resolutions - but not being able to play it.
I think we're entering into an era where we can finally have punk math, where some idiots get on stage and the people watching them go, "omg, this is terrible but fun, and I could do this better," and a thousand bands get launched. When I write stuff like that, it's because I don't mind acting as one of those idiots. I figure if most of my favourite bands can't read music, there's interesting math to be done by people who aren't proving anything or making progress, but intentionally or not, like all idiots, they exist as an example to inspire others. :)
> Out of curiosity, what does it look like to not-suck at math?
The speed at which you an understand, internalize and can put to use a new concept when it is presented to you.
This is usually combined with the practice of the trade providing you with actual pleasure, which is, of course, a self-reinforcing loop.
Some folks can take a single semester of linear algebra and absorb the majority of the thing, including learning far more than the course required because they truly liked it.
Others can take the first half of their career to finally understand the ideas and apply them properly.
Knowing how to solve problems in a mathematically precise way, such as writing down the formula for the expected value of a path-dependent investing strategy an hour after conceptualizing it. Like being a handyman but the formulas are your tools.
I have ten or so tantalizing questions which I don't know how to solve stuck in the back of my head at all times. Some of these are truly hopeless (i.e. P vs NP), others seem like something I can probably figure out but just haven't found the right perspective yet (these tend to be more obscure). This list of questions changes over time - sometimes problems actually get solved, sometimes I lose interest in them, sometimes I learn about a completely new area and add a bunch of new problems to my list of things to think about.
If I'm at a social gathering and the people are boring, I take out a piece of paper and start trying to visualize some aspect of a problem I've been stuck on for a while, or compute what happens in some particular special situation. In order to carry out the computations, I find myself making up paper-and-pencil algorithms, typically variations of dynamic programming with some specialized bookkeeping notation so that I can see at a glance what is going on on the paper. My scribbles probably only make sense to me - lots of bipartite graphs with labeled vertices, or directed graphs with decorations on their edges, or sequences of column vectors full of letters instead of numbers with groups of little dots underneath them, or attempts to draw small three-uniform hypergraphs...
Every so often I manage to rephrase one of the problems which is stuck in the back of my head in a new way. Then I think, hey, wait - maybe someone has studied this type of problem (i.e. the rephrased problem) before! I search around, and find some research area that is almost but not completely unlike what I was hoping for, and try to read some introductory material about it. Maybe I download a textbook on, say, "unification", and just read the chapter on "confluent rewriting systems", since I think those might help with the algebra problem I'm interested in. It doesn't, but it gives me a new pencil-and-paper algorithm to play with, so I fill up a blank piece of paper trying it out.
I also have an infinite backlog of books on math that is just plain interesting to me, but which I don't expect to find any use for. Things like advanced set theory, which is interesting from a philosophical point of view (how do we come to be convinced of new axioms? Is it possible to become convinced that "measurable cardinals" really exist?), or average case complexity (is providing a theoretical foundation to cryptography hopeless?), or statistical mechanics (what are all those physicists talking about when they bring up the "Ising model"?). I go through these at a much slower pace, sometimes only getting through the introduction before I have to put them to the side to focus on other things, but occasionally I get a solid two weeks of uninterrupted time to focus on one of these and blow through... well, the first two-thirds of a book, putting off the last third to some time when I actually need to know it.
About once a year, I'm in a situation (often a conference, sometimes an unusually interesting party) where there is someone else I can talk to about my interests.
Do you wake up in the morning and are reminded of constants and theorems in everyday things and laugh empathetically with donuts as you recognize your shared absurd topological homology, or go to the office and automatically recognize what's possible and not from its implied complexity class in office conversations? Are you checking Bayesian priors in your interpretation of the news or other risk?
This is only half kidding, as I also identify as useless at math, but I think its words and concepts can be very funny, and I wondered what someone who actually knew this stuff might think about. It begs the question of what one is actually doing when they are doing math as well. Are you reasoning with abstract and quantitative models, are you writing papers and proofs of new ideas, or are you encoding a narrative dynamic into a symbolically defined logical relationship? Maybe you're just being recognized as a peer by the community of people who recognize each other as good at it?
When I learned music again later in life, I found I appreciated the same things, but with better intuition and words for articulating and reproducing them. Working musicians have a trade where it's expected they can show up and perform in a group based on sight reading of the notation, same as a programmer.
All this is to say, I see a lot of these "I can't math / how do I math" threads and am always interested in them, but maybe we should start with, "how does anyone math" first. So, how do you math?