Whenever I hear this argument now, it just feels like a watered down version of A Mathematician's Lament, I don't think anyone will ever be able to form an argument as well rounded as Lockhart's on the subject.
This is an interesting read, thank you for posting it. It is worth noting that the author is a K-12 mathematics teacher and not a mathematics professor. Learning math at the K-12 level is probably different in many ways from learning math at the university level and above. Why say that creative expression is limited to even the conventional 'artists' and the mathematicians? Is creativity not the province of those of us in science, who must bend our minds around questions, formulate theories, and often devise methodologies that have never been developed? For that matter, there is a little bit of STEM in the arts: they use chemicals to paint on a canvas, new materials to craft sculptures, must understand to an extent that the buildings they design won't fall down, invent new kinds of art, invent new kinds of instruments and ways to manipulate vibrations in the air to produce sounds that move us... Again: "Poetic dreamers" and "rational thinkers"? Why can both not exist in the same person? There is a poeticness about the human desire to defeat disease and the elegance of the scientific process, or perhaps a particularly elegant bit of programming or an elegant theorem, and discovering new things about the universe with empirical investigation and rational thought is itself a way in which people dream and extend and express themselves; there is an element of rationality in the ways artists try to get people to appreciate their work and the ways in which they tug at people's heartstrings. Mathematics has a little bit of 'art' in it, as do medicine, science, and philosophy, but it, like - philosophy! - is in a class all its own in many ways. Mathematicians do not make patterns, really. They often discover them, and they theorize about them. What I guess it's easiest to say they do is define patterns.he first thing to understand is that mathematics is an art. The difference between math and the other arts, such as music and painting, is that our culture does not recognize it as such. Everyone understands that poets, painters, and musicians create works of art, and are expressing themselves in word, image, and sound. In fact, our society is rather generous when it comes to creative expression; architects, chefs, and even television directors are considered to be working artists. So why not mathematicians?
Part of the problem is that nobody has the faintest idea what it is that mathematicians do. The common perception seems to be that mathematicians are somehow connected with science— perhaps they help the scientists with their formulas, or feed big numbers into computers for some reason or other. There is no question that if the world had to be divided into the “poetic dreamers” and the “rational thinkers” most people would place mathematicians in the latter category.
Nevertheless, the fact is that there is nothing as dreamy and poetic, nothing as radical, subversive, and psychedelic, as mathematics. It is every bit as mind blowing as cosmology or physics (mathematicians conceived of black holes long before astronomers actually found any), and allows more freedom of expression than poetry, art, or music (which depend heavily on properties of the physical universe). Mathematics is the purest of the arts, as well as the most misunderstood.
I had a badge to give. Got it. Damn fine thinking there. I teach middle school math, yet had my eye on Parsons School of Design in Chicago at one time. I still share my art portfolio with my students every year several times to share math and art connections. They dig studies in proportions, perspective, and the golden mean, and most off all they think it's pretty wild that their math teacher somehow can produce art. Too many of them see math as a restrictive environment than a set of tools, in which to make their poetic dreams a reality as paint, pencil, or other media.
Aha, THANK you, I remember seeing this posted on Hubski a few weeks back, and I thoroughly enjoyed it.
To that end, whenever someone says they were bad at math like it's some kind of thing to boast about, I get a little murderous (I was literally the only science major in my English composition class when I took it about a year or two ago, and every time even the PROFESSOR joked about being shit at math I wanted to whack her over the head with my physics textbook). Why does a subset of people seem to think it's acceptable to go 'lol i suck at math' but FSM FORBID YOU CAN'T WRITE OR FIGURE OUT HISTORY LAWD NO AND FSM FORBID PEOPLE WHO ARE GOOD AT MATH SUCK AT THE HUMANITIES. Sucking at ANY OF THESE THINGS is UNACCEPTABLE. For the record, I am (obviously) high of aptitude in STEM, and have respectable enough ability in the humanities (though not to the extent of my ability in STEM, but still to the point that I got a higher grade in a Chinese literature class than the literature majors, the highest in the class, and the same thing occurred in my two semesters of psychology - highest grade in the class and outclassed the psych majors).
I don't think people say they're bad at math because it's a thing to boast about, it's just a belief that they could never be good at it. I had that same belief for a very long time, and I still feel that way now and then. That's because of people who talk the way you do, who say things like "Yeah, I'm great at math, and English is so easy, that's why I get A's in everything." For one, that's because those English classes were child's play. As JackTheBandit points out, in High School, "we never really learned anything at all, but were treated like we had." And another, comparing your grades in classes to other peoples' grades seems almost immature to me. It's a rat race about nothing. That's not a dig at you specifically, I know lots of students who are like that. In the end, I would say sucking at some of those things is acceptable. Obviously you don't want to be failing the stuff you aren't as good at, but being passable is just fine too. I can't believe I'm saying this because it seems like it's already something that people should know, but I keep hearing it over and over again, so I guess it isn't: nobody's fantastic at everything. It's about what you put your effort into. Sounds like you've got a bit of an Anti-Anti-Stem jerk goin' on. How do you know you had the highest grade in the class anyway? Do they post that shit on a wall? That sounds mortifying.
There's commiseration and affinity there, too. People who say they're bad at cooking will still cook. They're lowering expectations. Additionally, you can "check your math." If you say you're bad at math, run some numbers and then check it to find yourself wrong, you also found yourself right - and you can go back and fix it. Saying you're "bad at math" prepays for the time necessary to do it right. The main thing, though, is that nobody uses math. It's a safe thing to say you suck at. Once you're clear of college the only time most people whip out Excel is if they don't have a copy of TurboTax. I think the STEM crowd is uber-defensive about math because they're required to take so goddamn much of it and as soon as they're out in the real world, they rarely use it either.I don't think people say they're bad at math because it's a thing to boast about, it's just a belief that they could never be good at it.
Once pretty much any STEM professional is clear of college, and even in college when we're clear of our required math courses (including intro physics; intro physics is at its most fundamental a lot of empirically-validated math plus crashing shit into other shit or shining shit at other shit), we use computers to do our math. It's impossible to do ANOVAs by hand unless your data sets are, like, n=5 each, for example. Also physicists work with absurd numbers of significant figures. Knowing why you're using a given equation and when to use a given equation are the main things one takes away from the math we take. EDIT: And you most definitely use math, you just don't think about it. Tip calculation, building shit if you do DIY type things, calculating costs of things within a budget, etc. You probably don't use trigonometry, I guess, but I'll be damned if you don't at least do some algebra and geometry on a moderately frequent basis. EDIT 2: You actually might use some trigonometry, but I guess more in an intuitive sense. A lot of math actually gets used this way in practice as sort of a predictive tool. You have 4-function calculators; we have calculators with a bazillion functions. Nobody says they sucked in history or high school government or music like they were proud of it. When's the last time you had to whip out your knowledge of Greek civilization? Trivial Pursuit? And you can check your history by cracking open a book or Wikipedia. It doesn't help, either, that scientists got painted at one point by - somebody in the media, I guess - as social pariahs, the stereotypical 'geeks', or that one of the first Barbies was programmed to whine 'Math is hard'.The main thing, though, is that nobody uses math.
Computer's don't do math, they just do the computations.
Based on the fact that I never got an assignment back with points taken off of it. If not the highest, then one of the highest. It's just an inference.How do you know you had the highest grade in the class anyway?
These people usually also say they're not so good at math, though.
I'm not good at math but I've worked my way through linear algebra. I was always at the back of the pack of the people who were putting effort in. Oddly at least once a class I'd be the guy who'd crack open a group challenge that had everyone stummped for a few days. I will say I often had a better understanding of what the math was describing than mostof the better student, I'd just make a mess out of the calculations.
It is possible to be bad at math, but as long as you have a decent head on your shoulders you can earn the tools you need to do what you need them for.
It's upsetting to me how society likes to pigeon-hole scientists, like we're all expected to exhibit particular qualities. The TV show "The Big Bang Theory" springs to mind, and it repulses me. It's about as mindless of a show as you can create. If you meet me and inquire as to my profession, and then ask if I watch the show, I've already formed an unfavorable opinion of you. Hell, I don't even have TV. I work with plenty of other scientists who exhibit none of the "stereotypical" geeky behavior. There are a few who have some social awkwardness, but it's the exception rather than the rule. Also, glad to see another physicist (I think?) on Hubski. :)
Neurobiologist in training. If anyone says 'Oh, like Mayim Bialik!', I will splash them with capsaicin. SUCK ON THAT, TRPV1 RECEPTORS My mom likes The Big Bang Theory, actually, despite the fact that she fully acknowledges it's a sort of scientist blackface (she likes it for other reasons, and has complained about how it typifies scientists - she's not one herself, she's a sociologist by training and an analyst at a biomedical granting body, but she works with people like me and she's been supportive of me from the get-go and has gotten more scientifically aware herself as she's witnessed me going through my studies). I don't know any successful scientists who exhibit any of that behavior. The only ones I've known who have were extremely unsuccessful.
I'll be stealing that phrase, thank you very much. A little jealous that your mother has some scientific literacy, I've got Southern Baptists for parents. What I do professionally is pretty much magic to them. Yep. I disagree with 8-bit somewhat, I think well-roundedness is something we should all strive for. We live in a society hell-bent on developing a specialization, but if at all possible we shouldn't write off our flaws with "Oh, I was just never good with social skills", or whatever. If you're begging for funding or presenting a thesis whilst staring down at your shoes, things aren't gonna go well. Edit: I suppose I retain my title of Hubski's only physicist... Edit 2: Nevermind!scientist blackface
I don't know any successful scientists who exhibit any of that behavior. The only ones I've known who have were extremely unsuccessful.
I hope that's actually true, but I doubt it. On the other hand, it might explain the simple brilliance of Hubski's functionality... Edit: IS MY BIAS SHOWING?!?
I'm inferring that 2 people out of 5 have PhD's in physics? Which 2?
Honestly, I expected team Hubski to be solely web designers, coders, that sort of thing. I didn't mean anything by it. :)
You have called me out explicitly, although for some reason I wasn't notified via Hubski's HTML(?) mechanics. I concede that I am only a physicist in training! My professional title is officially "scientist". I work at a non-profit research center, but I am confined to (largely) engineering-focused work, due to the fact that I've only accrued a B.S. in physics. Spent 6 years between two universities, in between switching from engineering to physics, graduated with ~165 credit hours. Single major. I'm unfortunately well edjukated. Headed to graduate school in the fall of 2015. I'll be 28, and I got 50th percentile on the Physics GRE... not bad for an American who hardly studied! I can't wait to have my ass handed to me multiple times while I pursue my thesis and work under people worth 10x my reputation. What I consider truly important is that people I've worked with enjoy my contributions and my company. Anyone can say such a thing, but I smiled smugly while I typed that last sentence. Truly, I feel like such an elitist pig sometimes... until I look at my bank account and realize that if I was actually intelligent, I would have gone into business. ...Just kidding, fuck money worship and other facades that so many other Americans wrap around their psyches. I only want to contribute towards the knowledge-base of mankind, with my sole incentive being to brag about it on Hubski. :)
oky, I can't answer for am_Unition, but 'biologist' is a title that is often accepted as early as the beginning of grad school (and is an actual government/industrial job title, as well).
I think that people need to realise at a younger age that academics (no matter how illustrious) are normal people. I've had friends who have been on field trips and were surprised to find that when the professors went to the pub after work they would talk about the weather, football, hobbies, etc. They weren't so caught up in their work that it defined every aspect of their being. If people knew that they didn't have to be some bespectacled freak of nature to work in a physics lab (and that said physics labs were not filled with such people) then they would probably find those subjects much more appealing.
A lot of words to dodge around the main point... When's the last time you proved a theorem in calc? I'm talking about "integral tanh^-1(x) dx", not the tedious problems they give you in the beginning of your homework. When's the last time you played with the axioms of algebra? When's the last time you determined isomorphisms between geometric shapes? If you talk to a student in "mathematics", most don't talk about numbers, many don't even talk about symbols. My previous roommate used to describe organizations to me in terms of their fundamental axioms and theorems. A physicist friend who used to live across the hall from me once described jazz from the basis of musical keys and fractal patterns. The last conversation I had with the girl who shares my bathroom was about the properties of manifolds, functors, and automorphisms. To them, "inconsistent" means a specific idea that can be disproved from set of codified rules. They ask for definitions and properties work out the rest out for themselves. Not everyone needs to think this abstractly. Not everyone is practiced to perform it with the ease they do. But it's damn useful for rationalizing problems. Hell, finding the rules to turn a people problem into a graph theory problem is the sort of thing that the yuppies at Twitter get paid bank every year to do. It's only one aspect of the larger problem of debate -- logos won't get you far without ethos and pathos -- but understanding what makes an argument rock-solid and how to see that another is full of holes is an important skill to have in life.
Not entirely on-topic, but I get what he means. About four years ago I deleted all my Reddit comments. Most of them weren't worth keeping. A few of them were.
Thanks for the answer. I've had to learn some combinatorics and graph theory just to solve problems in CS, so they're definitely good ideas for further learning. I'll check out the book, I am not that confident writing proofs and will definitely need to know that stuff if I am to do something more mathematical (not sure what that'll be at the moment). Yes, I've tried looking at group theory and category theory as it has a bit of a link to computer science - I applied to Oxford for my MSc (rejected) and they do quite a bit of research using abstract algebra. I found it pretty heavy going.
A short story, courtesy of BE/bfx (whichever you prefer): Once upon a time I spent some of a summer studying abroad at a technical school in France. Think of it as being somewhat similar to a UC or other state run institution. While my courses were not math based (language and economics based), I did manage to expose myself to some of the math that was being taught there through becoming friends with some of the professors. They were more than happy to share some of their calculus material and homework assignments with me. The language barrier was easily overcome, but the interesting part was the content. The content was the same material that I had been taught, or was taught back at university following this study abroad. That did not change. What did change was the problems that were being asked, and how to approach them. These problems were much more challenging than what I had experienced in the United States, even at a high-ranked engineering based university. They required a deep understanding of calculus, algebra, and trigonometry in ways that were not taught to me. While I was able to solve a lot of these problems, it was more challenging than it should have been. From that I inferred that either the rigor of the course at this university in France was stronger than that of my university in the states, and that material is likely being taught with a greater emphasis on understanding and comprehension as opposed to identifying patterns and systems that lead to an answer without as much understanding of the significance of the math in between. It is scary just how true that statement can be, and I was able to see the educational differences that lead to that firsthand."I was very good at following obscure steps to manipulate mysterious symbols, without any real understanding of what I was doing.”
When I got to Calculus 1 in my 1st semester at college, I promptly realized that I'd never been good at math at all. All the honors awards and summer programs were a bunch of bullshit. Then, I ended up in the "Honors" Section for Physics 1 because the regular slots were filled and I needed the credit. I promptly realized that I never truly understood anything about Physics (the entire course was also proof based so we had to derive the formulas ourselves during exams which were all open book. I got a D). This is essentially the story of my collegiate journey; realizing time and time again that I never really learned anything at all, but was treated like I had. A master at filling out the paper the way I'd been told. I believed it fully and never pushed myself in individual efforts to learn and it made getting a Mechanical Engineering degree quite the process.