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Mathematicians are shitty communicators who like feeling special because they can understand their obscure language.
I’m a programmer and in this field there have been tons of books published, conference talks, and heated internet arguments about how to make your code as readable as possible: formatting, function length, naming of variables and functions, keeping number of cross references low, how to document intent, etc. Mathematicians do none of that - it’s all single-character names (preferably from the Greek alphabet to complicate it further) and they rarely communicate intent before throwing formulas at you. You can easily tell when a mathematician has written code because it’s typically hot garbage in terms of readability.
I feel personally attacked lol
I worked with a physicist who wrote code that was so unreadable, it actually made me laugh. He would often include his initials in variable names, even though he was pretty much the only person working in the code base. His functions usually included a
flagsargument, which was a list of (usually undocumented) integers that you could pass in to change the behavior of the function. For example, one time one of his functions wasn’t giving the expected output, so I asked him and he replied “oh did you put 32 in the flags list?” Like he just didn’t understand that you shouldn’t need to read the entire contents of a function in order to understand how to use it.Inb4 “well why didn’t you help him?” he was in his 70s and vehemently refused any advice.
This hurt to read
Code signing!
“The demonstration is trivial and left to the reader” or any variation of that. Fuck you, do the fucking demonstration.
Got this so much in my engineering courses.
To be fair, expression tend to be way, way smaller than a codebase. The math community was never forced to improve in the same way. Actually, the symbols were themselves an innovation; in ancient Greece they just had to try and explain that shit in long, tortured natural language sentences.
I really, really hope nobody feels like I’m trying to be unclear with them. I know I sometimes am, though.
If I had online resources growing up math would be easy, I relearned math weekly in college because it flowed out my brain, growing up having to learn off teachers/textbooks was always confusing and my parents were neve helpful. Also common thing is you just dont see how you’ll use math in your day to day (even tho it ends up being useful everywhere for anything)
I think ppl would like math more if they learned with better visuals, maybe blender will be used in the classroom to visualize expressions and formulas in the future, that is what made me like math.
Yeah, in school I had a maths teacher that could solve any equation…he couldn’t tell you how he’d done that to save his life though.
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Part of it has been how it is/was taught. Math was always the subject I had to work harder on than any other. The problem is that I was never taught to really conceptualize the problems. Once I started taking physics and real world applications came into play, it all sort of clicked and got much easier.
Edit: Also, math is really all about relationships and conceptualizing interesting problems or ideas. If it had been presented to me that way, I think I would have been more adept at it earlier.
This. Mu father and grandfather in law are mathematitians. I never liked or enjoyed math but they make it ao damn interesting when talking about it. It’s a real shame I never had a teacher with such passion and talent for it.
tl;dr
For me the ‘breakthrough’ with math was, simply to accept that at the higher levels we are speaking about symbols (abstractions) that follow certain rules and everything else is derived by pure logic. Just accepting that one is manipulating symbols with rules to get to other symbols and learning the rules, made it click for me. Disclaimer: Was lucky with great math teachers in university, but even in my university there were people who simply could not accept the game of mathematics and were frustrated, because they wanted easy question/answer style formulas in the sense: When you see this, substitute PI with 3.14 and multiply r by r and write down the number that your calculator shows. They never made any effort to understand where PI comes from, where the radius comes from and why it makes sense.
What is insane, is how many people studied computer science but are totally unable to apply mathematics to the problems they try to solve. Supposedly most of them learned relational algebra and discrete mathematics during their studies (and formal languages/complexity theory)… it is like something is missing in their ability to transfer what they learned in the university to basically the same problems where the symbols have different names. That is something I would love to understand.
Could you elaborate on this? My experience during my computer science education was that a lot of maths was required, but just usually not the same kind of maths as most of the rest of mathematics, because continuous stuff doesn’t apply most of the time.
I think a big difference between the way maths and programming is done however is the way it is written. Mathematics is usually about stating a relation as an equation, i.e. x = y^2. But programming can’t just state the relation, it needs to also state how to compute that relation. Honestly my confusion is that maths has never focused more on the computation part of it, it seems very weird to me.
GOOD post
Thank you, sir! :-)
Personally, my problem was always that math concepts were never presented in a way that actually made sense in the “real world.”
I was taught that complex numbers were real numbers with imaginary parts that had something to do with the square root of -1. Yeah, I get it, but… why?
Fast forward a few decades and I’m writing code that processes a digitized waveform. Now it makes sense. Math isn’t hard when you have a frame of reference. Learning math concepts solely for the sake of learning them is very hard.
I think people also quit before they can play the game. Calculus was the first time I felt it was all coming together and was really fun. Up until then it can seem like you are learning rules to a complicated game, and then people chose to just not play.
I work in maintenance …I’ll go to some jobs, fix the issue and walk away, I’ll go to some jobs and there will be some troubleshooting and I’ll walk away, other jobs I’ll have to leave and won’t be able to resolve the issue. The first two I’ll look back on and I might have learned something and I’ll be really happy. The third makes me feel like shit. I remember being the same about linear equations.
Yeah - wasn’t until later when I did some work with camera orientation in 3D that Linear Algebra and Matrix Transformations clicked a bit more for me.
This was always my experience as well. The deeper you go into mathematics, the more abstract / theoretical things seem to become.
Funny you should mention digitized waveforms, a class on signals and transforms was by far the hardest part of my degree. I really struggled with both the math and the visualization. Probably the thing that ended up helping me grasp some of the course’s concepts most was messing around with convolution reverb effects for audio processing.
Can you explain them? Not having worked with them, I’m still in the “but why?” phase of complex numbers.
(different person here)
I can’t give a satisfying explanation, but I can really recommend 3Blue1Brown on YT for great motivations for such things. He presents these topics in ways that make you want to understand them. I’m not sure which videos approach imaginary numbers - there might be standalone ones, but it definitely comes up in his explanation of the Fourier transformation.
Read “A Mathematician’s Lament” by Paul Lockhart, it’s free online.
He lays out a brutal critique of the modern mathematical curriculum in the Unites States but in summary:
We teach mathematics to children as a huge set of rules to memorize and use to get good scores on standardized tests so that they can “get into good colleges.”
We don’t treat mathematics with any reverence or care, like we do with the arts. Math is taught as a bunch of arbitrary brute facts that old wise men came up with centuries ago and we spend all of elementary and high school relentlessly drilling them into students heads no matter how much pain and suffering it causes.
There is no actual exploration of mathematical beauty, or mystery. There isn’t any discussion of the underlying philosophy of mathematics, or how any of the rich and fascinating history of its development as a field. It’s like if we taught music as just a way to write notes on a page in certain time signatures and keys, but never actually let students listen to a piece of music or discuss the great composers or cultural movements of music through the ages.
Of course that seems ridiculous to people, but for some reason when we do that exact same thing with mathematics, nobody bats an eye. In fact, people think it would be strange to do it any other way.
Seconded (from Finland). Math teaching is still boring and it doesn’t help that (too) many teachers don’t appreciate pedagogical studies that go with the curriculum in the university. It has its problems, but rarely do the students want to engage with what math education could be.
Coupled with society’s expectations on what math education is, it’s really difficult for a teacher to change course. Even the students have the expectation that they should always be doing exercises from books and everything else is ‘useless’. It is really a deep rooted issue.
I think this is it, tbh. I have to constantly remind my kids that math isn’t memorizing the answer, it’s knowing how to look at a problem, follow the rules, and figure it out. And it always seems so very arbitrary to them, as it used to for me as well.
Seriously, read it.
I can also recommend his books “Arithmetic” and “Measurement”.
Because it was taught wrong to most adults when they were children. Pedagogy has changed, though, and gen alpha are actually becoming numerate instead of being told to just memorize things like my generation was. Maybe the zoomers got lucky with that, too.
But seriously, as a mathematician and a teacher, you’re not bad at math because of something inherent to you. You’re bad at math because you weren’t taught numeracy.
Hmmm. I was taught to memorize a few things that accelerate some work/scenarios. But very little math I was taught involved memorization. Nearly all logic and calculation. And I’m late GenX.
I went through engineering school, and 20 years of work (not as an engineer), before finding a calculus text that explained why the derivative of x^2 is 2x. Along with many practical applications of calculus.
That book was Calculus Made Simple, published in 1914. Thanks, Project Gutenberg!
Edit: derivative of x^2 is 2x. Got my differentiation and integration confused!
I’m just being a pendant here, but the derivative of x²+C is 2x. You put the constant at the wrong place.
Also, i’m glad you found a textbook well suited for you. I have to wonder what you mean by ‘why’, do you mean a proof?
I’m guessing the derivation from first principles. I too learned the rules years before I was shown it, and it was just so cool to see where they came from.
That’s exactly right. The proof is quite simple and there’s no reason it shouldn’t be taught instead of just getting students to accept magic rules.
My first calculus class was in 2018 or 2019 and before they taught us any of the derivative rules they showed us the first principles derivation, so the fact that they just skipped right to the shortcuts for you is wack. For us it was more of “this is how you find the equation for the slope of a line at any point. But guess what, here’s some rules so you don’t have to do this squeeze formula every time!”
In my case because I was in gifted classes so I got this idea that I was just brilliant and never needed to study for anything. Then as soon as a subject got hard enough for me to not ace it without effort I just quit instead of knuckling down and doing the work. Math was the only subject where I truly ran into a wall cause some of that stuff is just not at all intuitive, it’s loaded down with obscure rules and memorization, etc.
It felt less like instruction on how to use a vital tool to make my life easier and more like someone was intentionally making my life harder by making me learn math. It’s like someone came up to me and said ‘Oh, you’re walking 10 miles uphill? Here, since you’re going this way, carry this 40lb rock with you. it’ll be real useful at the end, trust me bro.’ And I was like ‘This is already a hard enough walk, the fuck am I carrying this rock for?’ so I set it down.
I have since picked some of it back up, and I now recognize the utility of learning it and wish I’d learned it when I was younger cause it’s even harder now.
A lot of elementary school teachers don’t go into teaching to teach math.
A lot of them don’t even go into it to teach, it seems. More just to be the smartest person in the room.
Science and math pedagogy is fucking trash world over and it only serves to raise students’ anxiety levels on the subject matters until they check out of them entirely and the only ones left are those who have somehow evaded the microtrauma imposed on them
Where in other subjects the knowledge you gain is related but not completely contingent on everything else you were taught, e.g. you don’t need to remember too many exact details about the Mayflower pilgrims to understand the American Civil War, math requires a solid throughline from the basic arithmetic, through algebra, geometry, and so on. You can’t really do anything with trigonometry if you didn’t understand algebra well. You can’t really do algebra if you didn’t understand arithmetic. You definitely can’t do calculus if you struggled with any of the previous areas.
So the problem is the continuity required, combined with the way most students learn simply not being thorough enough to completely internalize the intuition for each math concept they’re being exposed to. Ask a 9th grader about the differences between rational numbers and irrational numbers that they may have learned in 7th grade: you’ll probably get answers that are about right, but might start to get a little vague or confused. Thankfully I might be overstating the interconnectedness a bit, but I know I definitely had some hiccups in college related to how I had only learned some of the advanced concepts halfway in previous courses, which led to me just barely understanding the really abstract concepts I started to get into like Stokes’ Theorem and Greene’s Theorem at the end of Calc 3.
Studying mathematics is a difficult but also rewarding activity. This requires having a positive relationship with the effort. By analogy we could compare this to sport. To give up practicing mathematics because it is difficult is equivalent to giving up sport because it tires.
For those interested in the education of mathematics, I would recommend this book by mathematician David Bessis.
Mathematica: A Secret World of Intuition and… by David Bessis
https://www.youtube.com/watch?v=KJafasuk4NQ
So is literally anything easier,math is just too hard for no reason.
Looking at the responses, I’m guessing Lemmy isn’t a representative sample.
I was a bad student, but a great standardized test taker.
I placed into advanced classes, but had zero interest in learning or studying.
Once I hit high school I was done for.
Geometry, Calculus, etc. I could never wrap my head around why I would ever need to know any of it in my daily life, nor could I envision the practical application of any of it.
So I would zone out or sleep.
Now, trying to help my daughters with their math, it might as well be hieroglyphics.
I can’t speak to most people but I have dyscalculia.