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> I think that's because mathematical papers place too much value on terseness and abstraction over exposition and intuition. If it only happened on mathematic

> I think that's because mathematical papers place too much value on terseness and abstraction over exposition and intuition. If it only happened on mathematical papers... It is all over the place, in books, classes, etc. Few professors tell you what are they doing and why; they just throw formulas, theorems and symbols at you. Intuition is not given its necessary importance, first because it's hard to grasp some concepts, and second because sometimes there's no easy intution behind them unless you have deeper knowledge in the subject. Regarding "unit tests", or descriptive names... That's very difficult once you get into advanced math. Examples are probably going to be trivial or too contrived to be useful. And if you have to give a name to a theorem or lemma, you'll end up describing its full contents.

rjzzleep 11y ago
In Germany you get to your advanced courses for the last two years of High school. I picked Math and Physics. We did a bunch of linear regression(with maple?) i believe. And some manual differential equations. I was one of the best in that class, but when I asked what we need this stuff for the other people in the class looked at me and said the following: "if you ask this question you're in the wrong class" I went on to study engineering, and i guarantee you the other two still don't know what that stuff is good for. They learned the formulas by heart and then went on with their lives. I mean it was fun for me, it was basically a coding exercise. And I was happy because I was faster than everyone else, but I didn't get why we were doing it. The same actually bothered my about the studies. Just one example: folding is a fairly easy concept. But for some reason they first want to drill it into your head, you learn a bunch of techniques and then if you're lucky and you stick with it, eventually it clicks and you'll realize why in a completely unrelated class. Why can't we just provide a simple real life example first and then go on explaining the details? Aren't things easier to grasp when you can have a real understanding/connection to it? Isn't that precisely why people that learn coding at home tend to be better than those that just studied it, because they were told it's a solid profession to study? I think with a good example and visual representation you can probably teach most of the stuff that's taught in Uni to young kids. But then you would be forced to admit that you wasted a lot of time during your own life, who'd want to admit such a thing.
- brachi 11y ago
  > Why can't we just provide a simple real life example first and then go on explaining the details? This. People learn differently, in my case, if I can't get the 'Why' first, I'm not that excited to learn it. I guess making 'simple' real life examples in many cases is hard. I also tend to learn things much better if they came from a real problem/need I have. There was a good discussion about a 'project based university' here: https://news.ycombinator.com/item?id=10989341 https://news.ycombinator.com/item?id=10989341
  - joslin01 11y ago
    I actually think you're in the norm. The "why" helps create a belief; a belief is something that ignites action. Without it, someone's belief as to why they should learn [X] is too often defined as "to get a good grade."
  - vlunkr 11y ago
    High school math was awful at this in the US. I went through a year of calculus and never knew what the heck it was for.
    - brachi 11y ago
      When I asked in high school what math was for to some professors, they said it was more to 'improve your thinking' than to use it in 'real life'. Now, a math course designed to be progressively easy to grasp, personalized when needed, entertaining and showing lots of examples from real life (e.g. relating algebra with 3d and video games) requires a very talented educator; teaching well is really hard and usually there's not enough time or resources to do it. That's why I think one of the most important skills to develop is to learn how to learn.
    - Symbiote 11y ago
      I think it very much depends on the teacher. It's not difficult to explain the first few topics on calculus in terms of distance, speed and acceleration. Other examples I remember were washing lines (a catenary), the path traced by a stream train's wheels and rocketry. My teacher in England always had a real world example, but students with the other teacher didn't.
techman9 11y ago
I don't know... I'm taking a theory of computability class right now and I'm sure glad that the pumping lemma for regular languages is called "the pumping lemma for regular languages"
- jimbokun 11y ago
  But isn't that an attempt at a "descriptive" name? The intuition for the person who discovered this lemma, clearly envisioned the underlying process as a device pumping out new strings belonging to the language.
  - techman9 11y ago
    I like to imagine they envisioned the strings themselves being "pumped" up by inserting new characters in the center.
  - VLM 11y ago
    I took a brick and mortar automata class a long time ago and a classmate who clearly wasn't reading the text before lecture, insisted the prof called it the "plumping lemma" because it was about growing wider strings. That might have been the only funny thing that ever happened in automata class, unfortunately. Education by satire / humor is a sadly under-explored field. "A satirical approach to linear algebra"... not sure if I'd kickstart support that, or turn around and start running. In the eternal spirit of "anything that sounds interesting and impossible is a great startup opportunity" I propose that someone ... etc etc, you know.
    - techman9 11y ago
      My professor has had some quality quotes this quarter: "Misspell Chomsky's name as Chompsky, and I'll give you a pass; Misspell Turing as Turning or something? I'll flunk you"
driverdan 11y ago
> Few professors tell you what are they doing and why; they just throw formulas, theorems and symbols at you. That's not true. Proofs are a core process of all mathematics. Writing proofs can take up a majority of your time in some classes.
conjectures 11y ago
+1 on the final point. It may be difficult to appreciate how terse terse is here.

rjzzleep 11y ago

In Germany you get to your advanced courses for the last two years of High school. I picked Math and Physics. We did a bunch of linear regression(with maple?) i believe. And some manual differential equations. I was one of the best in that class, but when I asked what we need this stuff for the other people in the class looked at me and said the following: "if you ask this question you're in the wrong class" I went on to study engineering, and i guarantee you the other two still don't know what that stuff is good for. They learned the formulas by heart and then went on with their lives. I mean it was fun for me, it was basically a coding exercise. And I was happy because I was faster than everyone else, but I didn't get why we were doing it. The same actually bothered my about the studies. Just one example: folding is a fairly easy concept. But for some reason they first want to drill it into your head, you learn a bunch of techniques and then if you're lucky and you stick with it, eventually it clicks and you'll realize why in a completely unrelated class. Why can't we just provide a simple real life example first and then go on explaining the details? Aren't things easier to grasp when you can have a real understanding/connection to it? Isn't that precisely why people that learn coding at home tend to be better than those that just studied it, because they were told it's a solid profession to study? I think with a good example and visual representation you can probably teach most of the stuff that's taught in Uni to young kids. But then you would be forced to admit that you wasted a lot of time during your own life, who'd want to admit such a thing.

brachi 11y ago
> Why can't we just provide a simple real life example first and then go on explaining the details? This. People learn differently, in my case, if I can't get the 'Why' first, I'm not that excited to learn it. I guess making 'simple' real life examples in many cases is hard. I also tend to learn things much better if they came from a real problem/need I have. There was a good discussion about a 'project based university' here: https://news.ycombinator.com/item?id=10989341 https://news.ycombinator.com/item?id=10989341
- joslin01 11y ago
  I actually think you're in the norm. The "why" helps create a belief; a belief is something that ignites action. Without it, someone's belief as to why they should learn [X] is too often defined as "to get a good grade."
- vlunkr 11y ago
  High school math was awful at this in the US. I went through a year of calculus and never knew what the heck it was for.
  - brachi 11y ago
    When I asked in high school what math was for to some professors, they said it was more to 'improve your thinking' than to use it in 'real life'. Now, a math course designed to be progressively easy to grasp, personalized when needed, entertaining and showing lots of examples from real life (e.g. relating algebra with 3d and video games) requires a very talented educator; teaching well is really hard and usually there's not enough time or resources to do it. That's why I think one of the most important skills to develop is to learn how to learn.
  - Symbiote 11y ago
    I think it very much depends on the teacher. It's not difficult to explain the first few topics on calculus in terms of distance, speed and acceleration. Other examples I remember were washing lines (a catenary), the path traced by a stream train's wheels and rocketry. My teacher in England always had a real world example, but students with the other teacher didn't.

techman9 11y ago

I don't know... I'm taking a theory of computability class right now and I'm sure glad that the pumping lemma for regular languages is called "the pumping lemma for regular languages"

jimbokun 11y ago
But isn't that an attempt at a "descriptive" name? The intuition for the person who discovered this lemma, clearly envisioned the underlying process as a device pumping out new strings belonging to the language.
- techman9 11y ago
  I like to imagine they envisioned the strings themselves being "pumped" up by inserting new characters in the center.
- VLM 11y ago
  I took a brick and mortar automata class a long time ago and a classmate who clearly wasn't reading the text before lecture, insisted the prof called it the "plumping lemma" because it was about growing wider strings. That might have been the only funny thing that ever happened in automata class, unfortunately. Education by satire / humor is a sadly under-explored field. "A satirical approach to linear algebra"... not sure if I'd kickstart support that, or turn around and start running. In the eternal spirit of "anything that sounds interesting and impossible is a great startup opportunity" I propose that someone ... etc etc, you know.
  - techman9 11y ago
    My professor has had some quality quotes this quarter: "Misspell Chomsky's name as Chompsky, and I'll give you a pass; Misspell Turing as Turning or something? I'll flunk you"

driverdan 11y ago

> Few professors tell you what are they doing and why; they just throw formulas, theorems and symbols at you. That's not true. Proofs are a core process of all mathematics. Writing proofs can take up a majority of your time in some classes.

conjectures 11y ago

+1 on the final point. It may be difficult to appreciate how terse terse is here.