6 ms·

> mathematics is orders of magnitude more intensive and difficult than most programming But what level of programming and mathematics are you comparing here th

by dysoco 4y ago

> mathematics is orders of magnitude more intensive and difficult than most programming But what level of programming and mathematics are you comparing here though? because college-level algebra and calculus is really not that hard imho (once it "clicks" for you, but it's the same for programming), and if we are comparing math as in what you see in a BSc/Msc of Mathematics (or research-level) then I agree it's hard but you have to compare for an equivalent level of programming. > simple fact that shows this is the amount of programmers who have no formal training in engineering or computer science but we’re able to self-teach the concepts. The same cannot be said of mathematics I would blame it more on the fact that programming is a very useful tool for people outside Computer-Science, it has very direct applications and you can monetize it very easily, so it's very likely that they might want to learn it, however, rarely you see someone deciding to take Calculus just for the sake of it if they never bothered with it in College. Overall I agree with you, but personally I find math more difficult, most people probably do but I don't think it's inherently more difficult, it's just that people are less used to study it.

nickelpro 4y ago
I would hard disagree that undergrad level Analysis or even just the trickier corners of vector calculus are within the bounds of what programmers can easily pick up without dedicated and guided study. Everybody's gangster until they have to parameterize some bullshit helical structure in R3. Comparable levels of programming, what we expect of CS juniors, are regularly picked up by "the guy who is good with Excel" in office settings as it's mostly a function of experience and exposure, not theory. And now my worthless anecdotal evidence: I self taught myself into professional programming and it was a simple matter of banging my head against a wall until shit started working. The feedback loop, "did the thing crash or not", permitted me to learn on my own. I wouldn't even begin to understand how to self-teach myself Stokes Theorem or some shit, and have zero ability to author the proofs required to reach the conclusions higher level mathematics are built on.
- zozbot234 4y ago
  > I wouldn't even begin to understand how to self-teach myself Stokes Theorem or some shit Input it into a proof assistant, and rely on the same sort of feedback "does the computer accept your proof, or get stuck". The hard job of formalizing stuff for this purpose has seen significant progress, e.g. by the Lean mathlib project.
  - dysoco 4y ago
    Do you have more information on this approach? Sounds very interesting. I've read and toyed a little with things like Lean and I'm interested in that field but the barrier seems a bit high (without pre-existing knowledge) to just "input" a theorem and toy with it.
  - nickelpro 4y ago
    I would quibble with whether this is exactly equivalent. In programming I knew I needed to sort a list or find a most efficient path because some practical problem I was trying to solve demanded that I do that. Frequently I had a basically crap but working independent solution before I learned the names "EWD" or "A*". I independently discovered that I needed virtual interfaces (before I knew them by that name, "I wish pointers to parent classes could call implementations in subclasses") and then discovered language facilities for polymorphism and OOP. Without formal or at least guided instruction I would never think to move towards or discover "I wonder if there's a relationship that makes these double integrals of curls of vector fields easier to solve for". Programming has a high coupling between necessity, experience, and theory. In mathematics that coupling is much, much, much looser. Self learners in programming regularly re-discover and re-implement, typically less efficiently, all sorts of fundamentals of CS. The equivalent in mathematics rarely happens post-algebra.
    - nextos 4y ago
      I think your comparison is a bit unfair. Essentially, CS is as hard as mathematics because it is mathematics. For example, take any good static analyzer that implements abstract interpretation. It generally works using Galois connections, which is just abstract algebra. Dijkstra's algorithm or A* came pretty early in the history of CS. It would be fair to compare their difficulty to something similar in mathematics, say some basic results in Euclidean geometry.
- hgsgm 4y ago
  [dead]
- geysersam 4y ago
  I think you're hitting the nail on the head here. Something about the learning process makes programming much easier to pick up. What if we had something similar for mathematics? Rapid feedback, error messages, maybe even linters and highlighting for the "mathematical syntax". I've though about this before and I think tools like this could unlock math for a lot of people, and also increase the effectiveness of professional mathematicians. When learning math / seeing other learning math I've noticed that simple errors such as typos often slow down or hinder understanding of the subject.
  - sillysaurusx 4y ago
    What a creative, delightful solution. I encourage you to pursue this!
  - kthielen 4y ago
    I think this is the goal of proof assistants based on the Curry-Howard isomorphism, which the original author thought to denigrate for some reason.
  - __MatrixMan__ 4y ago
    I'd love to play around with such tools, but I think they'd only get you so far before they'd start to become a hinderance. The linter in mathematics is whether the other mathematician (whoever you're proving to) knows what you mean. If you're locked into a rigidly defined syntax, an obvious line of questioning is: what's not expressible in this syntax? I fear that by the time the tooling was agreed on, built, and taught in schools, you'd have something like APL, which might be cool to code in, but from which the mathematical conversion would have moved on a while ago. Efforts like that, after all, are how math becomes engineering. Consider, for instance, Russel's theory of types, which was interesting math at the time and now strikes the student with an engineering background as "pretty much just Java" (or any "normal" statically typed language).
    - eternityforest 4y ago
      If you're learning math for career reasons rather than just pure curiosity, engineering is the main/possibly only place you'd use it besides statistical analysis.
throwoutway 4y ago
Calculus is significant more difficult and requires many Times more studying than algebra
deleted 4y ago
[deleted]
kovac 4y ago
College-level means undergraduate-level? If so, how is algebra/calculus not that hard? Abstract algebra is one of the hardest stuff I've come across. Calculus? Do you think it's not that hard to prove convergence/bounds/limits of random series and sequences... I agree though that calculus is not that hard, compared to the rest. Programming is child's play compared to undergraduate mathematics taught in math departments. It's important that you take a module from the math department, not from a physical science or engineering department if you want to experience what it is like.
- kthielen 4y ago
  > Programming is child's play compared to undergraduate mathematics taught in math departments. One thing you might learn in math is to avoid making overgeneralized statements that you can’t support. A valid substitution in your statement for “programming” is writing a compiler. And for “undergraduate mathematics taught in math departments”, basic differential calculus. Yet we regularly teach smart high school students and first-year undergraduates calculus, and almost never try to teach them to write a compiler, contradicting your proposition. But what do I know? I’m just a dumb programmer. I can’t read your mind, so maybe you had something a little more specific you wanted to say.
  - ThrowawayR2 4y ago
    > "Yet we regularly teach smart high school students and first-year undergraduates calculus..." High school students are taught plug-and-chug calculus where one uses rules and formulae without any real understanding of the underlying subtleties that make calculus work.
    - kthielen 4y ago
      Bulletproof counter argument, you sure showed me.
      - deleted 4y ago
        [deleted]
eternityforest 4y ago
For practical purposes, a fair comparison would be "a useful amount of programming" vs "A useful amount of math". You can get hired after a brief boot camp, although it's not common. A useful amount of math is like, ordinary differential equations in engineering school, since apps have taken over most use cases for simpler math. The only direct use is to learn to access the "New way of thinking" math people talk about, and even that seems harder than making detailed to do lists.
6451937099 4y ago
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6451937099 4y ago
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by dysoco 4y ago

nickelpro 4y ago

I would hard disagree that undergrad level Analysis or even just the trickier corners of vector calculus are within the bounds of what programmers can easily pick up without dedicated and guided study. Everybody's gangster until they have to parameterize some bullshit helical structure in R3. Comparable levels of programming, what we expect of CS juniors, are regularly picked up by "the guy who is good with Excel" in office settings as it's mostly a function of experience and exposure, not theory. And now my worthless anecdotal evidence: I self taught myself into professional programming and it was a simple matter of banging my head against a wall until shit started working. The feedback loop, "did the thing crash or not", permitted me to learn on my own. I wouldn't even begin to understand how to self-teach myself Stokes Theorem or some shit, and have zero ability to author the proofs required to reach the conclusions higher level mathematics are built on.

zozbot234 4y ago
> I wouldn't even begin to understand how to self-teach myself Stokes Theorem or some shit Input it into a proof assistant, and rely on the same sort of feedback "does the computer accept your proof, or get stuck". The hard job of formalizing stuff for this purpose has seen significant progress, e.g. by the Lean mathlib project.
- dysoco 4y ago
  Do you have more information on this approach? Sounds very interesting. I've read and toyed a little with things like Lean and I'm interested in that field but the barrier seems a bit high (without pre-existing knowledge) to just "input" a theorem and toy with it.
- nickelpro 4y ago
  I would quibble with whether this is exactly equivalent. In programming I knew I needed to sort a list or find a most efficient path because some practical problem I was trying to solve demanded that I do that. Frequently I had a basically crap but working independent solution before I learned the names "EWD" or "A*". I independently discovered that I needed virtual interfaces (before I knew them by that name, "I wish pointers to parent classes could call implementations in subclasses") and then discovered language facilities for polymorphism and OOP. Without formal or at least guided instruction I would never think to move towards or discover "I wonder if there's a relationship that makes these double integrals of curls of vector fields easier to solve for". Programming has a high coupling between necessity, experience, and theory. In mathematics that coupling is much, much, much looser. Self learners in programming regularly re-discover and re-implement, typically less efficiently, all sorts of fundamentals of CS. The equivalent in mathematics rarely happens post-algebra.
  - nextos 4y ago
    I think your comparison is a bit unfair. Essentially, CS is as hard as mathematics because it is mathematics. For example, take any good static analyzer that implements abstract interpretation. It generally works using Galois connections, which is just abstract algebra. Dijkstra's algorithm or A* came pretty early in the history of CS. It would be fair to compare their difficulty to something similar in mathematics, say some basic results in Euclidean geometry.
hgsgm 4y ago
[dead]
geysersam 4y ago
I think you're hitting the nail on the head here. Something about the learning process makes programming much easier to pick up. What if we had something similar for mathematics? Rapid feedback, error messages, maybe even linters and highlighting for the "mathematical syntax". I've though about this before and I think tools like this could unlock math for a lot of people, and also increase the effectiveness of professional mathematicians. When learning math / seeing other learning math I've noticed that simple errors such as typos often slow down or hinder understanding of the subject.
- sillysaurusx 4y ago
  What a creative, delightful solution. I encourage you to pursue this!
- kthielen 4y ago
  I think this is the goal of proof assistants based on the Curry-Howard isomorphism, which the original author thought to denigrate for some reason.
- __MatrixMan__ 4y ago
  I'd love to play around with such tools, but I think they'd only get you so far before they'd start to become a hinderance. The linter in mathematics is whether the other mathematician (whoever you're proving to) knows what you mean. If you're locked into a rigidly defined syntax, an obvious line of questioning is: what's not expressible in this syntax? I fear that by the time the tooling was agreed on, built, and taught in schools, you'd have something like APL, which might be cool to code in, but from which the mathematical conversion would have moved on a while ago. Efforts like that, after all, are how math becomes engineering. Consider, for instance, Russel's theory of types, which was interesting math at the time and now strikes the student with an engineering background as "pretty much just Java" (or any "normal" statically typed language).
  - eternityforest 4y ago
    If you're learning math for career reasons rather than just pure curiosity, engineering is the main/possibly only place you'd use it besides statistical analysis.

throwoutway 4y ago

Calculus is significant more difficult and requires many Times more studying than algebra

deleted 4y ago

[deleted]

kovac 4y ago

College-level means undergraduate-level? If so, how is algebra/calculus not that hard? Abstract algebra is one of the hardest stuff I've come across. Calculus? Do you think it's not that hard to prove convergence/bounds/limits of random series and sequences... I agree though that calculus is not that hard, compared to the rest. Programming is child's play compared to undergraduate mathematics taught in math departments. It's important that you take a module from the math department, not from a physical science or engineering department if you want to experience what it is like.

kthielen 4y ago
> Programming is child's play compared to undergraduate mathematics taught in math departments. One thing you might learn in math is to avoid making overgeneralized statements that you can’t support. A valid substitution in your statement for “programming” is writing a compiler. And for “undergraduate mathematics taught in math departments”, basic differential calculus. Yet we regularly teach smart high school students and first-year undergraduates calculus, and almost never try to teach them to write a compiler, contradicting your proposition. But what do I know? I’m just a dumb programmer. I can’t read your mind, so maybe you had something a little more specific you wanted to say.
- ThrowawayR2 4y ago
  > "Yet we regularly teach smart high school students and first-year undergraduates calculus..." High school students are taught plug-and-chug calculus where one uses rules and formulae without any real understanding of the underlying subtleties that make calculus work.
  - kthielen 4y ago
    Bulletproof counter argument, you sure showed me.
    - deleted 4y ago
      [deleted]

eternityforest 4y ago

For practical purposes, a fair comparison would be "a useful amount of programming" vs "A useful amount of math". You can get hired after a brief boot camp, although it's not common. A useful amount of math is like, ordinary differential equations in engineering school, since apps have taken over most use cases for simpler math. The only direct use is to learn to access the "New way of thinking" math people talk about, and even that seems harder than making detailed to do lists.

6451937099 4y ago

[dead]