3 ms·

Well, algebra and calculus have been around for a while. And then, Calculus took about 3 years for me to begin to scratch the surface... and realise I will nev

Well, algebra and calculus have been around for a while. And then, Calculus took about 3 years for me to begin to scratch the surface... and realise I will never need it as numeric methods took over completely with the advent of cheap compute.

constantcrying 3y ago
Nothing is more important for numerics than a veey good grasp of analysis.
- vkazanov 3y ago
  Yup. But there's understanding and there's understanding. If all you have is a piece of paper then there's no way around analytical approach. People used to be unbelievably good at it, including the applied crowd, like engineers. Having matlab at hand makes it possible to save years of analytical tinkering and simplifications and approximations. It is useful to understand what happens exactly but we no longer need 3-4 years of calculus depths... I mean, this used to be THE subject in most engineering programs round the world. These days it's more like bootstrapping the intuition.
  - commonlisp94 3y ago
    > Having matlab at hand makes it possible to save years of analytical tinkering and simplifications and approximations. And they use poor and imprecise approximations that they can't debug, because they just plug in numbers and hope for answer.
    - vkazanov 3y ago
      Understanding that something is fundamentally an approximation is important. Users of these packages are well aware of the fact. What point are you trying to make?
      - commonlisp94 3y ago
        > fundamentally an approximation is important. Yep, what you want is a good and predictable approximation. > What point are you trying to make? In practice most Matlab solutions you are describing are awful, in terms of performance and in terms of accuracy due to ignorance about underlying theory.
  - constantcrying 3y ago
    Solving integrals (beyond simple cases) has never been all that useful, simply because most integrals don't even have a solution. You do it in calculus to get a feeling for the subject. If you want to calculate a numerical solution to a novel analytic problem you absolutely need a good understanding of analysis. Being able to plug things into Matlab is only useful if Matlab implements a good solver for that problem. >It is useful to understand what happens exactly but we no longer need 3-4 years of calculus depths. Indeed. We need 5+ years of analysis now.
commonlisp94 3y ago
> I will never need it as numeric methods took over completely What if you want to make a numerical method for something you can't look up the recipe for?
- vkazanov 3y ago
  I don't think the point is that nobody needs to understand the theory. The point is that 3-5 years of analysis might be an overkill in most of practical situations. Numerical methods are quite well-studied by now. If you need a new method or a variation then you probably specialise in these things, and that's a different question.
  - commonlisp94 3y ago
    It's really not. No problem looks exactly like the textbook you have to use analytical knowledge to devise a solution. > The point is that 3-5 years of analysis might be an overkill Rarely have I met an engineer and said, wow that guy knows TOO much about math. What do you think they should substitute?
    - vkazanov 3y ago
      I didn't say "too much math" :-) if anything, I'd like MORE math. But the amount of time available is fundamentally limited and it has to be balanced. E.g., in my personal circumstances probability theory, statistics, deeper proof understanding would all be useful. I had all of these at varying depths. But it's only analysis that we were getting for years and years and years... And I see why and how this is such an important subject historically. It's just not that big anymore relative to other things.

constantcrying 3y ago

Nothing is more important for numerics than a veey good grasp of analysis.

vkazanov 3y ago
Yup. But there's understanding and there's understanding. If all you have is a piece of paper then there's no way around analytical approach. People used to be unbelievably good at it, including the applied crowd, like engineers. Having matlab at hand makes it possible to save years of analytical tinkering and simplifications and approximations. It is useful to understand what happens exactly but we no longer need 3-4 years of calculus depths... I mean, this used to be THE subject in most engineering programs round the world. These days it's more like bootstrapping the intuition.
- commonlisp94 3y ago
  > Having matlab at hand makes it possible to save years of analytical tinkering and simplifications and approximations. And they use poor and imprecise approximations that they can't debug, because they just plug in numbers and hope for answer.
  - vkazanov 3y ago
    Understanding that something is fundamentally an approximation is important. Users of these packages are well aware of the fact. What point are you trying to make?
    - commonlisp94 3y ago
      > fundamentally an approximation is important. Yep, what you want is a good and predictable approximation. > What point are you trying to make? In practice most Matlab solutions you are describing are awful, in terms of performance and in terms of accuracy due to ignorance about underlying theory.
- constantcrying 3y ago
  Solving integrals (beyond simple cases) has never been all that useful, simply because most integrals don't even have a solution. You do it in calculus to get a feeling for the subject. If you want to calculate a numerical solution to a novel analytic problem you absolutely need a good understanding of analysis. Being able to plug things into Matlab is only useful if Matlab implements a good solver for that problem. >It is useful to understand what happens exactly but we no longer need 3-4 years of calculus depths. Indeed. We need 5+ years of analysis now.

commonlisp94 3y ago

> I will never need it as numeric methods took over completely What if you want to make a numerical method for something you can't look up the recipe for?

vkazanov 3y ago
I don't think the point is that nobody needs to understand the theory. The point is that 3-5 years of analysis might be an overkill in most of practical situations. Numerical methods are quite well-studied by now. If you need a new method or a variation then you probably specialise in these things, and that's a different question.
- commonlisp94 3y ago
  It's really not. No problem looks exactly like the textbook you have to use analytical knowledge to devise a solution. > The point is that 3-5 years of analysis might be an overkill Rarely have I met an engineer and said, wow that guy knows TOO much about math. What do you think they should substitute?
  - vkazanov 3y ago
    I didn't say "too much math" :-) if anything, I'd like MORE math. But the amount of time available is fundamentally limited and it has to be balanced. E.g., in my personal circumstances probability theory, statistics, deeper proof understanding would all be useful. I had all of these at varying depths. But it's only analysis that we were getting for years and years and years... And I see why and how this is such an important subject historically. It's just not that big anymore relative to other things.