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I think Yegge is actually completely correct. I started to learn to program when I was 14, and once I understood the concept of functions, I found it much easie

I think Yegge is actually completely correct. I started to learn to program when I was 14, and once I understood the concept of functions, I found it much easier to do my calculus and physics work. Fundamentally I understood how to break things down into computable steps. Granted, I think get the impression we might be overloading the term "mathematics".

edgyquant 4y ago
I grew up programming (from 10 or so) and couldn’t agree more. I have almost no formal education yet I’ve picked up enough math to do ML and (mediocre) cryptography and keep up with people who have scary sounding degrees. in the process I’ve fallen in love with math and think as programmers we haven’t been meeting mathematicians half way.
bmitc 4y ago
Mathematics is not just functions and calculus. And it seems to me that you learned the concept of functions through programming first but that there's not evidence that you couldn't have learned it from mathematics at first. Functions are a pretty easy concept, so I think it's pretty easy to introduce it from a variety of points of view. So I'm not sure the anecdote backs up any argument about learning programming makes mathematics easy. I am of the opinion that programming can be used to explore and learn mathematical ideas and am a big proponent of that, but that is something different than "I know how to program so mathematics will be easy now".
- ngcc_hk 4y ago
  Always wonder about this. Other than foundation of maths, the function abd calculus view … my wonder is about the data part of the maths. Not the process. Yes one can view matrix as a function but could it be data. One can real number line, complex or integer as data?
dekhn 4y ago
functions in traditional programming and functions in math are two different things entirely. They should have been called procedures (I think there's historical debate about this but I can't find the reference). Obviously, functional programming is an attempt to address this.
BeetleB 4y ago
For most mathematicians, calculus as is often taught in typical undergrads is not "true" mathematics. It's just a tool for computation. For them, calculus is analysis (theorems/proofs that are used to build up calculus). So my question is: Did you study analysis and would you credit programming in helping you get good at it?
- c0balt 4y ago
  +1 for this comment. Calculus, i.e., Calculating with mostly finite numbers and (usually) a known set of well defined rules is only a part of mathematics. As a student that currently learns Analysis and linear algebra, it is far more complex and abstract than calculus. It is not neccessarily harder to learn but different. And adapting to this paradigma takes time (and effort). It is similiar to learning Assembley as a Python developer. Knowing Python will help with Assembley. But the levels of abstraction are obviously different and will require a lot of learning.
- edgyquant 4y ago
  Not them but I def would. I built a fintech/econometric-lite system in python years back and it was mostly just taking in a ton of “obvious” knowledge and realizing the cool stuff you could do in practice
- kaashif 4y ago
  I don't understand this comment. Calculus as taught to mathematics undergrads is analysis, right? Where is calculus "often taught" without "theorems/proofs that are used to build up calculus"?
  - deleted 4y ago
    [deleted]
  - jhanschoo 4y ago
    Not US, but for GCSE A's further math equivalent, calculus primarily involved applying intermediate rules (chain rules, trig identities, etc.) to evaluate differentiation/integrals on elementary functions, and a bit on geometric and arithmetic series. Analysis discusses less well behaved functions and spaces than these.
mathgladiator 4y ago
> get the impression we might be overloading the term "mathematics". We are; the challenge is there is a near infinite difficulty in both "programming" and "mathematics" and at a certain point, the skill sets diverge greatly.

edgyquant 4y ago

I grew up programming (from 10 or so) and couldn’t agree more. I have almost no formal education yet I’ve picked up enough math to do ML and (mediocre) cryptography and keep up with people who have scary sounding degrees. in the process I’ve fallen in love with math and think as programmers we haven’t been meeting mathematicians half way.

bmitc 4y ago

Mathematics is not just functions and calculus. And it seems to me that you learned the concept of functions through programming first but that there's not evidence that you couldn't have learned it from mathematics at first. Functions are a pretty easy concept, so I think it's pretty easy to introduce it from a variety of points of view. So I'm not sure the anecdote backs up any argument about learning programming makes mathematics easy. I am of the opinion that programming can be used to explore and learn mathematical ideas and am a big proponent of that, but that is something different than "I know how to program so mathematics will be easy now".

ngcc_hk 4y ago
Always wonder about this. Other than foundation of maths, the function abd calculus view … my wonder is about the data part of the maths. Not the process. Yes one can view matrix as a function but could it be data. One can real number line, complex or integer as data?

dekhn 4y ago

functions in traditional programming and functions in math are two different things entirely. They should have been called procedures (I think there's historical debate about this but I can't find the reference). Obviously, functional programming is an attempt to address this.

BeetleB 4y ago

For most mathematicians, calculus as is often taught in typical undergrads is not "true" mathematics. It's just a tool for computation. For them, calculus is analysis (theorems/proofs that are used to build up calculus). So my question is: Did you study analysis and would you credit programming in helping you get good at it?

c0balt 4y ago
+1 for this comment. Calculus, i.e., Calculating with mostly finite numbers and (usually) a known set of well defined rules is only a part of mathematics. As a student that currently learns Analysis and linear algebra, it is far more complex and abstract than calculus. It is not neccessarily harder to learn but different. And adapting to this paradigma takes time (and effort). It is similiar to learning Assembley as a Python developer. Knowing Python will help with Assembley. But the levels of abstraction are obviously different and will require a lot of learning.
edgyquant 4y ago
Not them but I def would. I built a fintech/econometric-lite system in python years back and it was mostly just taking in a ton of “obvious” knowledge and realizing the cool stuff you could do in practice
kaashif 4y ago
I don't understand this comment. Calculus as taught to mathematics undergrads is analysis, right? Where is calculus "often taught" without "theorems/proofs that are used to build up calculus"?
- deleted 4y ago
  [deleted]
- jhanschoo 4y ago
  Not US, but for GCSE A's further math equivalent, calculus primarily involved applying intermediate rules (chain rules, trig identities, etc.) to evaluate differentiation/integrals on elementary functions, and a bit on geometric and arithmetic series. Analysis discusses less well behaved functions and spaces than these.

mathgladiator 4y ago

> get the impression we might be overloading the term "mathematics". We are; the challenge is there is a near infinite difficulty in both "programming" and "mathematics" and at a certain point, the skill sets diverge greatly.