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Fantastic endeavour. I'm someone who has needed to force myself in mathematics for my career. I needed extra help at school, but had no real trouble in any othe

Fantastic endeavour. I'm someone who has needed to force myself in mathematics for my career. I needed extra help at school, but had no real trouble in any other class. I thought I was just too dumb for maths. I came to realise that my problem was not in mathematical concepts which it turns out are fairly easy, but in the language of maths itself and how it is taught (some exceptions such as Strang who is just a wonderful educator). Programming in particular really helped me to learn. That's not to say that certain areas aren't still difficult but reformulating away from the traditional notation and teaching style has helped me.

UncleOxidant 5y ago
I'm very similar. Show me a big mathematical formula and I'll have to dig into it for a while to understand it. Show me the code that implements the formula and it makes sense a lot quicker (for me anyway).
- mhh__ 5y ago
  I am the exact opposite. I look at code written by some analyst or whatever at work, and it's usually borderline unreadable if you ask me. Pretty print it as latex and I can visualize what it actually does almost immediately. Besides, I don't really care about "the code" i.e. the mechanics of computation but rather the properties of that expression that exist regardless of how it is communicated i.e. it's shape or how it behaves asymptotically etc.
- porknubbins 5y ago
  I have had this same experience of finally understanding a mathematical idea by seeing it implemented in a programming language. You can always eventually understand a program because there can't be any ambiguity or the compiler couldn't decide how to compile it. Math is not supposed to have ambiguity but it arises because there is too much convention and assumptions in the notation (granted sometimes they are saying something broader than can be expressed in code). But higher mathematics as a field seems to me to be like a programmer who uses single letter variables, never write comments and really like clever bitwise operators.
  - Jensson 5y ago
    Every math paper I've read and written have written out definitions for all the notation they use, even have a section called "notations". Don't you read math papers? Or do you mean applied math papers? Applied math is more like engineering though so they get sloppier with notation, I guess the same thing happens when computer scientists do maths. But that isn't really a problem with math, but a problem with sloppy people. Or you just didn't read the notation sections explaining everything.
    - porknubbins 5y ago
      As a programmer and occasional electronics hobbyist most math I encounter is in the context of whitepapers, or physics/EE texts or similar. I don’t really read papers in pure mathematics. Perhaps the difficulty is due to sloppiness by non professional mathematicians.
Jensson 5y ago
There is so little mathematical notation to learn though. A typical high school course has like a couple of symbols and a few keywords to learn, that can't really be the main reason you had a hard time to learn math when other courses has hundreds to thousands of words you have to learn?
- edge17 5y ago
  I think a lot of difficulty arises in math noation because most people (myself included) read a lot of math but don't actually write a ton to express my own thoughts. I'm decent at engineering math but grinding through problems, reading papers, and writing are all different skills.
- jcranmer 5y ago
  There are some big problems with mathematical notation. The first is that it is terse--often excessively so. The clearest way this manifests is the sheer predilection for single-variable names. Every variable in every equation invariably gets reduced down to a single letter, and sometimes you need to go so far as distinguishing based on font face or boldness or what random diacritic you can throw on that variable name to keep it a single-letter variable name. Even when it doesn't reach that extreme of an issue, it makes skimming difficult, because you now have to go back through the prose to figure out what 'H' means, and spotting the definition of a single-letter variable in prose is really easy, right? (No, no it is not). Another factor that can make it infuriating to read mathematical notation is the sheer overloading. Subscript notation is a good one for this--if you see a single letter subscripted by something else, it could mean either getting a particular entry in a sequence of entries, it could be an index into a vector or a matrix or a tensor (and are you getting a row or a column or whatnot? all of the above!), maybe it might be a derivative. Or maybe it's an elaboration of which of the possible terms that get summarized to that letter is actually being referred to (e.g., E_a for activation energy). Of course, the flip side of the notation problem is the fact that some concepts have multiple different notations. Multiplication is a common example: to multiply a and b, you can use a × b, a · b, or screw any symbol altogether and just say ab (thus a(b) is also a way to indicate multiplication, which totally has no potential confusion with applying a function [1]). Differentiation is the worst; virtually every introduction to derivatives starts with "oh there's multiple notations for this"--is it really necessary that so many need to exist? [1] There was one paper I once read where I literally had to spend several minutes staring at a key formula trying to figure it if I was looking at function application or multiplication.
_moog 5y ago
I found myself in a similar boat (I'm a software engineer with no college degree). I did well in school with geometry, algebra, and pre-calculus but I did so by memorizing not by understanding. A decade later I ended up going through a lot of Khan Academy videos to refresh myself and then diving into discrete math and linear algebra textbooks. It really helped me to finally understand the core mathematical concepts that we use in programming algorithms.

UncleOxidant 5y ago

I'm very similar. Show me a big mathematical formula and I'll have to dig into it for a while to understand it. Show me the code that implements the formula and it makes sense a lot quicker (for me anyway).

mhh__ 5y ago
I am the exact opposite. I look at code written by some analyst or whatever at work, and it's usually borderline unreadable if you ask me. Pretty print it as latex and I can visualize what it actually does almost immediately. Besides, I don't really care about "the code" i.e. the mechanics of computation but rather the properties of that expression that exist regardless of how it is communicated i.e. it's shape or how it behaves asymptotically etc.
porknubbins 5y ago
I have had this same experience of finally understanding a mathematical idea by seeing it implemented in a programming language. You can always eventually understand a program because there can't be any ambiguity or the compiler couldn't decide how to compile it. Math is not supposed to have ambiguity but it arises because there is too much convention and assumptions in the notation (granted sometimes they are saying something broader than can be expressed in code). But higher mathematics as a field seems to me to be like a programmer who uses single letter variables, never write comments and really like clever bitwise operators.
- Jensson 5y ago
  Every math paper I've read and written have written out definitions for all the notation they use, even have a section called "notations". Don't you read math papers? Or do you mean applied math papers? Applied math is more like engineering though so they get sloppier with notation, I guess the same thing happens when computer scientists do maths. But that isn't really a problem with math, but a problem with sloppy people. Or you just didn't read the notation sections explaining everything.
  - porknubbins 5y ago
    As a programmer and occasional electronics hobbyist most math I encounter is in the context of whitepapers, or physics/EE texts or similar. I don’t really read papers in pure mathematics. Perhaps the difficulty is due to sloppiness by non professional mathematicians.

Jensson 5y ago

There is so little mathematical notation to learn though. A typical high school course has like a couple of symbols and a few keywords to learn, that can't really be the main reason you had a hard time to learn math when other courses has hundreds to thousands of words you have to learn?

edge17 5y ago
I think a lot of difficulty arises in math noation because most people (myself included) read a lot of math but don't actually write a ton to express my own thoughts. I'm decent at engineering math but grinding through problems, reading papers, and writing are all different skills.
jcranmer 5y ago
There are some big problems with mathematical notation. The first is that it is terse--often excessively so. The clearest way this manifests is the sheer predilection for single-variable names. Every variable in every equation invariably gets reduced down to a single letter, and sometimes you need to go so far as distinguishing based on font face or boldness or what random diacritic you can throw on that variable name to keep it a single-letter variable name. Even when it doesn't reach that extreme of an issue, it makes skimming difficult, because you now have to go back through the prose to figure out what 'H' means, and spotting the definition of a single-letter variable in prose is really easy, right? (No, no it is not). Another factor that can make it infuriating to read mathematical notation is the sheer overloading. Subscript notation is a good one for this--if you see a single letter subscripted by something else, it could mean either getting a particular entry in a sequence of entries, it could be an index into a vector or a matrix or a tensor (and are you getting a row or a column or whatnot? all of the above!), maybe it might be a derivative. Or maybe it's an elaboration of which of the possible terms that get summarized to that letter is actually being referred to (e.g., E_a for activation energy). Of course, the flip side of the notation problem is the fact that some concepts have multiple different notations. Multiplication is a common example: to multiply a and b, you can use a × b, a · b, or screw any symbol altogether and just say ab (thus a(b) is also a way to indicate multiplication, which totally has no potential confusion with applying a function [1]). Differentiation is the worst; virtually every introduction to derivatives starts with "oh there's multiple notations for this"--is it really necessary that so many need to exist? [1] There was one paper I once read where I literally had to spend several minutes staring at a key formula trying to figure it if I was looking at function application or multiplication.

_moog 5y ago

I found myself in a similar boat (I'm a software engineer with no college degree). I did well in school with geometry, algebra, and pre-calculus but I did so by memorizing not by understanding. A decade later I ended up going through a lot of Khan Academy videos to refresh myself and then diving into discrete math and linear algebra textbooks. It really helped me to finally understand the core mathematical concepts that we use in programming algorithms.