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The biggest problem with math is the language. If it were a programming language, we would call it crufty and obscurantist. The language and notation really ne

by api 14y ago

The biggest problem with math is the language. If it were a programming language, we would call it crufty and obscurantist. The language and notation really needs to be rebooted and cleaned up. Math with a sane notation would be significantly easier to learn. The other -- and closely related -- problem is with how math is taught. It is taught procedure-first, not language-first and concept-first. It is impossible to understand math without being able to read the notation and translate it into relevant concepts. Doing the mechanics is secondary (and often done by computers these days).

guscost 14y ago
I agree 100% with this. Math will be a lot easier to learn with better tools.
- ChuckMcM 14y ago
  I think the dragonbox app [1] is a pretty solid empirical test of that thesis. [1] http://dragonboxapp.com/ http://dragonboxapp.com/
MaysonL 14y ago
Go back and look at Newton's and Leibniz's notation. Math notation, proof structure, and simplicity are continually getting cleaned up. The thing is, math is HARD.
- johnwatson11218 14y ago
  I read that Leibniz had studied Chinese and that it influenced some of the math notation that he introduced. Like using df/dx to express the derivative of f with respect to x as a kind of ratio. Whereas Newton just put f' to denote the same thing. I think Leibniz also came up with the elongated sigma for representing integrals as a type of summation.
  - btilly 14y ago
    No, Newton put a dot over y to represent a derivative. The f' notation came from Lagrange.
    - derleth 14y ago
      And Newton's dot notation could only represent differentiation with respect to time. Obviously what he was focused on, sure, but the more general notation was obviously also needed. Frankly, what annoys me is how mathematicians grab natural language words to represent their concepts, and often pick the worst possible of such words to use. For example: "Imaginary" numbers are no more imaginary than the "real" numbers are. They're just as well-defined, just as practically useful, and at least as interesting. But that idiotic name hangs on them, a relic from a more ignorant era, and scares away who knows how many students.
      - jules 14y ago
        The term imaginary was not chosen to be descriptive: > At the time, such numbers were poorly understood and regarded by some as fictitious or useless, much as zero and the negative numbers once were. Many other mathematicians were slow to adopt the use of imaginary numbers, including René Descartes, who wrote about them in his La Géométrie, where the term imaginary was used and meant to be derogatory. -- http://en.wikipedia.org/wiki/Imaginary_number http://en.wikipedia.org/wiki/Imaginary_number
  - tsahyt 14y ago
    df/dx is actually completely obvious. It tells you exactly what's going on, since df is the change of f and dx is the change of x, for very small changes. It's a lot more precise than simply writing f'. Newton wrote a dot over f and a lot of physicists still do that.
narrator 14y ago
I agree that math formula are hard to memorize because the language is terrible. It's from an age when things were handwritten and movements of the hand were to be conserved as much as possible. I used to have a bit of trouble with math but I found out , somewhat counter-intuitively, that the key, at least for me, is rote memorization of formula. When I was having trouble I always tried to understand how to derive rules from proof but this was impractical when trying to do higher mathematics as the level of abstraction got to be too much. I found it just easier to simply memorize algebraic formula, derivatives, integrals, properties of infinite series, etc with flash cards or repetitive exercises and then apply them as if they were simply given. Maybe I'll never be a great mathematician, but all I really want is to be able to read CS papers and understand analogue electronics.
- Someone 14y ago
  "movements of the hand were to be conserved as much as possible." Citation needed. I seriously doubt writing speed was the limiting factor for any mathematician (and that by at least an order of magnitude, but that is guessing). For some, paper might have been expensive, but even then, I doubt it forced them to write succinctly. Your method probably is a good one for being doing passive maths and probably will be of help for doing real math, too. Even the memorization of such things as multiplication tables helps there. For example, it may help you spot that all numbers in some sequence are prime, divisible by 17, or whatever, and that, in turn, can lead to a proof (I remember reading about a famous mathematician numerically approximating some integral, immediately seeing "hey, but that looks like X" (with X being something like log(27) or the sine of the square root of three or so), and from there, getting the inspiration to algebraically solve a class of problems, but cannot find a link for that)
ColinWright 14y ago
You know, I don't usually do this, but in this case I'll make an exception. > The biggest problem with math is the language. Citation needed. > Math with a sane notation would be significantly > easier to learn. Citation needed. > Doing the mechanics is secondary Citation needed. OK, so I speak from a different perspective from yours, because I have a PhD in math. I also do a lot of outreach, enrichment, and enhancement, dealing with reasonably bright (but very rarely genius level) kids, and in my direct personal experience I have found that (a) the notation is not a problem, and that (b) doing the mechanics opens the door to internalising the structures and enables the understanding of the ideas. In my experience, trying to grasp the ideas and concepts without working on what seem to be tedious, mechanical and apparently unnecessary processes results in a flailing about, an inability to anchor those concepts in experience or intuition. It's the mechanics and the processes that let you internalise the patterns and start to build your own structures, into which the ideas and concepts can then be fitted, making a coherent structure. So forgive me if I regard your pronouncements with a degree of suspicion and scepticism.
- kamaal 14y ago
  Have you ever worked with software projects going into several millions of lines? How would it be if all you are allowed is a Notepad to handle such a project? Will it be possible for you keep a cache of all the keywords, API's, documentation, their interplay and their heuristic all in your brain and still continue to modify and extend the codebase? If the answer to this question is yes. Then I presume you must either be a super genius with enormous brain power and memory to deal with so many symbols, their purpose and interplay. I find math to be similar. Going fluently with math forced to have many formulas learned and kept in brain. Those fundamentally acted as abstractions to shorten equations and represent them in a more concise way. Understanding others work forced me to go many steps below to see what and how they try to use their symbols to represent concepts. In fact many friends I know hated math because they needed to keep many things in their brain. Formulas, theorems, numbers, multiplication tables. Where is the space to put concepts? We are in serious need of IDE's for math.
  - Tloewald 14y ago
tsahyt 14y ago
Personally, I find the language to be brilliant.
chris_wot 14y ago
Congrats. https://twitter.com/shit_hn_says/status/234550205679271936 https://twitter.com/shit_hn_says/status/234550205679271936

by api 14y ago

guscost 14y ago

I agree 100% with this. Math will be a lot easier to learn with better tools.

ChuckMcM 14y ago
I think the dragonbox app [1] is a pretty solid empirical test of that thesis. [1] http://dragonboxapp.com/ http://dragonboxapp.com/

MaysonL 14y ago

Go back and look at Newton's and Leibniz's notation. Math notation, proof structure, and simplicity are continually getting cleaned up. The thing is, math is HARD.

johnwatson11218 14y ago
I read that Leibniz had studied Chinese and that it influenced some of the math notation that he introduced. Like using df/dx to express the derivative of f with respect to x as a kind of ratio. Whereas Newton just put f' to denote the same thing. I think Leibniz also came up with the elongated sigma for representing integrals as a type of summation.
- btilly 14y ago
  No, Newton put a dot over y to represent a derivative. The f' notation came from Lagrange.
  - derleth 14y ago
    And Newton's dot notation could only represent differentiation with respect to time. Obviously what he was focused on, sure, but the more general notation was obviously also needed. Frankly, what annoys me is how mathematicians grab natural language words to represent their concepts, and often pick the worst possible of such words to use. For example: "Imaginary" numbers are no more imaginary than the "real" numbers are. They're just as well-defined, just as practically useful, and at least as interesting. But that idiotic name hangs on them, a relic from a more ignorant era, and scares away who knows how many students.
    - jules 14y ago
      The term imaginary was not chosen to be descriptive: > At the time, such numbers were poorly understood and regarded by some as fictitious or useless, much as zero and the negative numbers once were. Many other mathematicians were slow to adopt the use of imaginary numbers, including René Descartes, who wrote about them in his La Géométrie, where the term imaginary was used and meant to be derogatory. -- http://en.wikipedia.org/wiki/Imaginary_number http://en.wikipedia.org/wiki/Imaginary_number
- tsahyt 14y ago
  df/dx is actually completely obvious. It tells you exactly what's going on, since df is the change of f and dx is the change of x, for very small changes. It's a lot more precise than simply writing f'. Newton wrote a dot over f and a lot of physicists still do that.

narrator 14y ago

I agree that math formula are hard to memorize because the language is terrible. It's from an age when things were handwritten and movements of the hand were to be conserved as much as possible. I used to have a bit of trouble with math but I found out , somewhat counter-intuitively, that the key, at least for me, is rote memorization of formula. When I was having trouble I always tried to understand how to derive rules from proof but this was impractical when trying to do higher mathematics as the level of abstraction got to be too much. I found it just easier to simply memorize algebraic formula, derivatives, integrals, properties of infinite series, etc with flash cards or repetitive exercises and then apply them as if they were simply given. Maybe I'll never be a great mathematician, but all I really want is to be able to read CS papers and understand analogue electronics.

Someone 14y ago
"movements of the hand were to be conserved as much as possible." Citation needed. I seriously doubt writing speed was the limiting factor for any mathematician (and that by at least an order of magnitude, but that is guessing). For some, paper might have been expensive, but even then, I doubt it forced them to write succinctly. Your method probably is a good one for being doing passive maths and probably will be of help for doing real math, too. Even the memorization of such things as multiplication tables helps there. For example, it may help you spot that all numbers in some sequence are prime, divisible by 17, or whatever, and that, in turn, can lead to a proof (I remember reading about a famous mathematician numerically approximating some integral, immediately seeing "hey, but that looks like X" (with X being something like log(27) or the sine of the square root of three or so), and from there, getting the inspiration to algebraically solve a class of problems, but cannot find a link for that)

ColinWright 14y ago

You know, I don't usually do this, but in this case I'll make an exception. > The biggest problem with math is the language. Citation needed. > Math with a sane notation would be significantly > easier to learn. Citation needed. > Doing the mechanics is secondary Citation needed. OK, so I speak from a different perspective from yours, because I have a PhD in math. I also do a lot of outreach, enrichment, and enhancement, dealing with reasonably bright (but very rarely genius level) kids, and in my direct personal experience I have found that (a) the notation is not a problem, and that (b) doing the mechanics opens the door to internalising the structures and enables the understanding of the ideas. In my experience, trying to grasp the ideas and concepts without working on what seem to be tedious, mechanical and apparently unnecessary processes results in a flailing about, an inability to anchor those concepts in experience or intuition. It's the mechanics and the processes that let you internalise the patterns and start to build your own structures, into which the ideas and concepts can then be fitted, making a coherent structure. So forgive me if I regard your pronouncements with a degree of suspicion and scepticism.

kamaal 14y ago
Have you ever worked with software projects going into several millions of lines? How would it be if all you are allowed is a Notepad to handle such a project? Will it be possible for you keep a cache of all the keywords, API's, documentation, their interplay and their heuristic all in your brain and still continue to modify and extend the codebase? If the answer to this question is yes. Then I presume you must either be a super genius with enormous brain power and memory to deal with so many symbols, their purpose and interplay. I find math to be similar. Going fluently with math forced to have many formulas learned and kept in brain. Those fundamentally acted as abstractions to shorten equations and represent them in a more concise way. Understanding others work forced me to go many steps below to see what and how they try to use their symbols to represent concepts. In fact many friends I know hated math because they needed to keep many things in their brain. Formulas, theorems, numbers, multiplication tables. Where is the space to put concepts? We are in serious need of IDE's for math.
- Tloewald 14y ago

tsahyt 14y ago

Personally, I find the language to be brilliant.

chris_wot 14y ago

Congrats. https://twitter.com/shit_hn_says/status/234550205679271936 https://twitter.com/shit_hn_says/status/234550205679271936