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A Computer Scientist Tells Mathematicians How to Write Proofs

20 points by ghosh 12y ago

uaygsfdbzf 12y ago
The proposal seems to be "use more hyperlinks than you already do", while being quite arrogant about it. Mathematicians already use numbered equations and steps in proofs and quite a bit of referals and links, while trying to keep things readable. Adding absolutely trivial remarks like "This corollary to the previous theorem uses the previous theorem" do not add any value and are thus rightfully dropped. Further, if you are already dropping trivial steps (e.g. working with fractions in step 5) then it boils down to: Number all your steps down to a level of triviality I want, which is going to be different from the one you want.
avmich 12y ago
Calling Leslie Lamport a computer scientist as opposed to mathematician is to be not very familiar with the matters.
mariodiana 12y ago
Actually, I wouldn't tell the mathematicians how to write proofs; I would tell them how to write code. I'm not a math guy, but I've at least seen math proofs. It's remarkable how much English is there. It's like there's a paragraph or two explaining what they're after, and then there's a mathematical equation. After the equation, there's more text, explaining some more, and then another equation. A math proof is replete with English. But then you get some of these guys writing code and it's like, "Great! No English!" There's not a comment to be found. Or, take variables. "Let i represent column and j represent row" -- because, you know, it would simply just aggravate their carpal tunnel syndrome to have to type out c-o-l-u-m-n and r-o-w. A real math he-man doesn't bother with descriptive variable names! That's for liberal arts majors! I just don't get it.
alexvoda 12y ago
My biggest problem with the way math is done is the insistence on using single letter names with at most some indices. How many good programmers would agree that naming variables and functions with only one letter is a good idea? The sad part is that this infiltrated all other fields related to mathematics. You can not even imagine how much did teachers annoy me in high school when all variables in Pascal(back then this was still the language that was thought) programs were named with one letter (I started programing when I was in elementary school) . I believe this is caused by the symbol-less notation of the multiplication operator. Since xy actually means x*y there is no way to have words as names. A side problem caused by this is the overloading of the symbol-less operator to mean something else in the case of mixed numerals ( http://en.wikipedia.org/wiki/Fraction_(mathematics)#Mixed_numbers http://en.wikipedia.org/wiki/Fraction_(mathematics)#Mixed_nu... ). Thankfully, where I am from, this notation is only used in middle school. But this caused a lot of problems when I was helping siblings with homework since I was no longer used to that notation. Oh, also, Tau is better than Pi ( http://www.tauday.com/ http://www.tauday.com/ ).
deleted 12y ago
[deleted]

20 points by ghosh 12y ago

The proposal seems to be "use more hyperlinks than you already do", while being quite arrogant about it. Mathematicians already use numbered equations and steps in proofs and quite a bit of referals and links, while trying to keep things readable. Adding absolutely trivial remarks like "This corollary to the previous theorem uses the previous theorem" do not add any value and are thus rightfully dropped. Further, if you are already dropping trivial steps (e.g. working with fractions in step 5) then it boils down to: Number all your steps down to a level of triviality I want, which is going to be different from the one you want.

avmich 12y ago

Calling Leslie Lamport a computer scientist as opposed to mathematician is to be not very familiar with the matters.

mariodiana 12y ago

Actually, I wouldn't tell the mathematicians how to write proofs; I would tell them how to write code. I'm not a math guy, but I've at least seen math proofs. It's remarkable how much English is there. It's like there's a paragraph or two explaining what they're after, and then there's a mathematical equation. After the equation, there's more text, explaining some more, and then another equation. A math proof is replete with English. But then you get some of these guys writing code and it's like, "Great! No English!" There's not a comment to be found. Or, take variables. "Let i represent column and j represent row" -- because, you know, it would simply just aggravate their carpal tunnel syndrome to have to type out c-o-l-u-m-n and r-o-w. A real math he-man doesn't bother with descriptive variable names! That's for liberal arts majors! I just don't get it.

alexvoda 12y ago

My biggest problem with the way math is done is the insistence on using single letter names with at most some indices. How many good programmers would agree that naming variables and functions with only one letter is a good idea? The sad part is that this infiltrated all other fields related to mathematics. You can not even imagine how much did teachers annoy me in high school when all variables in Pascal(back then this was still the language that was thought) programs were named with one letter (I started programing when I was in elementary school) . I believe this is caused by the symbol-less notation of the multiplication operator. Since xy actually means x*y there is no way to have words as names. A side problem caused by this is the overloading of the symbol-less operator to mean something else in the case of mixed numerals ( http://en.wikipedia.org/wiki/Fraction_(mathematics)#Mixed_numbers http://en.wikipedia.org/wiki/Fraction_(mathematics)#Mixed_nu... ). Thankfully, where I am from, this notation is only used in middle school. But this caused a lot of problems when I was helping siblings with homework since I was no longer used to that notation. Oh, also, Tau is better than Pi ( http://www.tauday.com/ http://www.tauday.com/ ).

deleted 12y ago

[deleted]