Why Mathematics is Boring (2007) [pdf]
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Why Mathematics is Boring (2007) [pdf]
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Re: Why Mathematics is Boring (2007) [pdf]
#2I believe this is actually a really great point. For instance, I didn't know that it was originally Brahmagupta who started using symbols in math. His initial use of symbols to represent numbers involved using color names like "blue" and "green".
More interestingly before using symbols as variables in math Egyptians were capable of doing Quadratic equations without these variables.
If I were teaching math today I would probably teach this. I would try to do algebra without using variables, and then I would use funny words like "blue" as Brahma Gupta use to. I think that this would probably stop a lot of the questions like "why are there letters in math!?"
Re: Why Mathematics is Boring (2007) [pdf]
#3If you read any science papers, they start with a clear introduction with the aims, claims, importance and novelty of the work. A lot of math papers (but not all) just start off with a dry statement of what the theorems being proved are, and jump right into the proofs.
I always wonder why editors don't understand the importance of these things and don't enforce them.
Re: Why Mathematics is Boring (2007) [pdf]
#4I believe this is actually a really great point. For instance, I didn't know that it was originally Brahmagupta who started using symbols in math. His initial use of symbols to represent numbers involved using color names like "blue" and "green". More interestingly before using symbols as variables in math Egyptians were capable of doing Quadratic equations without these variables. If I were teaching math today I wou…
> I think that this would probably stop a lot of the questions like "why are there letters in math!?"
Wouldn't people just instead ask "Why are there colours in maths?"?
I don't think that this:
blue + blue = 2*blue
x + x = 2*xRe: Why Mathematics is Boring (2007) [pdf]
#5To me it's the language.
You have to learn a whole new alphabet and signs.
This is done for the sake of quick communication between mathematicians, but it's necessary to make a study and see the pros and cons.
While it's true that it makes communication faster and straightforward it keeps so many people outside of the field.
Maybe the field would benefit to go more towards philosophy and logic, explaining it with words.
Re: Why Mathematics is Boring (2007) [pdf]
#6It's boring but usually everything is well-defined and hence well-understandable.
Not the case for most CS papers.
Re: Why Mathematics is Boring (2007) [pdf]
#7I believe this is actually a really great point. For instance, I didn't know that it was originally Brahmagupta who started using symbols in math. His initial use of symbols to represent numbers involved using color names like "blue" and "green". More interestingly before using symbols as variables in math Egyptians were capable of doing Quadratic equations without these variables. If I were teaching math today I wou…
I don't recall where I read this, but a young Feynman motivated himself to learn trig by imagining that he had been challenged by a mysterious stranger to answer riddles. For example (I'm making this up) "You only have a protractor and the ability to measure your paces - tell me the height of that flagpole!" The operation, then, is to pace out a distance from the base of flagpole, sight down the protractor to the top of the flagpole to get an angle, and compute. (Since tan(y/x) = a, arctan(a) = y/x, y=x * arctan(a)). So the motivation was imaginary and concrete. And it's dramatic, because there's an obstacle, a chance of failure, and a chance for glory.
I can't help but see a parallel with magicians, who can dazzle us because they are willing to go further than most of us, in terms of practice. In the same way, math gives you the ability to dazzle with surprising answers, to do a lot with a little.
Re: Why Mathematics is Boring (2007) [pdf]
#8If you read any science papers, they start with a clear introduction with the aims, claims, importance and novelty of the work. A lot of math papers (but not all) just start off with a dry statement of what the theorems being proved are, and jump right into the proofs. I always wonder why editors don't understand the importance of these things and don't enforce them.
I for one welcome the "dryness" of mathematical writing. It feels clean, like reading a story without distracting ads.
A beautiful advice that I received as a student was to write mathematics as a series of definitions, propositions and proofs. No text is allowed to exist outside of these three. In practice it is difficult to enforce, but it is helpful to keep this as an aim.
Re: Why Mathematics is Boring (2007) [pdf]
#9To me it's the language. You have to learn a whole new alphabet and signs. This is done for the sake of quick communication between mathematicians, but it's necessary to make a study and see the pros and cons. While it's true that it makes communication faster and straightforward it keeps so many people outside of the field. Maybe the field would benefit to go more towards philosophy and logic, explaining it with wor…
The idea that unfamiliar symbols and alphabets are a huge problem for the accessibility of math is common. As physicist I do not agree. Math is hard. It's damned difficult. Symbols and alphabets are the least of your concerns when dealing with a math paper. I know a lot of these symbols by name, I sometimes understand the notation or could familiarize myself with it but the math itself? Nope, no chance, usually. If one cannot deal with the symbols, there is no chance in hell one could deal with the ideas.
Re: Why Mathematics is Boring (2007) [pdf]
#10I believe this is actually a really great point. For instance, I didn't know that it was originally Brahmagupta who started using symbols in math. His initial use of symbols to represent numbers involved using color names like "blue" and "green". More interestingly before using symbols as variables in math Egyptians were capable of doing Quadratic equations without these variables. If I were teaching math today I wou…
> I think that this would probably stop a lot of the questions like "why are there letters in math!?" Wouldn't people just instead ask "Why are there colours in maths?"? I don't think that this: blue + blue = 2*blue Is any more meaningful or edifying than: x + x = 2*x
Yeah, I think the problem is not about variable names but giving meaning to these abstract objects. Beginners often have difficulty understanding abstract concepts and specific (concrete) examples are helpful for them to learn. I think 'Funny words' alone will not be helpful, or even detrimental to beginners' understanding as they may be distracted by unrelated concepts (e.g. what do you mean by adding blues together in this example?).