Research Math is an inside joke between friends. The jokes fall flat unless you know the same people and attend the same parties.
Why Mathematics is Boring (2007) [pdf]
11–20 of 129 posts
Re: Why Mathematics is Boring (2007) [pdf]
#12To 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 o…
I'll disagree. I read many papers with mathematics in them, and I get a lot of the concepts but the symbology used doesn't make sense to me so its hard for me to understand what is exactly going on. The sentence after the equation that explains each symbol is necessary for me, and many others as well. Not everyone has taken 8 math classes to know each kroniger delta by heart.
Re: Why Mathematics is Boring (2007) [pdf]
#13If 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.
Relatedly, a lot of recipe books just have a dry statement of what the ingredients are and how to combine them. They should be more like CS and science papers, and explain the narrative of why the recipe is exciting, and where it comes from, and what it means for the cook.
(Posted from a parallel universe.)
Re: Why Mathematics is Boring (2007) [pdf]
#14To 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 o…
Math will only emerge as a field when people will stop treating it as something that one only has to do at the frontier.
In other competitive fields such as banking, basketball and football you have the higher ups caring about the pyramid below them, if only as a place to recruit new talents.
Among the math higher ups, only Jim Simons cares about the "math pyramid" so to speak.
One has to be pragmatic, the goal of getting the population interested in math is GDP and median quality of life.
I know those things are very mundane for mathematicians who are absorbed in their world trying to be the ones cracking the Rienmann hypothesis, but even as that individual you have slightly better odds at making it if your surroundings look like Zurich or Cambridge vs. Baltimore or Mobile.
Matter of fact you have better odds if your country can extend the areas looking like Zurich and Cambridge and reduce the areas looking like Baltimore or Mobile.
Re: Why Mathematics is Boring (2007) [pdf]
#15To 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…
> Maybe the field would benefit to go more towards philosophy and logic, explaining it with words.
Interesting perspective.
I studied Philosophy and Logic in university:
https://en.wikipedia.org/wiki/List_of_logic_symbols
Much of it was familiar to me because, earlier, I took a class my Physics professor insisted we should take, as he put it, "if you want to get out of the dark ages": Programming in APL.
AS it turns out many of the symbols used in APL come from Logic.
To this day I find it disturbing that Python uses "^" for bitwise XOR, because both in Logic and APL, this is the symbol for AND. Anyone who studied Logic instantly recognizes the APL logic operators.
I say "interesting perspective" because the reality of what you are asking is precisely opposite what you think the outcome would be.
Re: Why Mathematics is Boring (2007) [pdf]
#16To 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…
> Maybe the field would benefit to go more towards philosophy and logic, explaining it with words. Interesting perspective. I studied Philosophy and Logic in university: https://en.wikipedia.org/wiki/List_of_logic_symbols Much of it was familiar to me because, earlier, I took a class my Physics professor insisted we should take, as he put it, "if you want to get out of the dark ages": Programming in APL. AS it turns…
> https://en.wikipedia.org/wiki/List_of_logic_symbols
Among all those symbols only ">" and "Even "=" is derivative of "" because by reasoning you can understand that you get to it by rotating the 2 lines about 30 degrees after realizing that you are dealing with 2 numbers which are in fact the same and not one being bigger than the other
Re: Why Mathematics is Boring (2007) [pdf]
#17I 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 they’re doing this more in schools. I was helping a first grader with homework recently and I was surprised the math worksheet was essentially simple algebra but with a shape or a little picture to represent the variable instead of a letter:
> 3 + circle = 7
> 10 - cloud = 4
It seems like a perfectly reasonable exercise for a first grader. Clouds and puppy faces and circles. But I have to admit if I’d seen “x” in place of the symbols I’m not sure I would’ve thought it was so reasonable.
Re: Why Mathematics is Boring (2007) [pdf]
#18Earlier quoted context omitted.
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 o…
I'll disagree. I read many papers with mathematics in them, and I get a lot of the concepts but the symbology used doesn't make sense to me so its hard for me to understand what is exactly going on. The sentence after the equation that explains each symbol is necessary for me, and many others as well. Not everyone has taken 8 math classes to know each kroniger delta by heart.
Well, musical notation looks like gibberish to someone who did not learn it. That said, I do agree with you 100% on scientific papers. Without an explanation of the formulas to cater to a wider audience a lot of papers fall into the "and then a miracle occurs" fallacy. Not because that's what they actually do. Not at all. I say this because to a large set of readers the impenetrable math has to be taken as a divine act that moves you from step n to n+1.
I remember going to lunch with one of my math professors in college. He was working on his PhD and was about to publish his thesis. As we sat down to eat he was very excited as he pulled out a sheet of paper from his pocket. It had been folded 3 or 4 times. You could tell he had been carrying this thing around, folding and unfolding it, for a long time because the folds showed wear.
This piece of paper was full of formulas, both sides, there was not a single blank area on the entire sheet.
He unfolded it and proceeded to give me a quick talk about what he was working on. He was very excited about it and I was happy for him. And yet that entire piece of paper looked like a language from another galaxy to me. I was on my third Calculus course. I had no clue what he was talking about.
Digressing a bit:
To this day I remember this when helping my kids with math, science and coding. As a matter of fact, I am currently working on an explanation of exponentiation and logarithms. In both cases everything looks great if things are even multiples of the base. The minute you do something like 2*2.1 or log_base_3(35.53) you hit the "and then a miracle occurs" problem, where you have to explain a thing by using the thing ("A white horse is a horse that is white").
I've spent the last couple of days working on cleaning-up an explanation of these things that makes sense without using a miracle to get to the answer. One of the problems is that there are natural explanations for things like square and cube (area and volume), but, what do powers of 2.1 and 3.25 mean? It is interesting how things completely break down. I don't think I have found a single mathematics text that bridges this gap.
If anyone has a sensible explanation of this I'd love to hear it!
Re: Why Mathematics is Boring (2007) [pdf]
#19To 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…
I think it would be better to just get away from ultra terseness. It's crazy to me how terse mathematics is compared to CS.
def velocity(time_ms): return ...
vs.
v(t) = ...
Like nearly every operation and variable is one character or symbol long (with the puzzling exception of trig where you get a whopping 3 characters - sin/cos/tan/etc.)
Re: Why Mathematics is Boring (2007) [pdf]
#20If 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.
As a non-mathematician this seems to be lacking a little something. Would you not want your paper to provide some indication of what you're attempting to communicate and why? Or is that information (as the joke goes) possible, and therefore trivial, to infer?