How to Read Mathematics
web.stonehill.edu
How to Read Mathematics
1–10 of 33 posts
Re: How to Read Mathematics
#2I've also found these to be helpful:
The Language and Grammar of Mathematics, from The Princeton Companion to Mathematics, by Timothy Gowers: http://press.princeton.edu/chapters/gowers/gowers_I_2.pdf
Reading Mathematics, by John Hamal Hubbard: http://www.math.cornell.edu/~hubbard/readingmath.pdf
Re: How to Read Mathematics
#3I also found this to be helpful - Write Mathematics Right, by L. Radhakrishna https://www.amazon.com/Write-Mathematics-Right-Professional-...
Re: How to Read Mathematics
#4I thought this was going to be about how to read Mathematics aloud, e.g. to describe it over the telephone. It seems that even something as common as $f : a \rightarrow b$ might be spoken aloud in different ways.
Re: How to Read Mathematics
#5I think it would be quiet interesting to crowdsource a math-to-english interpreter (a la 'explain shell' [0]) for math equations.
Re: How to Read Mathematics
#6I also found this to be helpful - Write Mathematics Right, by L. Radhakrishna https://www.amazon.com/Write-Mathematics-Right-Professional-...
Could you say a few more words about this book? It looks interesting, but I can't find a table of contents or a review of it. Is it intended for advanced mathematics, or can it be useful for basic math too?
Re: How to Read Mathematics
#7I think it would be quiet interesting to crowdsource a math-to-english interpreter (a la 'explain shell' [0]) for math equations. [0] https://explainshell.com/
There's some information on Wikipedia and Wolfram's MathWorld. But it's very hard to digest at times.
This guy produces excellent illustrations/explanations of math concepts: https://www.youtube.com/channel/UCYO_jab_esuFRV4b17AJtAw/vid...
I wish there could be software that could produce these style of explanations.
Re: How to Read Mathematics
#8As someone who struggled with math and hated it in high school and now loves it but still struggles with it I got a lot out of this article. It brought to mind this EdX course: "Effective Thinking Through Mathematics"[0] which I also found valuable.
Has anyone read the author's book[1] and can recommend it (or not)? It only has 2 reviews, a 5-star and a 3-star and the latter review is not helpful.
[0]https://www.edx.org/course/effective-thinking-through-mathem... [1]https://www.amazon.com/Rediscovering-Mathematics-Classroom-R...
Re: How to Read Mathematics
#9I think it would be quiet interesting to crowdsource a math-to-english interpreter (a la 'explain shell' [0]) for math equations. [0] https://explainshell.com/
This is not possible, at least not without a very sophisticated AI.
One thing that novices seem to not get about mathematics, especially those coming from programming languages, is that the syntax of mathematical formulae is not divorced from the natural language that surrounds it. Different authors use different symbols for the same concept or the same symbol with different meanings. That is, mathematical symbols have synonyms and homonyms, so to speak. You can read someone's "accent" when reading mathematics. The French consider 0 to be a positive number; the Americans don't. The Russians call it the Bunyakovsky inequality, most of Western Europe and America calls it the Schwarz or Cauchy-Schwarz inequality. The way they arrange their equations, the particular details of the notation, their preferred term for a particular concept, even tiny things like preferring upright or slant font for dx in an integral (and by the way, often fonts carry semantic meaning, but not in this case); all of these vary from author to author.
Mathematics is a very human activity. It is written by humans who write ambiguous things because it's meant to be read by humans who deal well with ambiguity. Reading human-written mathematics cannot be mechanised, at least, not anymore than reading a natural language can be mechanised.
Re: How to Read Mathematics
#10I thought this was going to be about how to read Mathematics aloud, e.g. to describe it over the telephone. It seems that even something as common as $f : a \rightarrow b$ might be spoken aloud in different ways.
This is in fact somewhat of a real problem. Mathematics is kind of meant to be learned while interacting other humans, not in pure cold isolation. A lot of what you absorb with other humans is how to pronounce things. A simple example for example is learning to pronounce binomial coefficients as "5 choose 2" or knowing that ŷ is pronounced "y hat".
Something kind of similar happens in hackerdom, where you may learn to pronounce "/etc" as "slash etsy" or "!" as "bang".