What is mathematical thinking? (2012)
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What is mathematical thinking? (2012)
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Re: What is mathematical thinking? (2012)
#2Davis and Davis/Hirsch wrote the book(s) on this. The mathematical experience (1981) is a great read.
What is mathematics really? (1997) also fine.
Re: What is mathematical thinking? (2012)
#3So, so much hubris.
- "My analogies are brilliant, but you need to already understand the field for them to be brilliant, which I learned after tons of people told me that the analogy is actually not brilliant. But they are brilliant!"
- "You need to identify as an X to be good at X" -- No. Polar opposite. The best people in any area don't identify as anything. If anything, the opposite is the case - once you think you're a great mathematician, you stop becoming exactly that.
- "If you had any difficulty following that first paragraph (only two sentences, each of pretty average length), then you are not a good mathematical thinker" -- or your semantics just suck and you're used to dealing with reading shitty semantics. That doesn't make you a good mathematical thinker, it just means that you opted for a bigger buffer than 99% of people need in their day to day jobs, even those which are able to either come up with or understand foreign omplex models on the fly. Also, the length of the sentence doesn't matter, its the density and arrangement of information in it - and, like I said, your semantics suck.
- "That then, is mathematical thinking. How do you teach it? Well, you can’t teach it; in fact there is very little anyone can teach anyone. People have to learn things for themselves; the best a “teacher” can do is help them to learn. " -- the entire paragraph just wastes the readers attention. Teaching is to help learn. What are you saying? Nothing of value.
Posts like these are why I can't take academics serious. This is high-school levels of ignorance, crossing into five different fields that the author is not even close to being competent in. What the hell?
Re: What is mathematical thinking? (2012)
#4If someone claims to be a "mathematical thinker" then probably they should be able to convey their thoughts in a precise and concise manner.
For example by starting with a definition and then expanding/explaining it.
Blogspam written by someone who sounds like a teenager with ADHD should be posted in the "iamverysmart" subreddit, not on HN.
Re: What is mathematical thinking? (2012)
#5[deleted]
Re: What is mathematical thinking? (2012)
#6So, so much hubris. - "My analogies are brilliant, but you need to already understand the field for them to be brilliant, which I learned after tons of people told me that the analogy is actually not brilliant. But they are brilliant!" - "You need to identify as an X to be good at X" -- No. Polar opposite. The best people in any area don't identify as anything. If anything, the opposite is the case - once you think y…
Also: “my work was extremely valuable to a group of academics, but not worth publishing.”
What?
Re: What is mathematical thinking? (2012)
#7This particular 10-year old post does a disservice to Prof. Devlin's work. I actually took his course on Mathematical Thinking and found it quite interesting, as was the book withe the same title I read several years ago. He is able to make certain concepts very clear, and I wish more profs had a similar attitude (many already do!).
That said, I believe most people here already took a course on discrete mathematics including logic and so on, so I don't think it would be particularly interesting to HN audience.
Re: What is mathematical thinking? (2012)
#8No post body was provided.
Re: What is mathematical thinking? (2012)
#9If someone claims to be a "mathematical thinker" then probably they should be able to convey their thoughts in a precise and concise manner. For example by starting with a definition and then expanding/explaining it. Blogspam written by someone who sounds like a teenager with ADHD should be posted in the "iamverysmart" subreddit, not on HN.
Ehe ...you do realise you're speaking about this guy here right? http://profkeithdevlin.com/
Re: What is mathematical thinking? (2012)
#10So, so much hubris. - "My analogies are brilliant, but you need to already understand the field for them to be brilliant, which I learned after tons of people told me that the analogy is actually not brilliant. But they are brilliant!" - "You need to identify as an X to be good at X" -- No. Polar opposite. The best people in any area don't identify as anything. If anything, the opposite is the case - once you think y…
I'm not sure you either read the entire post or if you did, you grasped the point of the post. Prof. Delvin [1], the author, has been pushing to make math literacy and mathematical thinking more accessible for a long time now. This post is a guide to what that means.
[1] http://profkeithdevlin.com/
..so much for the irony of calling out hubris and stating 'the author is not even close to being competent'