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If 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/
Read this ^ before reading the article
Earlier quoted context omitted.
Ehe ...you do realise you're speaking about this guy here right? http://profkeithdevlin.com/
Does he have a Putnam?
Wow, so, so much venom on this thread. For those of you who enjoyed the article (like myself), you'll see that his class ("Introduction to Mathematical Thinking") starts today as a Coursera Stanford MOOC here: https://www.coursera.org/learn/mathematical-thinking
>>> It’s one of those analogies that is brilliant if you are sufficiently familiar with all four components, but hopeless as a way to explain one in terms of the other three. Ah yes, one of those - also known as a completely useless analogy .
He doesn't have to spell out that those conditions makes the analogy irrelevant, it is an obvious conclusion, anyone who read to that part would realize his analogy was worthless so he doesn't have to spell it out, in a math proof what he did would be the same as spelling it out. But to you it looks like he wasn't himself aware the analogy was irrelevant, because he didn't' say it straight out. But he crafted the text in precisely such a manner that you and basically anyone else reading this text would realize the analogy was worthless without him stating so, that is a part of mathematical thinking: how to communicate things precisely.
Of course regular people like redundancy and repetition, which is why I repeat my self a lot when I write on forums like this, it looks like this mathematician hasn't fully realized that he can't state things just once when writing things for non-mathematicians to read.
* (Existential-Universal) quantification
* (Epsilon-Delta) language
I've seen also a lot of people struggle with definitions.
Earlier quoted context omitted.
>..so much for the irony of calling out hubris and stating 'the author is not even close to being competent' I don't see how your answer relates to my criticism at all. What I'm pointing out is that the author touches on a variety of topics where he clearly exceeds his field of expertise. I'm not saying that he is incompetent as a mathematician at all, nor that he is ill-intended in writing the post.
> I don't see how your answer relates to my criticism at all. What I'm pointing out is that the author touches on a variety of topics where he clearly exceeds his field of expertise. I'm not saying that he is incompetent as a mathematician at all, nor that he is ill-intended in writing the post. Forgive me, I'm confused. You did claim hubris. Which topics, precisely , does the good professor touch upon that is not wi…
>If you want to be good at activity X, you have to start to see yourself as an X-er – to act like an X-er.
This is what struck me the most. It's a terrible generalization (beyond the limits of a mathematicians competence) that doesn't hold up - you can be good at any given topic without actually identifying as anything. Since I have no degree in psychology, I'm in no position to actually claim to know better. That being said: the notion that identifying with anything somehow enables you to reach deeper ends of a field is simply off. Afaik, identifying with anything is more a blockage than anything else. Also, the mere fact that he is an educator is meaningless to me in this context, as some of the most ignorant/filled with hubris people I've come across can call themselves educators, so if anything I take that term as counter-indicative for general competence.
That being said, I may have judged too harshly given that I missed the clarification in the last paragraph.
Earlier quoted context omitted.
> I don't see how your answer relates to my criticism at all. What I'm pointing out is that the author touches on a variety of topics where he clearly exceeds his field of expertise. I'm not saying that he is incompetent as a mathematician at all, nor that he is ill-intended in writing the post. Forgive me, I'm confused. You did claim hubris. Which topics, precisely , does the good professor touch upon that is not wi…
From the post: > If you want to be good at activity X, you have to start to see yourself as an X-er – to act like an X-er. This is what struck me the most. It's a terrible generalization (beyond the limits of a mathematicians competence) that doesn't hold up - you can be good at any given topic without actually identifying as anything. Since I have no degree in psychology, I'm in no position to actually claim to know…
> Unless you get inside the activity and identify with it, you are not going to be good at it.
..taking the statement you quoted out of context ?
I don't quite agree it is a terrible generalization. I do not think you can become good at something without actually identifying as a 'do-er' of the said thing; without actually getting so involved with the thing that it becomes part of your identity.
Also, on the thing you say about educators -- who else, if not educators, would you listen to if the person telling you that math education needs to be impress upon students, mathematical thinking (as opposed to than bland mathematical procedures )? Wouldn't they have the most context ?
PS: also, unless you are a mathematician and/or an educator, I hope you do see the irony of your comments dismissing as 'exceeds his field of expertise', the opinions of someone who is both.
Wow, so, so much venom on this thread. For those of you who enjoyed the article (like myself), you'll see that his class ("Introduction to Mathematical Thinking") starts today as a Coursera Stanford MOOC here: https://www.coursera.org/learn/mathematical-thinking
Don't Coursera classes always start $TODAY?