31–40 of 50 posts
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.
> they should be able to convey their thoughts in a precise and concise manner. But that is exactly the thing, most people aren't able to convey their thoughts in a precise manner, it requires a lot of words. Programmers knows this as well, it is hard to describe things precisely, human written language is very imprecise. The difference is that mathematicians has to explain things precisely to other humans, while pro…
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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…
Isn't skipping the preceding statement: > 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…
This fails the mathematical thinking bar. Where's the causality? Evidence, applicability across domains?
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?
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> 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…
Two foundational mathematical thinking constructing constructs (if I may say): * (Existential-Universal) quantification * (Epsilon-Delta) language Once people start to not only understand it, but actually think that way, they start to be scientists and mathematicians. It opens the door of refutable and constructive thinking. I've seen also a lot of people struggle with definitions .
Two foundational mathematical thinking constructing constructs (if I may say): * (Existential-Universal) quantification * (Epsilon-Delta) language Once people start to not only understand it, but actually think that way, they start to be scientists and mathematicians. It opens the door of refutable and constructive thinking. I've seen also a lot of people struggle with definitions .
One problem with epsilon-delta definitions is that they don't scale. In many topological spaces, there's no concept of distance and so epsilon-delta stuff has to be replaced with more general open sets. About the same reason why sequences have to be replaced with nets and filters.
Earlier quoted context omitted.
One problem with epsilon-delta definitions is that they don't scale. In many topological spaces, there's no concept of distance and so epsilon-delta stuff has to be replaced with more general open sets. About the same reason why sequences have to be replaced with nets and filters.
yeah there are like 10 million ways of defining cont. or limits in R^N that turn out to be the same
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So he doesnt have a Putnam?
So you haven't actually read the post?