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Results tagged with soft-question
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user 689
Questions that are about research in mathematics, or about the job of a research mathematician, without being mathematical problems or statements in the strictest sense. Do not use this tag for easy or supposedly easy mathematical questions.
5
votes
Most harmful heuristic?
"Mathematical knowledge is contained and communicated primarily by documents."
I'm not sure if this is a heuristic, but in terms of beliefs that inhibit learning, this is definitely the one that hurt …
7
votes
9
answers
18k
views
"negative" vs "minus" [closed]
Not too long ago, whenever I was confronted with the expression, -x, and I was in a position where I needed to communicate it to someone verbally, I would say, "negative x", as opposed to "minus x", p …
31
votes
7
answers
5k
views
Why is it useful to classify the vector bundles of a space?
It seems to me that vector bundles are useful because they allow us to bring to bear all of the linear algebra we know to aid in the study of topological spaces. Now, I've read somewhere that it is a …
- 775
12
votes
2
answers
1k
views
What is the most compelling reason to believe Church's thesis? [closed]
Church's thesis states that the Turing machine is a universal model of computation. What is the most compelling argument supporting this assertion?
- 775
68
votes
Most harmful heuristic?
One extremely harmful heuristic I held until fairly recently: identifying math with algebraic manipulation. When asked to prove an identity or an inequality I would often dive straight into algebraic …
16
votes
Most harmful heuristic?
Any attempt to draw a fat Cantor set is a bad heuristic in my opinion. I saw such a diagram as an undergrad and believed for a while that there were intervals contained in the fat Cantor set. I don' …
3
votes
Most helpful heuristic?
I don't remember where I heard this, but I recall hearing about a mathematician who said that if an assertion was true for a general 3x3 matrix, then he would believe that same assertion with confiden …