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Results tagged with soft-question
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user 3154
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.
47
votes
Which mathematical ideas have done most to change history?
Euclid's axiomatic treatment of geometry. Very important in medieval thought.
0
votes
What subfields of mathematics better lend themselves to visualization?
If you can excuse the flippancy, one might define category theory as algebra that benefits from two-dimensional equations.
To be more serious, sketches in category theory, or the various classes of v …
- 2,283
12
votes
Why is it so difficult to write complete (computer verifiable) proofs?
Well, it was agony to come up with the original Jordan curve theorem...
Informal proofs make a lot of gestures at expert knowledge to avoid spelling out the mechanics of the less interesting steps in …
- 2,283
10
votes
What are some examples of colorful language in serious mathematics papers?
More Weyl, all Mancosu's translation, all in his fierce days advocating Brouwer's mathematics:
Weyl (1921) On the New Foundational Crisis of Mathematics,
It must have the effect of a deliverance …
3
votes
How seriously do professors take teaching evaluations?
You have excellent answers concerning anonymity. Regarding how seriously they are taken, it varies widely. In the faculties I have been involved in (except, I think, Yale, but my involvement was min …
3
votes
The Importance of ZF
This answer is essentially a Joel's version by another route.
ZF(C), possibly with appropriate large cardinal axioms, is one of the three most important formal axiomatisations in the foundations of m …
- 2,283
12
votes
3
answers
7k
views
Is functional programming a branch of mathematics?
In Theory mainly concerned with lambda-calculus?, F. G. Dorais wrote, of the idea that the lambda-calulus defines a domain of mathematics:
That would never stick unless there's another good reason …
2
votes
Models of ZFC Set Theory - Getting Started
From comment: how do we get from "the abstract" to "the concrete"?
In my partly informed opinion, not by formal model theory! The ability of set theory to describe its own models is one of the pilla …
- 2,283
6
votes
Theory mainly concerned with $\lambda$-calculus?
I don't know of one that seems sufficiently general. The theory's at an intersection:
It (in its untyped guise) is one of the four most important Turing-complete computation systems;
It is algebra …
- 2,283
3
votes
Periods and commas in mathematical writing
Mathematics is part of a text in the same way that poetry might be part of a literary essay. When citing poetry, a set off (i.e., displayed as a quote) part of a verse almost universally keeps exactl …