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Results tagged with soft-question
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user 1176
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.
30
votes
What does a theoretical mathematician do?
There are several things that mathematicians do:
teachers of mathematics teach math, and you surely know some of those,
applied mathematicians use their knowledge of mathematics to help engineers, p …
4
votes
classical typed higher order logic natural deduction
Russell & Whiteheads theory is perhaps a bit on the heavy side, but here are some references to support Andreas Blass' comment:
An early formulations of classical higher-order logic was given by Alo …
- 48.8k
12
votes
How to mentor an exceptional high school student?
And don't forget to play ball with him every once in a while.
32
votes
Depressed graduate student.
I find it helpful to always work on more than one project at a time. When I get stuck, depressed, or disinterested with one task, I can always switch to another. I find that helpful. The projects ran …
37
votes
What are some ways to stay engaged with the mathematical community from outside academia?
If you like computers, you could consider getting into formalized mathematics, which is mathematics done completely formally and verified by computer programs, known as proof assistants. Formalized ma …
6
votes
type theory that does not treat the terms of $\mathrm{Prop}$ as types
Before I actually answer the question asked, let me try to explain one way of thinking about proofs as elements of propositions. It is not the only way, but it should appeal to a mathematician with a …
- 48.8k
39
votes
Accepted
What is some current research going on in foundations about?
It is quite difficult to answer this question comprehensively. It's a bit like asking "so what's been going on in analysis lately?" It is probably best if logicians who work in various areas each answ …
23
votes
Mathematicians whose works were criticized by contemporaries but became widely accepted later
Brouwer's intuitionistic mathematics was heavily criticized by his contemporaries, most notably Hilbert. For almost a century it was casually ridiculed by mathematicians who had no clue whatsoever abo …
24
votes
Does the "propositions-as-types" paradigm match mathematical practice?
There are many aspects to the question "does a logical formalism reflect mathematical practice?" I will focus just on a very simple but important detail that every mathematician is familiar with.
In …
- 48.8k
159
votes
How to present mathematics to non-mathematicians?
I have given talks about mathematics to non-mathematicians, for example to a bunch of marketing people. To see an example of a talk of mine that was given to a general audience, see my talk Zeros, giv …
44
votes
Awfully sophisticated proof for simple facts
If two elements in a poset have the same lower bounds then they are equal by Yoneda lemma. (I actually said this in a seminar two weeks ago, and of course I explained I killed a mosquito with a nuke.) …
76
votes
On proof-verification using Coq
Coq is a proof assistant, and not the only one. Other popular ones are Agda, Isabelle and the related HOL light. They all use type theory as a mathematical foundation (as opposed to first-order logic …
- 48.8k
24
votes
Old books you would like to have reprinted with high-quality typesetting
Just for fun, Principia mathematica.
17
votes
Category theory and model theory as "natural" counterparts
You are comparing apples and organges. Model theory should be compared with categorical logic, not category theory. Conversely, category theory should be compared with algebra, not model theory.
Mode …
- 48.8k
9
votes
Accepted
New research on coding in reverse mathematics?
I can offer a computational perspective. In computable mathematics we are interested in "computing with mathematical objects" such as integers, finite sets, real numbers, infinite-dimensional Banach s …
- 48.8k