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Results tagged with soft-question
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user 1227
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.
104
votes
Accepted
How do pure mathematicians assess whether their research ambitions can be realistically achi...
Over decades, and across multiple research fields, I've noticed a way to predict I'm on track to make progress. I discover something interesting, only to learn it is already known.
As a student, this …
10
votes
Accepted
Geometric formulation of the subject of machine learning
There are several geometric aspects of machine learning.
You can think of the goal of ML as function approximation. Your question mentions reconstructing a characteristic function, but people often l …
- 6,571
8
votes
Accepted
What does the Jacobian of a vector field at an equilibrium tell you about local behavior of ...
The Jacobian alone doesn't have the information you need. For example, consider the two vector fields
$$f(x, y) = (-x^2, -y)$$
and
$$g(x, y) = (-x^3, -y)$$.
They have an isolated equilibrium at the or …
- 6,571
23
votes
Accepted
How to transition from pure math PhD to nonacademic career?
This is the perspective of someone who went from a math PhD to the media industry and then to software/tech (and enjoyed it immensely). I can't speak for finance.
Don't spend time on classes; instead …
25
votes
A clear map of mathematical approaches to Artificial Intelligence
I highly recommend the syllabus for Boaz Barak's Harvard course on Foundations of Deep Learning. It balances a mathematical point of view with a respect for the fast-moving empirical aspects of the fi …
61
votes
Fundamental Examples
For a picture that launched a thousand papers, I'd nominate the bifurcation diagram of the logistic map.
(image via Wikipedia).
Answered by Martin M. W.