Linked Questions
13 questions linked to/from What notions are used but not clearly defined in modern mathematics?
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Paradoxical Mathematical Objects Pending for Construction [duplicate]
The possible properties and applications of some mathematical objects have been described far before their rigorous mathematical definition. Some of them even had a seemingly paradoxical description ...
164
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14
answers
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What is an integrable system?
What is an integrable system, and what is the significance of such systems? (Maybe it is easier to explain what a non-integrable system is.) In particular, is there a dichotomy between "...
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114
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19
answers
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What is the definition of "canonical"?
I just received a referee report criticizing that I would too often use the word "canonical". I have a certain understanding of what "canonical" should stand for, but the report ...
43
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8
answers
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Approaches to Riemann hypothesis using methods outside number theory [closed]
Background: Once an analytic number theorist remarked to me that all attempts to prove the Riemann hypothesis using number theoretic methods have failed. Since then that remark stuck in my mind.
The ...
63
votes
3
answers
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A roadmap to Hairer's theory for taming infinities
Background
Martin Hairer gave recently some beautiful lectures in Israel on "taming infinities," namely on finding a mathematical theory that supports the highly successful computations from quantum ...
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31
votes
5
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Is there a mathematically precise definition of turbulence for solutions of Navier-Stokes?
Given a solution $S$ of the Navier-Stokes equations, is there a way to make mathematically precise a statement like: "$S$ is turbulent in the spacetime region $U$"?
And if such a definition ...
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22
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4
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What's a noncommutative set?
This issue is for logicians and operator algebraists (but also for anyone who is interested).
Let's start by short reminders on von Neumann algebra (for more details, see [J], [T], [W]):
Let $H$ ...
21
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6
answers
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Defining variable, symbol, indeterminate and parameter
Are there precise definitions for what a variable, a symbol, a name, an indeterminate, a meta-variable, and a parameter are?
In informal mathematics, they are used in a variety of ways, and often in ...
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5
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5
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Fractal questions: Weierstraß-Mandelbrot
Coming from a specific field in algebraic geometry, I am a total noob in Fractal Theory and I'd like to learn it a bit. I hope I am tolerated for my maybe-trivial questions. I just read about the ...
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12
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2
answers
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Is it ever unnecessary to mathematically formalize a concept?
From my understanding, mathematics sometimes gives rise to new physical/tangible laws and the converse is also true. In particular, physical phenomena give rise to new mathematics.
In all of the cases ...
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15
votes
1
answer
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Digital physics and "Gandy-like" machines
Various physicists, famously John Wheeler, have asserted that physical information is the central object of study in physics, in the sense that an object or concept is "physically meaningful" if it ...
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9
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What's the detailed proof of "the composition of planar tangles is well-defined"?
In the planar algebra theory (see here or there section 2), a planar tangle is an isotopy class; then to define the composition of two tangles, we need to choose a representative in each classes. See ...
25
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What, precisely, do we mean when we say that a f.d. vector space is canonically isomorphic to its double dual?
I've been reading the Xena Project blog, which has been loads of fun. In the linked post Kevin gives the natural isomorphism $V \to V^{\ast \ast}$ from a f.d. vector space to its dual as an example of ...
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