Examples of mathematical results discovered "late"
What are examples of mathematical results that were discovered surprisingly late in history? Maybe the result is a straightforward corollary of an established theorem, or maybe it's just so simple that...
View ArticleWhat kind of interesting properties that make exponential cone attractive?
I am a network engineer who is studied some optimization problem in the field of communication theory mostly for pleasure. Out of pure curiosity, I see that there is some optimization problem in which...
View ArticleIs there a topos-theoretic notion of "dimension"?
It seems like almost any "topological" phenomenon has a generalization to toposes. For instance, in Site Characterizations for Geometeric Properties of Toposes, Olivia Caramello shows how we can...
View ArticleTheorems with simple proofs with one method of proof, and incredibly...
This is a very soft and potentially naive question, but I've always wondered about this seemingly common phenomenon where a theorem has some method of proof which makes the statement easy to prove, but...
View ArticleIs there a way to determine if the n-th roots of a polynomial is a polynomial?
I was this problem: $$\int\frac{dx}{\sqrt{x^4+2x^3+3x^2+2x+1}}$$I solved this question because I just knew that $(1+x+x^2)^2=x^4+2x^3+3x^2+2x+1$ but this made me wonder is there is a way to know if the...
View ArticleHow to find the equation of an ellipse using three points?
I came across this interesting problem yesterday and I am not quite able to find the equation of the ellipse after it has performed that roll. The original problem shows the ellipse to rotate till it...
View ArticleUnusual approach of calculating probability (no use of conditional probability)
A bag contains $4$ red balls and $6$ black balls. A person randomly takes out one ball from the bag, sees it's color and put the ball back into the bag alongwith two additional balls of the color he...
View ArticleIs it possible to order proper classes?
Let's assume that we have NBG/MK, with its global choice.Assume a relation F, a family of classes, is given. (a class-function, such that $F(x)=\bigcup\{s|(x,s)\in F\}$ is considered to be "in" a...
View ArticleAttempt to generalize the notion of absolute continuity to multidimensional...
Recall the notion of absolute continuity over a 1-dimensional domain:Definition. A function $f: I \to \mathbb{R}$, where $I$ is a compact subspace of $\mathbb{R}$, is said to be absolutely continuous...
View ArticleBasis of $\mathbb{R}$ over $\mathbb{Q}$ exists by Axiom of choice, but is it...
Is it hard or proven to be impossible to construct basis $B$ of $\mathbb{R}$ over $\mathbb{Q}$?Small question regarding the cardinality:(If some miracle happened and CH turned out to be false, then...
View ArticleCategoriсal perspective on the Disjuntion property of the intuitionistic...
I came about four different proofs of the disjunction property:formulated in the language of Heyting algebras;done using Kripke models;using the fact that every topological space is an open subspace of...
View ArticleCreating larger structures from smaller ones without an explicit construction
I'm asking this question as a replacement for my previous one, which I admit isn't clear, and which I am voting to close. Hopefully I'll be clearer now.Admittedly, I'm not sure if this question...
View ArticleTerminology and notation for maps between topological vector spaces that...
I am interested in learning what terminology and notation, other than the small-$o$ notation, exist in the literature for describing the maps $\mathbf{R}\to\mathbf{R}$ that vanish at $0$"faster than...
View ArticleAre quasi-sets (and therefore Schrödinger logic(s)) studied by mathematicians...
Context:I'm a fan of different kinds of logic. I'm conflicted about whether different logics actually exist beyond, say, a philosophical oddity.The Question:Are quasi-sets (and therefore Schrödinger...
View ArticleIs the pi constant the proof of the Demiurge's existence? [closed]
Consider the following infinite continued fraction for $\pi$ :$$\pi=4-\cfrac{2}{1+ \cfrac{1}{1- \cfrac{1}{1+\cfrac{2}{ 1-\cfrac{2 }{ 1+\cfrac{3}{ 1-\cfrac{3 }{\cdots}}}}}}}$$The pattern is obvious. Can...
View ArticleODE book for a computer science researcher (Birkoff/Rota vs Arnold)
I've have been looking for a book on ODEs and have narrowed it down to 2 candidates: Birkoff and Rota's 'ordinary differential equations' or Arnold's 'ordinary differential equations: 3rd edition'.From...
View ArticleIs there something to the "let $\varepsilon < 0$" joke that I'm missing?
Sorry if this is the wrong place to ask this, but I feel it's a question of vital importance to the future of math education.I hear this listed as a "math joke" all the time and I've never got it. I've...
View ArticleWhy is math so difficult for me? [closed]
I'm an aspiring software engineer and currenly in college for computer science. For some reason, no matter what I try, math is so unbearably difficult and indecipherable until I design a program for...
View ArticleWhat is the best/most effective way to gain experince in using set theory to...
Note: While this question as phrased in the title is somewhat subjective, what I'm looking for as an answer should be specific enough to still have a clear/valid answer(s) to it. Also, apologies in...
View ArticleCollection of surprising identities and equations.
What are some surprising equations/identities that you have seen, which you would not have expected?This could be complex numbers, trigonometric identities, combinatorial results, algebraic results,...
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