I want to do mathematics similar to style of Grothendieck. How is that possible?
I am a person who enjoys math. Out of interest, I would like to ask a (soft) question. One of the reasons that I am posting this question is because in doing mathematics, it is hard to get rid of the...
View ArticleWhat would be the consequences if we assume that the assertion "P=NP is true"...
It is well understood that there can exist undecidable statements for which it is completely impossible to prove these statements are undecidable; this raises an interesting question about if there are...
View ArticleDo theories and proofs in decimal mathematics work in other numeral systems?...
The mathematics we use today is based on the decimal system. I was wondering if some or all of these proofs would hold true in other numeral systems. For example binary or hexadecimal. Is there any...
View ArticleIs there a textbook series that uses semantic naming for mathematical theorems?
One of my biggest pet peeves with traditional mathematical pedagogy is the ubiquity of non-semantic names (naming things after people being the typical offense...), even when an appropriate semantic...
View ArticleVisually stunning math concepts that are easy to explain
Since I'm not that good at (as I like to call it) 'die-hard-mathematics', I've always liked concepts like the golden ratio or the dragon curve, which are both accessible (easy to explain and...
View ArticleWhich area of combinatorics is this?
There are $n$ assassins numbered from 1 to n, and all assassins areinitially alive. The assassins play a game in which they take turns inincreasing order of number, with assassin 1 getting the first...
View ArticleIf all of mathematics are based on sets of axioms that are arbitrarily...
Are asking these kinds of questions even meaningful? Should we accept axioms so long as they produce "useful" theorems?
View ArticleIntuition of conditional expectation: Williams's take, applied to E[E[R |...
Let $(\mathit{\Omega}, \mathcal{F}, P)$ be a probability space. Take $\mathcal{G} \subseteq \mathcal{F}$ to be any sigma-algebra. Be given an extended real-valued random variable $\mathcal{R}\colon...
View ArticleDimension Notation for Topological Spaces
Lots of families of topological spaces get superscripts denoting dimension: $\mathbb{R}^n$, $B^n$, $D^n$, $\Delta^n$, $S^n$, $\mathbb{R}P^n$, $T^n$. There's a niceness to this: $S^n$ is the boundary of...
View ArticleTo what extent can the study of logic give me a broader perspective on...
I am very interested in knowing what is the fundamental logical structure of any given theory (does it handle first-order logic? second-order logic? what would be its formal language? what are the...
View ArticleSuggested books that have an extensive treatment on Summation Notation
at the moment I'm looking for a book that has the following properties:Is accessible to math undergraduates, preferably not much higher than first or second year undergraduates.Treats summation...
View ArticleProving algorithms' correctness
I am working in a computational subfield of mathematics, so there are algorithms whose correctness I have to prove. Usually, algorithms are formulated in an imperative manner, i.e., as a sequence of...
View ArticleSmall ambiguity with Lie Algebras [closed]
https://en.wikipedia.org/wiki/Lie_algebraOn wikipedia here it describes Lie algebras as a "vector" space, but then immediately defines the Lie bracket as containing both a sum, AND a product.This is...
View ArticleGenius mathematicians who never published anything
Amongst philosophers, Socrates is an example of a genius with a great influence on human history who never wrote anything. Almost all facts which are known about his revolutionary ideas are written by...
View ArticleHow do I write a personal statement for US math PhD programs if I am not a...
I am currently applying for PhD programs in Mathematics in the United States for the upcoming fall semester. Some universities require a personal statement in addition to the statement of purpose or...
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Circle/ Ellipse geometry problem from Ramanujan
Does someone have detail of the problem and his solution? I saw it in youtube. A rough hand sketch remade seeing YouTube video SR geometry problem (17 min 51 sec). I have no access to the TIFR book...
View ArticleIs the "product rule" for the boundary of a Cartesian product of closed sets...
Given two closed sets $A$ and $B$ living in topological spaces $X$ and $Y$, the boundary of $A\times B$ in the product topology, denoted (suggestively) by $\partial(A\times B)$, is given...
View ArticleReading groups: Where to find them? [closed]
Hi if I want to find a reading group, for instance I want to read abbot's analysis, is there anywhere where I can find a group of people who have a reading group? Any forum etc?
View ArticleDoes logic "come before" mathematics, or vice versa?
I always thought of mathematics as being founded on logic. After all, even the most basic mathematical definition is based on logic. When we enunciate ZFC axioms, we're relying on the concepts of...
View Article"Low tech" proof that the square of the Hopf map is stable.
Recall the Hopf fibration $\eta\colon S^3 \to S^2$, which is the generator of $\pi_3S^2 \cong \mathbb{Z}$. Also recall theFreudenthal Suspension Theorem.If $n>k +1$ then the suspension homomorphism...
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