Why do structured sets, like (N, +) often get referred to just by their set? Under this way of speaking, where N denotes the natural numbers, + addition, and * multiplication, (N, +, *) and (N, +) both can get referred to as N. But, due to our ancestors we can readily talk about (N, […]

Background: Due to some unfortunate sequencing, I have developed my abstract algebra skills before most of my linear algebra skills. I’ve worked through Topics in Algebra by Herstein and generally liked his approach to vector spaces and modules. Besides a very elementary course in linear algebra (where most of the time went towards matrix multiplication), […]

I came across this site and am wondering if there is a similar page for Mathematics or its sub-areas. Would be very nice if there is one such site which provides ‘canonical’ references for each sub area and preferably is editable like the Wikipedia system so that it reflects entire community’s opinion and not just […]

What is a vector? As the question says what is a vector and what are its uses or, I mean, when should we use vectors? Is this a branch of geometry or algebra or trigonometry?

I suspect in the future we might be able to build computers that research math for us. And I also suspect they will probably be way more efficient at doing research than we are. I do think this question is relevant to this site, even though it doesn’t have a definitive answer (hence the tag: […]

Who invented or used very first the double lined symbols $\mathbb{R},\mathbb{Q},\mathbb{N}$ etc. to represent the real number system, rational number system, natural number system respectively?

To celebrate the recent neuroscientific study that shows the beauty of math is in the mind, what is your most beautiful proof that $e^{i \pi} = -1$?

I just noticed something funky. Let $X$ denote an $I$-indexed family of sets. There is a projection $$\pi_X: \bigsqcup_{i:I} X_i \rightarrow I.$$ It isn’t necessarily surjective, of course, because one or more of the $X_i$ may be empty. Anyway, I noticed that the set $\prod_{i:I} X_i$ can be identified with the set of sections of […]

I’m an adult who tries to learn math from the ground up in his free time. I don’t know anything about anything. I’ve decided to start with arithmetic, but I don’t know where to go next. I’m a type of person who learns by reading and going in depth in topics. Please, provide me with […]

3 days ago , i had a discussion with a close friend who studies physics – still a student – . and i was telling her about the biggest known numbers in maths , so i told her about numbers such googol and googolplex, then about Graham number and she asked me , what is […]

Intereting Posts

What is the group of units of the localization of a number field?
How can I develop a reduction formula for $\int \sin^n d x$ in 1 step jumps
Prove a square is homeomorphic to a circle
Convergence in topologies
Exists $C = C(\epsilon, p)$ where $\|u\|_{L^\infty(0, 1)} \le \epsilon\|u'\|_{L^p(0, 1)} + C\|u\|_{L^1(0, 1)}$ for all $u \in W^{1, p}(0, 1)$?
If $A$ and $B$ are bounded subsets of $\mathbb{R}$, show that $\sup{A\cup B}=\sup\{\sup A, \sup B\}$.
What conditions must the constants b1,b2 and b3 satisfy so that the system below has a solution
If Gal(K,Q) is abelian then |Gal(K,Q)|=n
Why not just define equivalence relations on objects and morphisms for equivalent categories?
What are the finite subgroups of $GL_2(\mathbb{Z})$?
Natural deduction proof / Formal proof : Complicated conclusion with no premise
Improper Integral Question: $ \int_0 ^ \infty\frac{x\log x}{(1+x^2)^2} dx $
Unexpected approximations which have led to important mathematical discoveries
Existence of a subset $S\subset\mathbb R$ s.t. $\forall a<b$, $S\cap $ has Lebesgue measure $(b-a)/2$?
Show that the parameterized curve is a periodic solution to the system of nonlinear equations