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2
votes
0answers
89 views

Why are large cardinal axioms actually axioms?

A cardinal is an isomorphism class in ZFC, or a representative of one. I'm not asking what the significant uses of large cardinals are, or why we would want to find them or construct them; I'm ...
3
votes
2answers
121 views

What jobs in Mathematics are always in demand, and are deeply Mathematically specialised or greatly general?

I am wondering what jobs in the field of Mathematics are (seemingly) always in demand. I am also wondering what jobs there are that are (once again seemingly) greatly Mathematically demanding in ...
2
votes
1answer
96 views

Is it worth it? [closed]

I am studying pure mathematics at university, as well as minoring in physics. I am soon to finish to BSc degree, and I am considering continuing on with studying pure mathematics. However, I do have a ...
1
vote
0answers
46 views

R. Jeffrey and the Three Prisoners

Here’s something curious, from p. 26 of the estimable Richard Jeffrey’s last, posthumously-published book, Subjective Probability: The correct (or at least orthodox) answer to this puzzle would be ...
3
votes
3answers
124 views

Can a mathematician be a multi-discipline expert?

My professor says: If you be a mathematician then you can easily learn any discipline like physics, chemistry, engineering and even medical! Is he right? I am an enthusiast of all scientific ...
3
votes
3answers
131 views

Do all mathematical symbols in LaTeX have a meaning?

I debated whether I should post this on the TeX forum or here. Mathematics seemed more appropriate. LaTeX has a ridiculous amount of symbols, including countless variations of the integral sign and ...
2
votes
0answers
78 views

How do we pronounce this symbol $'$ for $p',q'$, etc. And why?

This symbol $'$ for $p',q'$, etc; I know $'$, it is called prum(?) or something close to that, and $p',q'$ are p prum, q prum. But what exactly is $'$ written or pronounced? Thanks. And why is that ...
5
votes
0answers
112 views

Riemann Zeta function, quaternions and physics

Disclaimer: This question is rather vague, and thus probably not suitable for Mathoverflow, so I prefer to ask it here. I'm sorry if it doesn't meet the standards of this site. Several years ago, I ...
3
votes
3answers
46 views

Confusing -Probabilities.!!

Ok so far what i understand is this lets say...Having to draw a card from 52card-deck its probability is of course 1/52.Now the probability to say that i will keep drawing this same card 10 times of ...
1
vote
1answer
38 views

Literature on Sabermetrics in baseball

For my bachelor's thesis, I would like to study the use of Sabermetrics in baseball. I was fascinated by the book 'Moneyball: The Art of Winning an Unfair Game' by Michael Lewis, and to me, it ...
0
votes
1answer
57 views

How can I learn to write proofs more formally or rigourusly?

I'm studying math for a while now and still, even if I understand the question, on my own I'll probably mess up with a very informal "proof" that is mostly verbal. Even if I write down the definitions ...
141
votes
62answers
32k views

'Obvious' theorems that are actually false

It's one of my real analysis professor's favourite sayings that "being obvious does not imply that it's true". Now, I know a fair few examples of things that are obviously true and that can be proved ...
1
vote
1answer
39 views

A special kind of metric-spaces

Is there a special name for those metric-spaces or topological spaces in which every non-empty open set is uncountable ?
3
votes
1answer
91 views

How do high-achieving students in math study for their exams?

I'm taking a real analysis course that is a bit more advanced than usual in that it introduces you to the Lebesgue theory and has some deeper concepts in metric spaces. This is an honors and advanced ...
12
votes
3answers
578 views

Why are groups “abelian” but rings “commutative”?

I have never seen, in any text, a ring whose multiplication is commutative being called an "abelian ring", even though this would make perfect sense, because this term would necessarily refer to ...
0
votes
1answer
68 views

Numbers that pass every known primality test

Was having fun reminding myself of the inner workings of a few primality tests today and wondered if there exists a composite number that (perhaps provably) passes all known tests? (Ignoring tests ...
1
vote
1answer
28 views

What is a Parabolic Fixed Point?

I know the definitions of hyperbolic and elliptic fixed point (or equilibrium). However, when I google I find references to 'parabolic elliptic points' but not a proper definition.
1
vote
1answer
25 views

Limit of the “productory”

With the term "productory" I just mean $\Pi_{i=m}^nx_i$ but I do not know the english term. My question is: is there a limit for such an expression in the same sense as the limit of a sum is an ...
6
votes
0answers
63 views

Origins of the name “Q” and “R” for cofibrant and fibrant replacement functors.

In a model category $\mathscr M$ (in the modern sense, i.e. closed and with functorial factorizations), there is a notion of fibrant and cofibrant replacement functors. Specifically, for any object ...
4
votes
1answer
140 views

Number Theory: Easy Question, Difficult Answer [closed]

A common impression about number theory is that its questions can sound elementary but their solutions can be extremely difficult. For examples we need to look no further than Fermat's Last Theorem, ...
3
votes
0answers
54 views

Is there a website where one can talk about math?

Math stack exchange is a great website where one can ask and answer math questions. However, it is not quite what I want, which is, real-time conversations about mathematics. Is there such a website?
9
votes
1answer
80 views

Relationship between radii in Riemannian manifolds

S.T. Yau raised an (somewhat) interesting question in a lecture today, which I thought I would ask for thoughts on from the good people here. The context is as follows: Consider a 3-manifold $M$ with ...
17
votes
2answers
320 views

Pure mathematics curriculum for self study with interests in foundational issues

I wonder if I want to make my own pure mathematics curriculum to study along the next 4 or 5 years. What topics should I include? I want it to be like one which an undergraduate student of pure ...
9
votes
0answers
183 views

Paradoxical models of $\sf ZF$ without choice [closed]

There are some models of $\sf ZF$ without the Axiom of choice, where some paradoxical statements hold that are not possible in $\sf ZFC$ (we do not require that all those statements necessarily hold ...
3
votes
3answers
115 views

Is it meaningful to publish results that are not interesting? [closed]

(I'm by no means in the situation described below, I'm just hypothesizing/daydreaming.) Say that a professional mathematician thinks that he can get some interesting results by applying a certain ...
16
votes
6answers
1k views

Best Math books or apps for adults to learn math from the beginning

I lost a possible job because I didn't know how to multiply and subtract negative valued integers. I also don't know how fraction manipulation works. What reference books can I read that can help for ...
0
votes
1answer
100 views

Going to math grad school with low GPA [closed]

I am a pure mathematics major and I want to do Ph.D in math, however I want to change to Applied math. I have a low 3.2 < GPA < 3.3 though. I have taken most of Pure math requirements, and ...
4
votes
0answers
48 views

Let $\Phi$ denote the statement that $\mathrm{GCH}$ holds, and that no inaccessible cardinals exist. Is $\Phi$ limiting?

By an "inner model," let us mean a transitive subclass of the universe satisfying $\mathrm{ZFC}.$ Given that, here's an (intentionally) vague definition. Definition. Call a set of axioms $\Phi$ in ...
1
vote
1answer
51 views

Can we start studying number theory before abstract algebra?

I have started studying elementary number theory independently. I was wondering that is it necessary to first finish abstract algebra
0
votes
0answers
67 views

What if infinity does not exist? [duplicate]

I am trying to realize the importance of the infinity concept. Where will we find great problems if by axiom infinity does not exist?
5
votes
4answers
292 views

Are problems about finding the next term of a sequence mathematical? [closed]

I have run through many questions like "given the few first terms of a sequence, find the next one". My question is "are such problems mathematical?". This is something like given $f(1), f(2), f(3)$, ...
2
votes
2answers
43 views

Normal groups: Abstract question about abstract algebra.

Let $G$ be a group, and $H\triangleleft G$ be a normal subgroup of $G$. To my best understanding,the group $^G/_H$ is often used to "simplify" groups, meaning it enables us to deal with a simple form ...
6
votes
1answer
173 views

Chinese estimate for $\pi$. Were they lucky?

The famous chinese estimate $\pi\approx\frac{355}{113}$ is good. I think that is too good. As a continued fraction: $$\pi=[3:7,15,1,292,\ldots]$$ That $292$ is a bit too big. Is there a reason for a ...
2
votes
3answers
46 views

are there meaningful binary operations on the set of Catalan objects?

Is it possible to come up with some kind of meaningful closed binary operation $\star$ on sets $C_n$ of Catalan objects? By Catalan objects I mean objects that correspond to a given Catalan number. ...
21
votes
8answers
711 views

Is $e^{i\pi}+1=0$ all it's cracked up to be?

While it is beautiful and elegant and all that, isn't it true that Euler's identity is really just an artifact of how we define the radian? I'm speaking of those who say that it's great because it ...
1
vote
1answer
64 views

Sphere homeomorphic to plane?

I just took a course in general topology about a month back, and I was wondering whether it was possible to explain why the Earth seems flat from our point of view but is in fact a sphere using the ...
0
votes
1answer
55 views

Revisiting algebra for the proofs

As I was reading over Galois' wikipedia page, I noticed that he (Galois) read a book called "Réflexions sur la résolution algébrique des équations" at age 15, which I then read has to do with the ...
0
votes
2answers
71 views

Known easy problems statement and hard unsoled problems [closed]

Do know some problems that look easy when you read them but they are in fact still unsolved (hard) For example: Given a number, find its prime factors. ... Thanks
2
votes
2answers
41 views

Subgroup Lattices and Dimension

I apologize in advance in the case that this question is nonsensical. If the idea isn't clear, I can perhaps explain more below. In the fall I am taking an undergraduate abstract algebra course, and ...
20
votes
10answers
2k views

How can Zeno's dichotomy paradox be disproved using mathematics?

A brief description of the paradox taken from Wikipedia: Suppose Sam wants to catch a stationary bus. Before he can get there, he must get halfway there. Before he can get halfway there, he must ...
5
votes
0answers
65 views

Note-taking software which is capable of representing mathematical relation

After quite a few studying experiences (both alone and following a class, studying topology, algebra, analysis, measure theory, differential geometry) I have acquired a lot of notes that I have either ...
3
votes
1answer
82 views

How much of mathematics could be created now using computers [closed]

What great mathematical achievements of the previous times could be easily gotten today using computers and heuristic algorithms of CS. I do not mean calculation of constants, but mostly proving ...
3
votes
2answers
61 views

Why are hyperbolic functions significant?

I'm currently covering Stewart's Early Transcendentals, and there is a whole section dedicated to defining and differentiating hyperbolic functions. The same amount of space is used to cover other ...
4
votes
1answer
110 views

What should be in your graduate toolbox?

I've just finished my undergraduate degree at an average uni in the UK. Clearly the content will not be as in depth or rigorous as some of the higher ranked universities. I intend (well, hope!) to ...
0
votes
0answers
27 views

trigonometric-like function that do not care about the cartesian coordinate system

Is there a common name for the function that maps from an angle inside a circle - to a relation between the length of the radius and the length of the edge (AB) between the two points A and B where ...
-5
votes
1answer
79 views

Difficulty of coursework offsetting grades (graduate admissions) [closed]

Sorry to post another graduate admissions related question, but I hope a discussion on this would be helpful to people, in particular undergrads worrying about grades. I am an undergrad at a top 5 ...
5
votes
1answer
59 views

Exact rank of Elkies curve

A naïve question. We definitely know an elliptic curve of rank $28$ or more exists by Elkies but no one knows exactly what the rank is for this curve (and for similar examples given previously). ...
2
votes
1answer
89 views

Structured Self-Learning Program for Calculus I & II

I'm interested in a organised program which comprehensively covers the topics of Calculus I and Calculus II. I've recently finished taking my secondary school's university-level Calculus I course, ...
1
vote
1answer
54 views

Research Area Choice: PDE vs Optimization

I am on track to starting in applied math PhD this coming Fall. My area of interest is PDE where I have a strong background and have even published a paper. It seems the particular area of PDE I am ...
35
votes
5answers
1k views

Understanding the Laplace operator conceptually

The Laplace operator: those of you who now understand it, how would you explain what it "does" conceptually? How do you wish you had been taught it? Any good essays (combining both history and ...