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Adam Hughes's user avatar
Adam Hughes's user avatar
Adam Hughes's user avatar
Adam Hughes
  • Member for 11 years, 4 months
  • Last seen more than a month ago
156 votes
Accepted

What makes a theorem "fundamental"?

56 votes

Difference between "≈", "≃", and "≅"

51 votes

Percentage of natural numbers that are perfect squares?

43 votes

How would you show that the series $\sum_{n=1}^\infty \frac{(2n)!}{4^n (n!)^2}$ diverges?

29 votes
Accepted

Why is quadratic integer ring defined in that way?

28 votes
Accepted

Sum of compact sets

27 votes
Accepted

In a PID every nonzero prime ideal is maximal

26 votes
Accepted

Proof that $26$ is the one and only number between square and cube

26 votes

Proof that $S_3$ isomorphic to $D_3$

25 votes
Accepted

Galois group of $x^4-2$

23 votes
Accepted

If $F[x]$ is a principal domain does $F$ have to be necessarily a field?

22 votes
Accepted

Integration by substitution, why do we change the limits?

20 votes
Accepted

$\sum_{p \in \mathcal P} \frac1{p\ln p}$ converges or diverges?

19 votes
Accepted

Transitivity of Algebraic Field Extensions

16 votes
Accepted

Finding a Galois extension of $\Bbb Q$ of degree $3$

16 votes
Accepted

Proving an expression is composite

15 votes
Accepted

Which number is larger?

15 votes

Is it required to use brackets inside an integral?

14 votes
Accepted

Why does $\int_{-\infty}^\infty x \ dx$ not converge?

14 votes

prove that $2^n+2^{n-1}+2^{n-2}+8^n-8^{n-2}$ is a multiple of 7

14 votes

Why are $x$, $x^3+1$ and $x^2+x+1$ always mutually co-prime, for any natural number $x$?

14 votes
Accepted

Dimension of $\Bbb R$ over $\Bbb Q$ without cardinality argument.

13 votes
Accepted

What is the difference between field theory and Galois theory

13 votes

Galois group of the splitting field of the polynomial $x^5 - 2$ over $\mathbb Q$

13 votes
Accepted

Is a function defined at a single point continuous?

13 votes

Must an injective or surjective map in an infinite dimensional vector space be a bijection?

12 votes

What are the integers of $\textbf Q(\sqrt 2 + i)$?

12 votes
Accepted

Why were proofs avoiding complex analysis preferred in number theory? Is this distinction still important?

12 votes

Integral becomes improper after a substitution

12 votes

Is $f(z)=z^n$ holomorphic?

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