Watson

Homo Mathematicus

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Is there a notion of polynomial ring in "one half variable"?

ct.category-theory ac.commutative-algebra polynomials asked Jun 2, 2020 at 11:43

mathoverflow.net

30 votes

Is there any perfect square in the sequence $12,123,1234,12345,...$?

elementary-number-theory decimal-expansion square-numbers asked Aug 24, 2016 at 21:10

math.stackexchange.com

29 votes

Is there a field $F$ which is isomorphic to $F(X,Y)$ but not to $F(X)$?

ra.rings-and-algebras examples fields asked Jan 3, 2017 at 11:25

mathoverflow.net

27 votes

Is there any palindromic power of $2$?

number-theory elementary-number-theory recreational-mathematics decimal-expansion open-problem asked Feb 13, 2016 at 10:53

math.stackexchange.com

26 votes

If $A[X] \cong B[X]$ as rings, are the degrees of irreducible polynomials the same in $A$ and in $B$?

abstract-algebra polynomials ring-theory irreducible-polynomials asked Jul 25, 2016 at 20:42

math.stackexchange.com

22 votes

Does $A^2 \cong B^2$ imply $A \cong B$ for rings?

abstract-algebra ring-theory examples-counterexamples asked Jul 24, 2016 at 14:11

math.stackexchange.com

21 votes

Quotient ring of Gaussian integers $\mathbb{Z}[i]/(a+bi)$ when $a$ and $b$ are NOT coprime

abstract-algebra ring-theory commutative-algebra algebraic-number-theory gaussian-integers asked Jul 23, 2016 at 10:00

math.stackexchange.com

21 votes

Is there no formula for $\cos(x^2)$?

trigonometry asked Feb 4, 2016 at 15:15

math.stackexchange.com

20 votes

Curves over number fields with everywhere good reduction

ag.algebraic-geometry nt.number-theory reference-request arithmetic-geometry asked Dec 4, 2018 at 11:10

mathoverflow.net

19 votes

Is $0.248163264128…$ a transcendental number?

number-theory reference-request decimal-expansion transcendental-numbers open-problem asked Feb 17, 2016 at 10:03

math.stackexchange.com

Top Answers

Non-abelian group with infinitely many abelian subgroups

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Do there exist numbers normal in every base except for one?

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How do you simplify this square root of sum: $\sqrt{7+4\sqrt3}$?

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Call a number "holy" if it contains no $666$ in its decimal expansion. Are there infinitely many holy powers of $2$?

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Would this solution of the limit of the sequence be correct?

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How prove this inequality??

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A field extension of degree 2 is a Normal Extension.

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Are the plane and the third dimensional space homeomorphic?

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Existence of at least one inert prime

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Why is $ (2+\sqrt{3})^n+(2-\sqrt{3})^n$ an integer?

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Find the two values of $k$ for which $2x^3-9x^2+12x-k$ has a double real root.

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Which mathematicians died very young or in a tragic way?

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Prove that every bilinear map can be written as a sum of bilinear symmetric map and a bilinear anti-symmetric map.

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What is the order of $ab$ in an abelian group?

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Interesting and unexpected applications of $\pi$

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Does $R[[x]] \cong S[[x]]$ imply $R\cong S$

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Prove that if $n \in \mathbb{Z}[\sqrt{2}]$ has an even norm, then $\sqrt{2} \mid n$

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Is there a continuous function such that $\int_0^{\infty} f(x)dx$ converges, yet $\lim_{x\rightarrow \infty}f(x) \ne 0$?

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Abelian Galois group of $f$ implies splitting is simple extensions by a root of $f$.

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Problem with inequality: $ \left| \sqrt{2}-\frac{p}{q} \right| > \frac{1}{3q^2}$

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Let $d\in \mathbb Q$ , to prove $\mathbb Q(\sqrt d) \subseteq \mathbb Q(e^{2i\pi/n})$ for some positive integer $n$ (without Kronecker-Weber)

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Alternative form of Eisenstein integers

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Does the commutator group of $S_n$ equal $A_n$ in general?

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Express the ideal $(6) \subset\mathbb Z\left[\sqrt {-5}\right]$ as a product of prime ideals.

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Determinant of a matrix $P$ such that $AP=BP$.

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A question on Hartshorne Chapter III Proposition 2.6

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A holomorphic map between complex tori (proposition 1.3.2 in Diamond–Shurman)

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Countable ordinal

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What is the characteristic of p-adic number fields?

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Examples nonzero polynomial in abstract algebra (with modulo) with more roots than its degree

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