Related papers: Another simple proof of the 1-dimensional flat cha…
I give a proof of the uniform boundedness theorem that is elementary (i.e. does not use any version of the Baire category theorem) and also extremely simple.
In this note we prove that alternating chainmail links are L-space links. The proof is inspired by corresponding proofs for double branched covers of alternating links. We also more generally show that flat augmented chainmail links are…
Some symmetry problems are formulated and solved. New simple proofs are given for the earlier studied symmetry problems.
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
We present another proof for the well-known {\em small model property} of two-variable logic. As far as we know, existing proofs of this property rely heavily on model theoretic concepts. In contrast, ours is purely combinatorial and uses…
The shortest known proof of the law of quadratic reciprocity (without supplements) is presented.
We give a simple proof of the Lalonde-McDuff conjecture for aspherical manifolds.
We present an astonishingly simple and elegant proof of the celebrated Basel problem.
A short proof of the elliptical range theorem concerning the numerical range of $2\times2$ complex matrices is given.
We give a simple direct proof of Fermat's two squares theorem. Our argument uses no intricate notions or ideas; one might say that it is a proof by careful bookkeeping. As such, the proof may be particularly easy to comprehend by students…
We prove Hochster's small MCM conjecture for three-dimensional complete F-pure rings. We deduce this from a more general criterion, and show that only a weakening of the notion of F-purity is needed, to wit, being weakly F-split. We…
Most of the assertions in the theory of well ordered sets are quite simple. However, one of its central statements, Zermelo's theorem, stands out of this rule, for its well-known proofs are rather complicated. The aim of the current paper…
The article presents the proof of Casas-Alvero conjecture.
We give a simple proof of the increasing strengthening of Arhangel'skii's Theorem. Our proof naturally leads to a refinement of this result of Juh\'asz.
We give a proof of the existence of radial (smooth) parallel sections of vector bundles endowed with a linear connection.
In the current note, we present a new, short proof of the famous AM-GM-HM inequality using only induction and basic calculus.
We prove new results, related to the Littlewood and Mixed Littlewood conjectures in Diophantine approximation.
We present a new, elementary, dynamical proof of the prime number theorem.
I give an elementary proof of Wall's continued-fraction characterization of Hausdorff moment sequences.
We give a short proof -- not relying on ideal classes or the geometry of numbers -- of a known criterion for quadratic orders to possess unique factorization.