Related papers: A short proof of the Hilton-Milner Theorem
In this paper we present a surprisingly short proof of Minkowski's second theorem. The author hopes there is no mistake in it, though the argument seems to be too plain to contain one. Also, we apply the main construction of the proof to…
We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.
Proofs that a smooth morphism is flat available in the literature are long and difficult. We give a short proof of this fact.
We present an elementary proof of Fermat's Last Theorem. No ancillary results are used, not even the most basic ones. The proof directly leads to a contradiction of the Fermat equation in the set of integers.
We expose here a short proof of Cramer's theorem in R based on convex duality.
Assuming the Riemann Hypothesis, we derive explicit bounds for the error terms in short interval analogues of the prime number theorem and Mertens' theorems using a smoothing argument. Our results improve upon previous bounds in both…
We present a short proof of the central limit theorem which is elementary in the sense that no knowledge of characteristic functions, linear operators, or other advanced results are needed. Our proof is based on Lindeberg's trick of…
This paper proposes a totally constructive approach for the proof of Hilbert's theorem on ternary quartic forms. The main contribution is the ladder technique, with which the Hilbert's theorem is proved vividly.
In this paper we provide a short proof of the Riemann Hypothesis for Drinfeld modules which uses only basic notions from the theory of global function fields and of Drinfeld modules.
Arguably the simplest variation of this style of proof as we avoid reducing to the cubic case entirely.
It is discussed that Zeeman's theorem can be directly obtained from Liouville's theorem if we assume sufficient differentiability.
We give a very short proof of the Golden-Thompson inequality
Using nonstandard analysis, an intuitive and very short proof of the Radon-Nikodym theorem is provided
In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.
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.
A one-line proof of a minimax theorem due to Steinerberger is given.
We give a proof of the Bourgain-Milman theorem using complex methods. The proof is inspired by Kuperberg's, but considerably shorter.
This expository note presents a constructive proof of Wigner's theorem using only a few basic facts about Hilbert spaces, such as the existence of orthonormal bases and the Fourier decomposition of a vector. Our proof is based on a proof by…
We give an alternative proof of the Kulikov-Persson-Pinkham Theorem for a proper K\"ahler degeneration of K-trivial smooth surfaces. After running the Minimal Model Program, the obtained minimal dlt model has mild singularities which we…
In this paper, we give a simple counter example to the famous Hodge conjecture.