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We give a new simpler proof of a theorem of Jayne and Rogers.

We give a new proof of Lucas' Theorem in elementary number theory.

In this paper, we provide an easy proof of the Four-colour Theorem in a special case indeed.

We give a pen and paper and (comparatively) much simpler proof to verify of the Four Colour Theorem.

We present simple and direct proof to an important case of Nash-Moser-Ekeland theorem.

We give a remarkably elementary proof of the Brouwer fixed point theorem. The proof is verifiable for most of the mathematicians.

In this note, we combine ideas of several previous proofs in order to obtain a quite short proof of Gr\"otzsch theorem.

I present a simple, elementary proof of Morley's theorem, highlighting the naturalness of this theorem.

The better title is "Yet another FALSE proof of the 4-colour theorem." Please consider all versions of this paper as historical material on the way to a non-computer proof of the 4-colour theorem. Interpreted as proofs, all versions are…

We present a new, elementary, dynamical proof of the prime number theorem.

We announce here that Fermat's Last theorem was solved, but there is an easy proof of it on the basis of elemetary undergraduate mathematics. We shall disclose such an easy proof.

We give a very simple proof of a strengthened version of Chernoff's Inequality. We derive the same conclusion from much weaker assumptions.

In this paper, we give a new and short proof of a Theorem on k-hypertournament losing scores due to Zhou et al.[7].

We provide a simple proof of Kamp's theorem.

We give a simple proof of the Fourier Inversion Theorem, using the methods of nonstandard analysis.

Our goal in the present paper is to give a new ergodic proof of a well-known Veech's result, build upon our previous works.

The paper contains an alternative proof of M. Kontsevich Formality Theorem.

We prove a central limit theorem with aassumptions which are many weak than classical conditions

The aim of this short note is to present an elementary, self-contained, and direct proof for the classical Lebesgue decomposition theorem.

We present a simple short proof of the Fundamental Theorem of Algebra, without complex analysis and with a minimal use of topology. It can be taught in a first year calculus class.