相关论文: Six proofs of the F\'ary--Milnor theorem

We give an infinite number of proofs of Pythagoras theorem.Some can be classified as `self-similar proofs'.

We give a short and relatively elementary proof of the Hilton-Milner Theorem.

These are some notes on the two Milnor conjectures and their proofs (due to Voevodsky, Orlov-Vishik-Voevodsky, and Morel).

We prove the Milnor conjecture for Lie groups and the Friedlander conjecture for complex algebraic Lie groups.

We prove several extensions of the Erdos-Fuchs theorem.

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

We proved three theorems of $S$-version of the mulyiplicity one.

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

We provide elementary proof of several congruences involving single sum and multisums of binomial coefficients.

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

We illustrate the concept of mathematical proof.

A proof is given of Rosenthal's \(\ell_1\) theorem.

We prove a generalization of Istvan F\'ary's celebrated theorem to higher dimension.

In this note, we give an alternate proof of the multinomial theorem using a probabilistic approach. Although the multinomial theorem is basically a combinatorial result, our proof may be simpler for a student familiar with only basic…

We make an attempt at proving the Four Colour Theorem in six pages.

We give four new proofs of the directed version of Brook's Theorem and an NP-completeness result.

We give an elementary proof of Kelley's theorem based on a minimax argument. Some applications to related problems are also developed.

Many proofs of the Fundamental Theorem of Algebra, including various proofs based on the theory of analytic functions of a complex variable, are known. To the best of our knowledge, this proof is different from the existing ones.

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.

In this note we give a detailed proof of a theorem of Aubin.