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We prove Kontsevich's cyclic formality conjecture.
Although there are many simple proofs of Jordan's decomposition theorem in the literature (see [1], the references mentioned there, and [2]), our proof seems to be even more elementary. In fact, all we need is the theorem on the dimensions…
We propose the use of lattice field theory for the study of string field theory at the non-perturbative quantum level. We identify many potential obstacles and examine possible resolutions thereof. We then experiment with our approach in…
We present a short and self-contained proof of the choosability version of Brooks' theorem.
Standard proofs of Lusin's theorem, using simple functions, are sometimes quite elaborate. Here, we give a one-sentence proof of Lusin's theorem. We do not believe our approach, by way of inverse images, is new. However, this particular…
By changing variables in a suitable way and using dominated convergence methods, this note gives a short proof of Stirling's formula and its refinement.
We give a simple proof of Bourgain's theorem on the singularity of Ornstein's maps.
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.
The connected sum of two flat virtual knots depends on the choice of diagrams and basepoints. We show that any minimal crossing diagram of a composite flat virtual knot is a connected sum diagram. We also show the crossing number of flat…
We provide a proof and a counterexample to two conjectures made by N. Kuznetsov.
We outline an approach to prove the two dimensional Jacobian Conjecture using the theory of fractals.
A new simple proof of Stirling's formula via the partial fraction expansion for the tangent function is presented.
We derive the Gallai-Edmonds Structure Theorem from Hall's Theorem.
Some simple facts are proved ruling the Collatz tree and the chains of vertices appearing in it, leading to the reduction of the number of significant elements appearing in the tree. Although the Collatz conjecture remains open, these fact…
Using geometric homology and cohomology we give a simple and conceptual proof of the Thom isomorphism theorem.
We give an elementary and self-contained proof of the uniformization theorem for non-compact simply-connected Riemann surfaces.
We give a short and self-contained proof of Levi's Extension Lemma for pseudoline arrangements.
In this note, a simple proof Jordan normal form and rational form of matrices over a field is given.
This is a summary of the proof of BAB conjecture. All material are taken from the two BAB paper in the reference. The aim of this summary is to help reader to understand the more technical side of the proof of BAB.