Related papers: Constructive proof of the Carpenter's Theorem
An age-old controversy in mathematics concerns the necessity and the possibility of constructive proofs. The controversy has been rekindled by recent advances which demonstrate the feasibility of a fully constructive mathematics. This…
The paper contains an alternative proof of M. Kontsevich Formality Theorem.
Carleson's Theorem asserts the pointwise convergence of Fourier series of square integrable functions. We give a complete proof, following joint work of the author and C. Thiele. Over 20 exercises are also detailed. We also discuss the…
We provide a rigorous proof of the CPT theorem within the framework of 'Lagrangian' quantum field theory. This is in contrast to the usual rigorous proofs in purely axiomatic frameworks, and non-rigorous proof-sketches within the Lagrangian…
This note was written in Jan. 23, 2015 to answer a problem raised by G. Moser, who asked a constructive proof of a theorem by Ferreira-Zantema.
We give in the present work a new methodology that allows to give isoperimetric proofs, for Kneser's Theorem and Kemperman's structure Theory and most sophisticated results of this type. As an illustration we present a new proof of Kneser's…
We present a new proof of the Joints Theorem without taking derivatives. Then we generalize the proof to prove the Multijoints Conjecture and Carbery's generalization. All results are in any dimension over an arbitrary field.
The aim of this paper is to present a very simple original, purely formal, proof of Quillen's adjunction theorem for derived functors, and of some more recent variations and generalizations of this theorem. This is obtained by proving an…
This note is purely expository. The statement of the Gauss theorem on the constructibility of regular polygons by means of compass and ruler is simple and well-known. However, its proofs given in most textbooks rely upon much unmotivated…
This article presents a clear proof of the Riemann Mapping Theorem via Riemann's method, uncompromised by any appeals to topological intuition.
Generalizing a geometric idea due to J. Sondow, we give a geometric proof for the Cantor's Theorem. Moreover, it is given an irrationality measure for some Cantor series.
Constructor theory seeks to express all fundamental scientific theories in terms of a dichotomy between possible and impossible physical transformations - those that can be caused to happen and those that cannot. This is a departure from…
We give a sufficient condition for a model theoretic structure $B$ to 'inherit' quantifier elimination from another structure $A$. This yields an alternative proof of one of the main result from \cite{kle}, namely quantifier elimination for…
In this paper we consider Kakutani's extension of the Brouwer fixed point theorem within the framework of Bishop's constructive mathematics. Kakutani's fixed point theorem is classically equivalent to Brouwer's fixed point theorem. The…
We suggest an alternative proof of a theorem due to Lambek and Moser using a perceptible model.
In this paper, we propose a generalization of a congruence due to Carlitz.
We present a short new proof of Cobham's theorem without using Kronecker's approximation theorem, making it suitable for generalization beyond automatic sequences.
Based on the results people have obtained, we try to prove the Jacobian conjecture, but there is a gap in the proof.
The purpose of this note is to rephrase Speyer's elegant topological proof for Kasteleyn's Theorem in a simple graph theoretical manner.
We give a descriptive construction of trees for multi-ended graphs, which yields yet another proof of Stallings' theorem on ends of groups. Even though our proof is, in principle, not very different from already existing proofs and it draws…