Related papers: A new and elementary proof of Newton's "favorite" …

We give a concise proof of the fundamental theorem of smoothing theory in the special case when a smoothing exists.

We give a new proof of Tietze Theorem on the convergence of infinite semi-regular continued fractions.

Remarks on mathematical proof and the practice of mathematics.

We give a new proof of Brooks' theorem that immediately implies a strengthening of Brooks' theorem, known as Catlin's theorem.

The article gives a survey of mathematical proofs that rely on computer calculations and formal proofs.

We prove an abstract Nyquist criterion in a general set up. As applications, we recover various versions of the Nyquist criterion, some of which are new.

We introduce a new criterion which if satisfied implies the Riemann hypothesis.

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.

We present a short new proof of the canonical polynomial van der Waerden theorem, recently established by Girao [arXiv:2004.07766].

New cases of the multiplicity conjecture are considered.

We reformulate, in the context of continuous logic, an oscillation theorem originally proved by G. Hjorth. We give a proof of the theorem in that setting which is similar to, but simpler than, Hjorth's original one. The point of view…

An introduction and survey of homotopy type theory in honor of W.W. Tait.

In this paper we present new, short and elementary proofs of the famous projection and section theorems that are used in Stochastic Calculus.

We determine the Newton trees of the rational polynomials of simple type, thus filling a gap in the proof of the classification of these polynomials given by Neumann and Norbury.

The Cayley--Hamilton--Newton theorem for half-quantum matrices is proven.

We prove a recent conjecture by Ulas on reducible polynomial substitutions.

This paper proposes and develops a new Newton-type algorithm to solve subdifferential inclusions defined by subgradients of extended-real-valued prox-regular functions. The proposed algorithm is formulated in terms of the second-order…

I develop the decision-theoretic approach to quantum probability, originally proposed by David Deutsch, into a mathematically rigorous proof of the Born rule in (Everett-interpreted) quantum mechanics. I sketch the argument informally, then…

In this paper, by combining the algorithm New Q-Newton's method - developed in previous joint work of the author - with Armijo's Backtracking line search, we resolve convergence issues encountered by Newton's method (e.g. convergence to a…

We present in this work a new and simple proof of the false centre theorem.