相关论文: Plane Geometry: An Elementary School Textbook (ca.…

Most major discoveries in astronomy are unplanned, and result from surveying the Universe in a new way, rather than by testing a hypothesis or conducting an investigation with planned outcomes. For example, of the 10 greatest discoveries…

This is a historian's view of how modern astronomy data can be used to discuss the shifting historical worldview of Late Antiquity. In this article an attemp is made to construct an approximate model of how the cycles of astronomical…

This paper shares a classroom story from Fall 2022 to Spring 2025 about a learner centered routine in undergraduate mathematics. I use four steps: an opening question, a short mini lecture about meaning, structured small group work, and a…

Here I indulge in wide-ranging speculations on the shape of physics, and technology closely related to physics, over the next one hundred years. Themes include the many faces of unification, the re-imagining of quantum theory, and new forms…

A popular curve shown in introductory maths textbooks, seems like a circle. But it is actually a different curve. This paper discusses some elementary approaches to identify the geometric object, including novel technological means by using…

Mathematical aspects of contemporary classical and quantum gauge theory are sketched.

We introduce a probabilistic approach for dating historical manuscript pages from visual features alone. Instead of aggregating centuries into classes as is standard in the previous literature, we pose dating as an evidential deep…

In the last two decades recurrence plots (RPs) were introduced in many different scientific disciplines. It turned out how powerful this method is. After introducing approaches of quantification of RPs and by the study of relationships…

This article focuses on evolvement of the history of mathematics as a science and development of its methodology from the 4th century B.C. to the age of Enlightenment.

Research on the development of science has focused on the creation of multidisciplinary teams. However, while this coming together of people is symmetrical, the ideas, methods, and vocabulary of science have a directional flow. We present a…

During their first years of life, infants learn the language(s) of their environment at an amazing speed despite large cross cultural variations in amount and complexity of the available language input. Understanding this simple fact still…

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…

This article is a review of theoretical advances in the research field of algebraic geometry and Bayesian statistics in the last two decades. Many statistical models and learning machines which contain hierarchical structures or latent…

This book is a textbook for the course of foundations of geometry. It is addressed to mathematics students in Universities and to High School students for deeper learning the elementary geometry. It can also be used in mathematics coteries…

In 1981 W.L. Edge discovered and studied a pencil $\mathcal{C}$ of highly symmetric genus $6$ projective curves with remarkable properties. Edge's work was based on an 1895 paper of A. Wiman. Both papers were written in the satisfying style…

Currently it is widely accepted that the language of science is mathematics. This book explores an alternative idea where the future of science is based on the language of algorithms and programs. How such a language can actually be…

We review the recent programme of using machine-learning to explore the landscape of mathematical problems. With this paradigm as a model for human intuition - complementary to and in contrast with the more formalistic approach of automated…

The advent of computational statistical disciplines, such as machine learning, is leading to a paradigm shift in the way we conceive the design of new compounds. Today computational science does not only provide a sound understanding of…

The purpose of this essay is to bring out the unique role of Mathematics in providing a base to the diverse sciences which conform to its rigid structure. Of these the physical and economic sciences are so intimately linked with…

Combinatorics is a powerful tool for dealing with relations among objectives mushroomed in the past century. However, an more important work for mathematician is to apply combinatorics to other mathematics and other sciences not merely to…