相关论文: Grothendieck's use of equality

Euclid uses an undefined notion of "equal figures", to which he applies the common notions about equals added to equals or subtracted from equals. When (in previous work) we formalized Euclid Book~I for computer proof-checking, we had to…

A new generation of educational mathematics software is being shaped in ThEdu and other academic communities on the side of computer mathematics. Respective concepts and technologies have been clarified to an extent, which calls for…

The goal of this paper is to experiment new math concepts and theories, especially if they run counter to the classical ones. To prove that contradiction is not a catastrophe, and to learn to handle it in an (un)usual way. To transform the…

We study some examples when there is actually an equality in the linear algebra bound. When the vectors considered span in fact the entire space. We would like to point out that in some cases this provides some interesting extra information…

Symmetries and isomorphisms play similar conceptual roles when we consider how models represent physical situations, but they are formally distinct, as two models related by symmetries are not typically isomorphic. I offer a rigorous…

The explosion in the use of software in important sociotechnical systems has renewed focus on the study of the way technical constructs reflect policies, norms, and human values. This effort requires the engagement of scholars and…

Mathematical maturity is a key concept for the professional life of a mathematician. This paper is not only a brief discussion of the importance of mathematical maturity but also presents some unusual ways we can use the concept to help our…

Many mathematicians find mathematics aesthetically beautiful and even comparable to art forms such as music or painting. On the other hand, every year a great number of school students leave mathematics with total disillusionment and…

The numerous ways of introducing spatial gravitational forces are fit together in a single framework enabling their interrelationships to be clarified. This framework is then used to treat the ``acceleration equals force" equation and…

Notions of "fair classification" that have arisen in computer science generally revolve around equalizing certain statistics across protected groups. This approach has been criticized as ignoring societal issues, including how errors can…

With an eye on developing a quantum theory of gravity, many physicists have recently searched for quantum challenges to the equivalence principle of general relativity. However, as historians and philosophers of science are well aware, the…

Since its existence, the computer tool has often supported mathematicians, whether it is to implement an approximation method (numerical calculation of a root, of an integral, ...) or to simulate a phenomenon (geometric in nature,…

Substructural logics naturally support a quantitative interpretation of formulas, as they are seen as consumable resources. Distances are the quantitative counterpart of equivalence relations: they measure how much two objects are similar,…

This article discusses epistemological problems in the philosophy of mathematics and issues concerning the reliability of the mathematical literature.

A major question in philosophy of science involves the unreasonable effectiveness of mathematics in physics. Why should mathematics, created or discovered, with nothing empirical in mind be so perfectly suited to describe the laws of the…

Physics makes powerful use of mathematics, yet the way this use is made is often poorly understood. Professionals closely integrate their mathematical symbology with physical meaning, resulting in a powerful and productive structure. But…

A generalization of the triangle inequality is introduced by a mapping similar to a t-conorm mapping. This generalization leads us to a notion for which we use the $\star$-metric terminology. We are interested in the topological space…

An argument is provided for the equality case of the high dimensional Bonnesen inequality for sections. The known equality case of the Bonnesen inequality for projections is presented as a consequence.

We offer a view of mathematics as an experimental science where axioms play the role of foundational theories like general relativity and quantum mechanics in physics. Under this view, axioms are provisional and inferred from experience…

The literature dealing with G\"{o}del's legacy is largely preoccupied with challenging his philosophical views, regarding them as outdated. We believe that such an approach prevents us from seeing G\"{o}del's views in the right light and…