Related papers: Tarski's influence on computer science
Detlef D\"urr (1951-2021) was a theoretical and mathematical physicist who worked particularly on the foundations of quantum mechanics, electromagnetism, and statistical mechanics. This piece is a rather personal look back at him and his…
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 give a brief historical overview of the development of the Computer Algebra System SINGULAR: why it came about and how the development was related to the attempt to refute Zariski's multiplicity conjecture.
This paper considers a formalisation of classical logic using general introduction rules and general elimination rules. It proposes a definition of `maximal formula', `segment' and `maximal segment' suitable to the system, and gives…
Euclid's reasoning is essentially constructive. Tarski's elegant and concise first-order theory of Euclidean geometry, on the other hand, is essentially non-constructive, even if we restrict attention (as we do here) to the theory with…
Computational philosophy is the use of mechanized computational techniques to unearth philosophical insights that are either difficult or impossible to find using traditional philosophical methods. Computational metaphysics is computational…
The objective of this paper is to describe the structure of Zariski closed algebras, which provide a useful generalization to finite dimensional algebras in the study of representable algebras over finite fields. Our results include a…
This article reflects on the life and mathematical contributions of Pierre Cartier, a distinguished figure in 20th- and 21st-century mathematics. As a key member of the Bourbaki collective, Cartier played a pivotal role in the formalization…
This is an overview of the life and works of Pavel Florensky, an important and singular figure of the period rightly described as the \emph{Silver Age of Russian mathematics}, with a substantial overlap with the \emph{Silver Age of Russian…
This paper describes a formalization of discrete real closed fields in the Coq proof assistant. This abstract structure captures for instance the theory of real algebraic numbers, a decidable subset of real numbers with good algorithmic…
In order to understand the source and extent of the greater-than-classical information processing power of quantum systems, one wants to characterize both classical and quantum mechanics as points in a broader space of possible theories.…
The universal object oriented languages made programming more simple and efficient. In the article is considered possibilities of using similar methods in computer algebra. A clear and powerful universal language is useful if particular…
The impact of the computer on present and especially future mathematics is illustrated by means of the iconic example of WZ theory.
An algebraic method is used to study the semantics of exceptions in computer languages. The exceptions form a computational effect, in the sense that there is an apparent mismatch between the syntax of exceptions and their intended…
Machine learning and deep learning techniques are contributing much to the advancement of science. Their powerful predictive capabilities appear in numerous disciplines, including chaotic dynamics, but they miss understanding. The main…
In this paper we discuss about properties of lattices and its application in theoretical and algorithmic number theory. This result of Minkowski regarding the lattices initiated the subject of Geometry of Numbers, which uses geometry to…
Tropical geometry is a piecewise linear "shadow" of algebraic geometry. It allows for the computation of several cohomological invariants of an algebraic variety. In particular, its application to enumerative algebraic geometry led to…
This work proposes a complete algebraic model for classical information theory. As a precursor the essential probabilistic concepts have been defined and analyzed in the algebraic setting. Examples from probability and information theory…
The Theory of Everything ($S_{\text{ToE}}$) seeks to unify all fundamental forces of nature, including quantum gravity, into a single theoretical framework. This theory would be defined internally using a set of axioms, and this paper…
The author argues to Silicon Valley that the most important and powerful part of computer science is work that is simultaneously theoretical and practical. He particularly considers the intersection of the theory of algorithms and practical…