Grossone Infinity Computing

A New Computational Paradigm Using Numerical Infinities and Infinitesimals
Erscheinungsjahr 2026
ISBN: 978-3-032-41073-3
Verlag: Springer

Buch, Englisch, 381 Seiten, Format (B × H): 155 mm x 235 mm

Reihe: Emergence, Complexity and Computation

This book introduces a disruptive computational paradigm, explaining its motivations, breakthroughs, and wide-ranging applications. For the first time, it enables numerical computations with quantities containing finite, infinite, and infinitesimal components, performed on the patented Infinity Computer. Accessible yet rigorous, the book provides a clear introduction to the paradigm and presents pioneering theoretical results, innovative numerical algorithms, efficient software implementations, and practical case studies demonstrating the transformative potential of Infinity Computing across mathematics and computer science. The author is internationally recognized for his pioneering contributions, receiving prestigious awards and delivering more than one hundred plenary lectures and tutorials worldwide. The book contains prefaces written by experts in Computer Science, Logic, Numerical Analysis, Optimization, Philosophy of Mathematics, and Set Theory. This forward-looking volume opens new horizons for researchers, engineers, professors, and students interested in next-generation supercomputing, advanced numerical methods, and the foundations of mathematics and computer science.

Reviews

“Mathematicians have never been comfortable handling infinities… But an entirely new type of mathematics looks set to by-pass the problem… Today, Yaroslav Sergeyev, a mathematician at the University of Calabria in Italy solves this problem… ”

“So, the idea that Sergeyev asks us to accept as natural is in fact a bold one, the boldest among a heap of bold proposals, but it works precisely for its boldness.”

G. Lolli, .

The numerical nature of these new infinities and infinitesimals is one of the key differences with respect to traditional theories (Cantor, Levi-Civita, Nelson, Robinson, etc.) giving advantages in practice and opening new horizons for computer science and applied mathematics.

J. Gillard,

“These ideas and future hardware prototypes may be productive in all fields of science where infinite and infinitesimal numbers (derivatives, integrals, series, fractals) are used.”

A. Adamatzky, Editor-in-Chief of the

Zielgruppe

Research

Autoren/Hrsg.

Sergeyev, Yaroslav D.

Fachgebiete

• Mathematik | Informatik Mathematik Numerik und Wissenschaftliches Rechnen Optimierung
• Technische Wissenschaften Technik Allgemein Mathematik für Ingenieure
• Mathematik | Informatik EDV | Informatik Daten / Datenbanken
• Mathematik | Informatik EDV | Informatik Business Application Mathematische & Statistische Software
• Mathematik | Informatik Mathematik Stochastik

Inhaltsverzeichnis

1 Motivations and aims of this book.- 2 From a deeper understanding of numeral systems to the emergence of a new computational paradigm.- 3 A new paradigm for counting infinite and infinitesimal quantities with grossone.- 4 Measuring infinite sets and the Continuum Hypothesis.- 5 Turing machines and computability.- 6 Reframing infinite series.- 7 Quantitative analysis of traditional and blinking fractals.- 8 Extending Calculus to functions with infinite and infinitesimal domains and ranges.- 9 Infinite sample spaces and infinitesimal probabilities.- 10 Numerical infinities and infinitesimals in optimization.- 11 Applied Infinity Computing: Further applications and methods.- 12 Software implementations of the Infinity Computer.- 13 Mathematics education: Comparing the ?-based methodology and traditional views.- 14 Concluding remarks that are not a conclusion.- Appendix A The difficulty of prime factorization is a consequence of the positional numeral system.

Über Autor(innen)

Yaroslav D. Sergeyev is a Distinguished Professor at the University of Calabria, Italy (appointed by direct invitation of the Italian Ministry of Education, Universities and Research in 2002), and Head of the Numerical Calculus Laboratory at the same university. He is Editor-in-Chief of Spinger’s Journal “Operations Research Forum”. He also works part-time as a Professor at Lobachevsky University of Nizhni Novgorod, Russia, and is an Affiliated Faculty at the Center for Applied Optimization, University of Florida, Gainesville, USA. For several decades, he was also an Affiliated Researcher at the Institute of High-Performance Computing and Networking of the Italian National Research Council.
He was awarded his Ph.D. (1990) from Lobachevsky Gorky State University and his D.Sc. degree (1996) from Lomonosov State University, Moscow (this degree is Habilitation for the Full Professorship in Russian universities). His research interests include infinity computing and calculus (the field he has founded), global optimization (he was President of the International Society of Global Optimization, 2017–2021), numerical computations, scientific computing, philosophy of computations, foundations of mathematics, set theory, number theory, fractals, parallel computing, and interval analysis.
He was awarded several research prizes (International Constantin Carathéodory Prize, International ICNAAM Research Excellence Award, International Prize of the city of Gioacchino da Fiore, all in 2023; Khwarizmi International Award, 2017; Pythagoras International Prize in Mathematics, 2010; EUROPT Fellow, 2016; Outstanding Achievement Award from the 2015 World Congress in Computer Science, Computer Engineering, and Applied Computing, USA; Honorary Fellowship, the highest distinction of the European Society of Computational Methods in Sciences, Engineering and Technology, 2015; The 2015 Journal of Global Optimization (Springer) Best Paper Award; Lagrange Lecture, Turin University, Italy, 2010 and Distinguished Lectures at Lancaster University, UK, 2020 and at Venice School of Management, Ca’ Foscari University, Venice, Italy, 2024; MAIK Prize for the best scientific monograph published in Russian, Moscow, 2008, etc.). In 2020, he was elected corresponding member of Accademia Peloritana dei Pericolanti in Messina, Italy.
Since 2020, he is included in the ranking “Top 2% highly cited authors in Scopus” produced by Stanford University, the list of top researchers in mathematics produced by Research.com, the list “Top Italian Scientists. Mathematics”, lists of highly cited Russian scientists in mathematics, computer science, and cybernetics, etc.
His list of publications contains more than 300 items (among them 6 authored and 12 edited books and more than 130 articles in international journals). He is a member of editorial boards of 12 international and 3 national journals and coeditor of 16 special issues. He delivered more than 100 plenary/keynote lectures and tutorials at prestigious international congresses. He was Chairman of 7 and Co-Chairman of 8 international conferences and a member of Scientific Committees of more than 110 international congresses.