Numerical Infinity and the Infinity
Computer: Books, patents, research papers, presentations, visitors 
Awards and distinctions · Pythagoras International Prize
for Mathematics (Premio Internazionale Pitagora per la Matematica),
Croton, Italy, 2010; ·
Honorary Fellowship, the highest
distinction of the European Society of Computational Methods in Sciences,
Engineering and Technology, 2015 ·
Achievement
Award from the
World Congress in Computer Science, Computer Engineering, and Applied
Computing, USA, 2015; for more
information see 

The 2^{nd} International Conference and Summer
School “Numerical Computations: Theory and Algorithms”, June 1925, 2016, Italy Previous conferences: 2013 2010 Sergeyev
Ya.D. (2015) Un semplice modo per trattare le
grandezze infinite ed infinitesime, La
Matematica nella Società e nella Cultura: Rivista dell’Unione Matematica
Italiana, Serie I, Vol.8, 111147. 

Video
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записи
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науки" 

Yaroslav D. Sergeyev, Arithmetic of Infinity 
Media citations 

Paperback edition is available at European Amazon sites: UK, DE, FR, IT, ES 

Revised electronic edition is available at Amazon sites: COM, UK, DE, FR, IT, ES, CA, JP, BR, IN, MX 12.02.2016 Amazon.it Kindle Store Best
Sellers Rank: #
1 in eBook Kindle > eBook in lingua
straniera > eBook in inglese > Scienze,
tecnologia e medicina > Matematica 

The book presents a new
methodology that allows one to represent infinite and infinitesimal numbers
by a finite number of symbols and to execute arithmetical operations with all
of them in the same manner as we are used to do with finite quantities. The
new approach is not related to the nonstandard analysis and infinity is
considered in the book in a coherent way different from those proposed by
Georg Cantor, Abraham Robinson, and John Conway. However, the new approach
does not contradict Cantor, it evolves his theory and supplies new more
powerful tools to deal with different infinite and infinitesimal quantities. From the methodological point of
view, the principle of Ancient Greeks ‘The part is less than the whole’ is
adopted and applied to all quantities (finite, infinite, and infinitesimal)
and to all sets and processes (finite and infinite). The new positional
system with the infinite radix introduced in the book allows one to consider
infinite, finite, and infinitesimal numbers as particular cases of a unique
framework. The new viewpoint gives detailed answers to many questions and
paradoxes regarding infinite and infinitesimal quantities. Particularly,
applications of the new approach to limit theory, measure theory, and set
theory are given. The book is mainly addressed to
mathematicians, computer scientists, philosophers, physicists, and students.
However, it is written in a popular way in order to allow any person having a
high school education and interests in the foundations of these sciences to
understand it easily. 13.06.2014 Amazon.com Best Sellers Rank: #1 in Books > Science &
Math > Mathematics > Infinity #1 in Kindle Store > Kindle
eBooks > Nonfiction > Science > Mathematics > Infinity 
Reviews published
in International Journals · Article,
MIT Technology Review, 2012 · Computational Management Science, 2007, vol. 4(1), pages 8586, written by Prof. D. Trigiante · Cybernetics & Systems Analysis, 2006, vol. 42(6), page 183, written by Prof. V.P. Shylo · Optimization Methods and Software, 2006, vol. 21(6), pages 995–996, written by Prof. O. Prokopyev · International Journal of Unconventional
Computing, 2006, vol. 2(2), pages 193194, written by the
EditorinChief Prof. A. Adamatzky ·
Journal
of Global Optimization, 2006, vol. 34, pages 157–158, written by the EditorinChief Prof. P.M. Pardalos 

The Infinity Computer (European patent EP 1728149, Russian patent
2395111, US patent 7,860,914) The main difference of the new
approach with respect to nonstandard analysis theories is its strong
computational character opening a new exiting area in the theory and practice
of computations – Infinity Computing. European patent 1728149 issued 03.06.2009
introducing “Computer system for storing infinite, infinitesimal, and
finite quantities and executing arithmetical operations with them” describes
the Infinity Computer able to execute computations with infinite, finite, and
infinitesimal numbers numerically (not symbolically) in a unique framework.
Russian patent 2395111 has been granted 20.07.2010 and USA patent 7,860,914
has been awarded 28.12.2010. There exist the first software
prototype of the Infinity Computer and the Infinity Calculator able to execute
arithmetical operations with numbers having finite parts and/or infinitesimal
and infinite parts of different orders. Here you can see a screenshot of the Infinity Calculator with
an example of division and a brief comment. The interested investors are invited to contact the author. 
News · Lolli G. (2015) Metamathematical investigations on the theory of Grossone, Applied Mathematics and Computation, 255, 314. · Sergeyev Ya.D. (2015) Un semplice modo per trattare le grandezze infinite ed infinitesime, La Matematica nella Società e nella Cultura: Rivista dell’Unione Matematica Italiana, Serie I, Vol.8, 111147. · Special
Issue of the journal Communications in Nonlinear Science and
Numerical Simulation (Elsevier, IF 2.569), vol. 21, (2015) dedicated
to the International Conference NUMTA2013, Falerna, Italy,
2013 · Interview
to Russia Beyond The Headlines · Special
Issue of the journal Applied Mathematics and Computation (Elsevier,
IF 1.6), vol. 255 (2015) dedicated
to the International Conference NUMTA2013 · Article,
MIT Technology Review ·
Special
Issue of the international journal Applied Mathematics and Computation
(Elsevier, IF 1.6), vol. 218, Issue 16, (2012) dedicated to the international
workshop "Infinite
and Infinitesimal in Mathematics, Computing and Natural Sciences" Cetraro, Italy, 2010 · Articolo del Prof. G. Lolli per “Newton” 

About the author
Top of this page Yaroslav
D. Sergeyev Ph.D., D.Sc., D.H.C. is Distinguished Professor at the University of Calabria, Rende,
Italy and Head of Numerical Calculus Laboratory at the same university. He is
also Professor (parttime) at the Lobachevsky State University, Nizhni Novgorod, Russia and
Affiliated Researcher at the Institute of High Performance
Computing and Networking, Rende, Italy. His research interests
include numerical analysis, set theory, number theory, global optimization,
parallel computing, and fractals. His list of
publications contains more than 200 items including 5 books and more than
80 papers in prestigious international journals. He is a member of editorial
boards of 5 international journals. He has been awarded several research prizes
(Pythagoras International Prize in Mathematics, Italy, 2010; Outstanding
Achievement Award from the 2015 World Congress in Computer Science, Computer
Engineering, and Applied Computing, USA; Honorary Fellowship being the
highest distinction of the European Society of Computational Methods in
Sciences, Engineering and Technology, 2015; Lagrange Lecture, Turin
University, Italy, 2010; MAIK Prize for the best scientific monograph
published in Russian, Moscow, 2008, etc.). Additional information about Prof. Sergeyev can be found here. 

Selected research
papers Top of this page


Presentations Top of this
page The Infinity Computer technology
and its applications together with the respective mathematical and
methodological issues have been presented at the following congresses: 1. plenary lecture, the 7th
International Workshop “Data Analysis Methods for Software Systems”, Druskininkai, Lithuania,
December 3 – 5, 2015 2. plenary lecture, International
Conference and School “HighPerformance Computing, Optimization and
Applications”, Nizhni Novgorod, Russia, November 1620, 2015 3. plenary lecture, the 13th
International Conference of Numerical Analysis and Applied Mathematics ICNAAM
2015, Rhodes, Greece, September 2329, 2015 4. plenary lecture, the 14th
International Conference on Unconventional Computation & Natural
Computation, Auckland, New Zealand, 31 August – 4 September, 2015 5. keynote lecture, the 2015 World
Congress in Computer Science, Computer Engineering, and Applied Computing, Las
Vegas, USA, July 2730, 2015 6. plenary lecture, 1st International
Summer School for Sciences, History and Philosophy of Sciences & Science
Education, Lille, France, June 2226, 2015 7. invited semiplenary lecture, New
Trends in Numerical Analysis: Theory, Methods, Algorithms and Applications, Falerna (CZ), Italy June 1821, 2015tutorial,
International Conference “Theory and Practice of Systems Analysis”, Rybinsk, Russia, May 2124, 2014; 8. plenary lecture, the 9th Italian Workshop
on Artificial Life and Evolutionary Computation, Vietri
sul Mare, Salerno, Italy, May 1415, 2014; 9. plenary lecture opening the 11th
International Conference “Theory and Applications of Models of Computation”,
Chennai, India, April 1113, 2014; 10. tutorial, EURO Miniconference on
Optimization in the Natural Sciences, Aveiro,
Portugal, February 59, 2014; 11. plenary lecture, International
Conference “Optimal decisions in statistics and data analysis”, Cardiff, UK,
December 1618, 2013; 12. plenary lecture, International
Science and Information Conference, London, UK, October 79, 2013; 13. invited 90 minutes lecture,
International Workshop “The Number Road”, Erice,
Italy, September 27, 2013; 14. tutorial, International Conference
and Summer School “Numerical Computations: Theory and Algorithms”, Falerna (CZ), Italy, June 17–23, 2013; 15. keynote lecture opening the 4th
International Joint Conference on Computational Intelligence, Barcelona,
Spain, October 37, 2012; 16. tutorial, the 15th GAMMIMACS
International Symposium on Scientific Computing, Computer Arithmetic and
Verified Numerical Computations, Novosibirsk, Russia, September 2428, 2012; 17. plenary lecture, the 4th
International Conference on the Dynamics of Information Systems, Gainesville,
Florida, USA, February 20  22, 2012; 18. invited lecture, the 12th
International Symposium “Frontiers of Fundamental Physics”, Udine, Italy,
November 2123, 2011; 19. plenary lecture, the 7th
International Asian Summer School “Optimization of Complex Systems”,
Tashkent, Uzbekistan, October 1727, 2011; 20. tutorial, Summer School
“Achievements and Applications of Contemporary Informatics, Mathematics and
Physics”, Kiev, Ukraine, August 1219, 2011; 21. plenary lecture, the 4th
International conference "Mathematics, its Applications and Mathematical
Education" Russia, UlanUde, Baikal, June 27  July 1, 2011; 22. invited lecture, the International
Workshop “New Worlds of Computation”, Orléans,
France, May 2324, 2011; 23. invited onehour lecture,
International Workshop of Natural Computing of the Ninth International
Conference on Cellular Automata for Research and Industry, Ascoli Piceno, Italy, September,
2124, 2010; 24. plenary lecture, the Second
International Conference on Mathematical Physics and Its Applications,
Samara, Russia, August 29  September 4, 2010; 25. keynote lecture, the 3rd Yalta
Optimization Conference, Yalta, Ukraine, August, 24, 2010; 26. plenary lecture, International
Conference on Optimization, Simulation and Control, Ulaanbaatar, Mongolia,
July 2528, 2010; 27. keynote lecture, the 2010 World Congress in Computer Science, Computer Engineering,
and Applied Computing, Las Vegas, USA, July 1215, 2010; 28. joint keynote lecture, the 2010
International Conference on Scientific Computing and Workshop on Cellular
Automata, Theory and Applications, Las Vegas, USA, July 14, 2010; 29. tutorial, International workshop
“Infinite and Infinitesimal in Mathematics, Computing, and Natural Sciences”,
Cetraro, Italy, May 1721, 2010; 30. plenary lecture, International
conference "Optimization and Applications" (OPTIMA2009), Petrovac, Montenegro, September 2125, 2009; 31. tutorial, the international
workshop “Optimization
and Control with Applications”, Harbin, China, June 611, 2009 32. invited one hour lecture, the
First World Congress on Global Optimization in Engineering & Science,
Hunan, China, June 15, 2009; 33. invited one hour lecture, the
International Workshop “New Worlds of Computation”, Orléans,
France, January 12, 2009 34. keynote lecture, Yalta Conference
on Discrete and Global Optimization, Yalta, Ukraine, July, 31 – August, 2, 2008; 35. keynote lecture, the general
plenary session of the World MultiConference WMSCI 2008 held jointly with
the conferences RMCI 2008, MEI 2008, EIC 2008, and BMIC 2008, Orlando,
Florida, June, 29  July, 2, 2008; 36. invited one hour lecture, the World
Congress of Nonlinear Analysts WCNA2008, Orlando, Florida, July, 29, 2008; 37. tutorial, the 48th international
workshop on Nonsmooth Analysis, Optimization and
Applications, Erice, Italy, under the auspices of
the International School of Mathematics “G. Stampacchia”, May, 9–17, 2008; 38. plenary lecture, International
Conference of Numerical Analysis and Applied Mathematics ICNAAM 2007,
September 1620, 2007; 39. invited lecture, the 8th
Mediterranean Workshop and Topical Meeting "Novel Optical Materials and Applications",
Cetraro, Italy, June 39, 2007; 40. tutorial, the International
Workshop on Learning and Intelligent Optimization, Andalo,
Italy, February 1218, 2007; 41. invited one hour lecture, the 15th
Euromicro Conference on Parallel, Distributed and
Networkbased Processing, Naples, February 79, 2007; 42. plenary lecture opening the
MATHESIS Congress, Trento, Italy, November 24, 2006; 43. plenary lecture, the Third
International Conference of Applied Mathematics, Plovdiv, Bulgaria, August
1218, 2006; 44. plenary lecture, International
Conference “Applied Optimization and Metaheuristic Innovations”, Yalta,
Ukraine, July 1723, 2006; 45. invited lecture, the second
International Workshop on Variational Analysis and
Partial Differential Equations, Erice, Italy, under
the auspices of the International School of Mathematics “G. Stampacchia”, July 514, 2006; 46. round table “Infinity Computer and
Calculus”, the 8th Congress of SIMAI (La Societa' Italiana di Matematica Applicata e Industriale),
Ragusa (Sicily), May 2226, 2006; 47. plenary lecture, the XXI Autumn
Meeting of the Polish Information Processing Society, Katowice, Poland,
December 59, 2005; 48. plenary lecture, the International
Workshop on Global Optimization, Almeria, Spain, September 1822, 2005; 49. tutorial, the International Conference
on Complementarity, Duality, and Global Optimization in Science and
Engineering, Blacksburg, Virginia, USA, August 1517, 2005; 50. plenary lecture, International
Conference on Difference Equations, Special Functions and Applications,
Munich, July 2530, 2005; 51. plenary lecture, International
Conference “Numerical Analysis: the State of the Art”, Rende
(CS), Italy, May, 1921, 2005; 52. invited semiplenary lecture at
the International conference on Selected Problems of Modern Mathematics,
dedicated to the 200th anniversary of K.G. Jacobi and the 750th anniversary
of the Koenigsberg foundation, Kaliningrad, April,
48, 2005; 53. tutorial, the Workshop
"Numerical Methods and Mathematical Software", Montecatini
Terme (PT), January 31  February 1, 2005; 54. plenary lecture, the VIth International Congress on Mathematical Modelling,
Nizhni Novgorod, Russia, September, 2126, 2004; 55. opening invited lecture, the
congress “Infinity in Mathematics, Physics, and Philosophy”, Pisa, Italy,
26.03.2004. Results described in the book and
in the patent have been also presented at the following universities,
research institutes, and organizations:
