Related 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
Previous conferences: 2013
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, 111-147.
Yaroslav D. Sergeyev, Arithmetic of Infinity
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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 non-standard 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.
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published in International Journals
· Article, MIT Technology Review, 2012
· 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 193-194, written by the Editor-in-Chief Prof. A. Adamatzky
· Journal of Global Optimization, 2006, vol. 34, pages 157–158, written by the Editor-in-Chief 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 non-standard 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 .
The interested investors are invited to contact the author.
· Conference “Teaching the Arithmetic of Infinity”, 5 July 2016, University of East Anglia, Norwich, UK
· La nuova aritmetica dell'infinito: GRAVITÀ ZERO intervista il Prof. Davide Rizza
· GRAVITÀ ZERO: Sotto la lente logica di Gabriele Lolli
· Lolli G. (2015) Metamathematical investigations on the theory of Grossone, Applied Mathematics and Computation, 255, 3-14.
· 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, 111-147.
· Special Issue of the journal Communications in Nonlinear Science and Numerical Simulation (Elsevier), vol. 21, (2015) dedicated to the, Falerna, Italy, 2013
· Special Issue of the journal Applied Mathematics and Computation (Elsevier), vol. 255 (2015) dedicated to the
· Article, MIT Technology Review
· 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 , Rende, Italy and Head of Numerical Calculus Laboratory at the same university. He is also Professor (part-time) at the , Nizhni Novgorod, Russia and Affiliated Researcher at the , 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
The Infinity Computer technology and its applications together with the respective mathematical and methodological issues have been presented at the following congresses:
1. tutorial, the 2nd International Conference and Summer School “Numerical Computations: Theory and Algorithms”, Pizzo Calabro, Italy, June 19–25, 2016
2. plenary lecture, the 7th International Workshop “Data Analysis Methods for Software Systems”, Druskininkai, Lithuania, December 3 – 5, 2015
3. plenary lecture, International Conference and School “High-Performance Computing, Optimization and Applications”, Nizhni Novgorod, Russia, November 16-20, 2015
4. plenary lecture, the 13th International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2015, Rhodes, Greece, September 23-29, 2015
5. plenary lecture, the 14th International Conference on Unconventional Computation & Natural Computation, Auckland, New Zealand, 31 August – 4 September, 2015
6. keynote lecture, the 2015 World Congress in Computer Science, Computer Engineering, and Applied Computing, Las Vegas, USA, July 27-30, 2015
7. plenary lecture, 1st International Summer School for Sciences, History and Philosophy of Sciences & Science Education, Lille, France, June 22-26, 2015
8. invited semi-plenary lecture, New Trends in Numerical Analysis: Theory, Methods, Algorithms and Applications, Falerna (CZ), Italy June 18-21, 2015tutorial, International Conference “Theory and Practice of Systems Analysis”, Rybinsk, Russia, May 21-24, 2014;
9. plenary lecture, the 9th Italian Workshop on Artificial Life and Evolutionary Computation, Vietri sul Mare, Salerno, Italy, May 14-15, 2014;
10. plenary lecture opening the 11th International Conference “Theory and Applications of Models of Computation”, Chennai, India, April 11-13, 2014;
11. tutorial, EURO Mini-conference on Optimization in the Natural Sciences, Aveiro, Portugal, February 5-9, 2014;
12. plenary lecture, International Conference “Optimal decisions in statistics and data analysis”, Cardiff, UK, December 16-18, 2013;
13. plenary lecture, International Science and Information Conference, London, UK, October 7-9, 2013;
14. invited 90 minutes lecture, International Workshop “The Number Road”, Erice, Italy, September 27, 2013;
15. tutorial, International Conference and Summer School “Numerical Computations: Theory and Algorithms”, Falerna (CZ), Italy, June 17–23, 2013;
16. keynote lecture opening the 4th International Joint Conference on Computational Intelligence, Barcelona, Spain, October 3-7, 2012;
17. tutorial, the 15th GAMM-IMACS International Symposium on Scientific Computing, Computer Arithmetic and Verified Numerical Computations, Novosibirsk, Russia, September 24-28, 2012;
18. plenary lecture, the 4th International Conference on the Dynamics of Information Systems, Gainesville, Florida, USA, February 20 - 22, 2012;
19. invited lecture, the 12th International Symposium “Frontiers of Fundamental Physics”, Udine, Italy, November 21-23, 2011;
20. plenary lecture, the 7th International Asian Summer School “Optimization of Complex Systems”, Tashkent, Uzbekistan, October 17-27, 2011;
21. tutorial, Summer School “Achievements and Applications of Contemporary Informatics, Mathematics and Physics”, Kiev, Ukraine, August 12-19, 2011;
22. plenary lecture, the 4th International conference "Mathematics, its Applications and Mathematical Education" Russia, Ulan-Ude, Baikal, June 27 - July 1, 2011;
23. invited lecture, the International Workshop “New Worlds of Computation”, Orléans, France, May 23-24, 2011;
24. invited one-hour lecture, International Workshop of Natural Computing of the Ninth International Conference on Cellular Automata for Research and Industry, Ascoli Piceno, Italy, September, 21-24, 2010;
25. plenary lecture, the Second International Conference on Mathematical Physics and Its Applications, Samara, Russia, August 29 - September 4, 2010;
26. keynote lecture, the 3rd Yalta Optimization Conference, Yalta, Ukraine, August, 2-4, 2010;
27. plenary lecture, International Conference on Optimization, Simulation and Control, Ulaanbaatar, Mongolia, July 25-28, 2010;
28. keynote lecture, the 2010 World Congress in Computer Science, Computer Engineering, and Applied Computing, Las Vegas, USA, July 12-15, 2010;
29. joint keynote lecture, the 2010 International Conference on Scientific Computing and Workshop on Cellular Automata, Theory and Applications, Las Vegas, USA, July 14, 2010;
30. tutorial, International workshop “Infinite and Infinitesimal in Mathematics, Computing, and Natural Sciences”, Cetraro, Italy, May 17-21, 2010;
31. plenary lecture, International conference "Optimization and Applications" (OPTIMA2009), Petrovac, Montenegro, September 21-25, 2009;
32. tutorial, the international workshop “Optimization and Control with Applications”, Harbin, China, June 6-11, 2009
33. invited one hour lecture, the First World Congress on Global Optimization in Engineering & Science, Hunan, China, June 1-5, 2009;
34. invited one hour lecture, the International Workshop “New Worlds of Computation”, Orléans, France, January 12, 2009
35. keynote lecture, Yalta Conference on Discrete and Global Optimization, Yalta, Ukraine, July, 31 – August, 2, 2008;
36. keynote lecture, the general plenary session of the World Multi-Conference WMSCI 2008 held jointly with the conferences RMCI 2008, MEI 2008, EIC 2008, and BMIC 2008, Orlando, Florida, June, 29 - July, 2, 2008;
37. invited one hour lecture, the World Congress of Nonlinear Analysts WCNA-2008, Orlando, Florida, July, 2-9, 2008;
38. 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;
39. plenary lecture, International Conference of Numerical Analysis and Applied Mathematics ICNAAM 2007, September 16-20, 2007;
40. invited lecture, the 8th Mediterranean Workshop and Topical Meeting "Novel Optical Materials and Applications", Cetraro, Italy, June 3-9, 2007;
41. tutorial, the International Workshop on Learning and Intelligent Optimization, Andalo, Italy, February 12-18, 2007;
42. invited one hour lecture, the 15th Euromicro Conference on Parallel, Distributed and Network-based Processing, Naples, February 7-9, 2007;
43. plenary lecture opening the MATHESIS Congress, Trento, Italy, November 2-4, 2006;
44. plenary lecture, the Third International Conference of Applied Mathematics, Plovdiv, Bulgaria, August 12-18, 2006;
45. plenary lecture, International Conference “Applied Optimization and Metaheuristic Innovations”, Yalta, Ukraine, July 17-23, 2006;
46. 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 5-14, 2006;
47. round table “Infinity Computer and Calculus”, the 8th Congress of SIMAI (La Societa' Italiana di Matematica Applicata e Industriale), Ragusa (Sicily), May 22-26, 2006;
48. plenary lecture, the XXI Autumn Meeting of the Polish Information Processing Society, Katowice, Poland, December 5-9, 2005;
49. plenary lecture, the International Workshop on Global Optimization, Almeria, Spain, September 18-22, 2005;
50. tutorial, the International Conference on Complementarity, Duality, and Global Optimization in Science and Engineering, Blacksburg, Virginia, USA, August 15-17, 2005;
51. plenary lecture, International Conference on Difference Equations, Special Functions and Applications, Munich, July 25-30, 2005;
52. plenary lecture, International Conference “Numerical Analysis: the State of the Art”, Rende (CS), Italy, May, 19-21, 2005;
53. invited semi-plenary 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, 4-8, 2005;
54. tutorial, the Workshop "Numerical Methods and Mathematical Software", Montecatini Terme (PT), January 31 - February 1, 2005;
55. plenary lecture, the VI-th International Congress on Mathematical Modelling, Nizhni Novgorod, Russia, September, 21-26, 2004;
56. 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: