Selected research papers
 Surveys in English, Italian, and Russian

Foundations, logic, philosophy, and
relations to traditional views  Optimization and numerical differentiation

Turing machines and cellular automata
 Solving ordinary differential equations
 Fractals and tilings

Probability, summation, and factorisation

Game theory, ordering, and
infinite decision processes  Teaching
Sergeyev Ya.D. (2017) Numerical infinities and infinitesimals: Methodology, applications, and repercussions on two Hilbert problems, EMS Surveys in Mathematical Sciences, 4(2), 219–320.
Sergeyev Ya.D, (2010) Lagrange Lecture: Methodology of numerical computations with infinities and infinitesimals, Rendiconti del Seminario Matematico dell'Università e del Politecnico di Torino, 68(2), 95–113.
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.
Sergeyev Ya.D. (2023) Lower and upper estimates of the quantity of algebraic numbers, Mediterranean Journal of Mathematics, 20(1), article 12.
Tohmé F., Caterina G., Gangle R. (2022) Observability in the Univalent Universe, Mediterranean Journal of Mathematics, 19, article 216.
Sergeyev Ya.D. (2022) Some paradoxes of infinity revisited, Mediterranean Journal of Mathematics, 19, article 143.
Gangle R., Caterina G., Tohmé F. (2020) A constructive sequence algebra for the calculus of indications, Soft Computing, 24, 1762117629.
Tohmé F., Caterina G., Gangle R. (2020) Computing Truth Values in the Topos of Infinite Peirce’s αExistential Graphs, Applied Mathematics and Computation, 385, article number 125343.
Caldarola F., Cortese D., d’Atri G., Maiolo M. (2020) Paradoxes of the Infinite and Ontological Dilemmas Between Ancient Philosophy and Modern Mathematical Solutions, Lecture Notes in Computer Science, LNCS 11973, 358372.
Sergeyev Ya.D. (2019) Independence of the grossonebased infinity methodology from nonstandard analysis and comments upon logical fallacies in some texts asserting the opposite, Foundations of Science, 24(1), 153–170.
Lolli G. (2015) Metamathematical investigations on the theory of Grossone, Applied Mathematics and Computation, 255, 314.
Sergeyev Ya.D. (2015) Computations with grossonebased infinities, C.S. Calude, M.J. Dinneen (Eds.), Proc. of the 14th International Conference “Unconventional Computation and Natural Computation”, Lecture Notes in Computer Science, vol. 9252, Springer, 89106.
Montagna F., Simi G., Sorbi A. (2015) Taking the Pirahã seriously, Communications in Nonlinear Science and Numerical Simulation, 21(1–3), 5269.
Lolli G. (2012) Infinitesimals and infinites in the history of Mathematics: A brief survey, Applied Mathematics and Computation, 218(16), 79797988.
Margenstern M. (2011) Using Grossone to count the number of elements of infinite sets and the connection with bijections, pAdic Numbers, UltrametricAnalysis and Applications, 3(3), 196204.
Sergeyev Ya.D. (2010) Counting systems and the First Hilbert problem, Nonlinear Analysis Series A: Theory, Methods & Applications, 72(34), 17011708.
Falcone A., Garro A., Mukhametzhanov M.S., Sergeyev Ya.D. (2022) Simulation of hybrid systems under Zeno behavior using numerical infinitesimals, Communications in Nonlinear Science and Numerical Simulation, 111, article number 106443.
Falcone A., Garro A., Mukhametzhanov M.S., Sergeyev Y.D. (2021) A Simulinkbased software solution using the Infinity Computer methodology for higher order differentiation, Applied Mathematics and Computation, 409, article 125606.
Fiaschi L., Cococcioni M. (2021) The BigM method with the numerical infinite M, Optimization Letters, 15 (7), 24552468.
Lai L., Fiaschi L., Cococcioni M., Deb K. (2021) Solving mixed ParetoLexicographic multiobjective optimization problems: The case of priority levels, IEEE Transactions on Evolutionary Computation, 25 (5), 971–985.
Iavernaro F., Mazzia F., Mukhametzhanov M.S., Sergeyev Y.D. (2021) Computation of higher order Lie derivatives on the Infinity Computer, Journal of Computational and Applied Mathematics, 383, article number 113135.
Sergeyev Y.D., Nasso M.C., Mukhametzhanov M.S., Kvasov, D.E (2021) Novel local tuning techniques for speeding up onedimensional algorithms in expensive global optimization using Lipschitz derivatives, Journal of Computational and Applied Mathematics, 383, article number 113134.
De Leone R., Egidi N., Fatone L. (2020) The use of grossone in elastic net regularization and sparse support vector machines, Soft Computing, 24, 1766917677.
Astorino A., Fuduli A. (2020) Spherical separation with infinitely far center, Soft Computing, 24, 1775117759.
Falcone A., Garro A., Mukhametzhanov M.S., Sergeyev Y.D. (2020) Representation of grossonebased arithmetic in Simulink for scientific computing, Soft Computing, 24, 1752517539.
De Leone R., Fasano G., Roma M., Sergeyev Y.D. (2020) Iterative grossonebased computation of negative curvature directions in largescale optimization, Journal of Optimization Theory and Applications, 186(2), 554589.
Lai L., Fiaschi L., Cococcioni M. (2020) Solving Mixed ParetoLexicographic MultiObjective Optimization Problems: The Case of Priority Chains, Swarm and Evolutionary Computation, 55, 100687.
Cococcioni M., Cudazzo A., Pappalardo M., Sergeyev Ya.D. (2020) Solving the Lexicographic MultiObjective MixedInteger Linear Programming Problem Using BranchandBound and Grossone Methodology, Communications in Nonlinear Science and Numerical Simulation, 84, 105177.
De Leone R., Fasano G., Roma M., Sergeyev Ya D., (2019) How Grossone can be helpful to iteratively compute negative curvature directions, R. Battiti et al. (Eds.): Proc. of the 12th International Conference LION 12, Lecture Notes in Computer Science, vol. 11353, Springer, 80–183.
Sergeyev Ya.D., Kvasov D.E., Mukhametzhanov M.S. (2018) On strong homogeneity of a class of global optimization algorithms working with infinite and infinitesimal scales, Communications in Nonlinear Science and Numerical Simulation, 59, 319330.
De Leone R., Fasano G., Sergeyev Ya.D. (2018) Planar methods and grossone for the Conjugate Gradient breakdown in nonlinear programming, Computational Optimization and Applications, 71(1), 7393.
Gaudioso M., Giallombardo G., Mukhametzhanov M.S. (2018) Numerical infinitesimals in a variable metric method for convex nonsmooth optimization, Applied Mathematics and Computation, 318, 312–320.
De Leone R. (2018) Nonlinear programming and grossone: Quadratic programming and the role of constraint qualifications, Applied Mathematics and Computation, 318, 290–297.
Cococcioni M., Pappalardo M., Sergeyev Ya.D. (2018) Lexicographic multiobjective linear programming using grossone methodology: Theory and algorithm, Applied Mathematics and Computation, 318, 298–311.
De Cosmis S., R. De Leone (2012) The use of Grossone in Mathematical Programming and Operations Research, Applied Mathematics and Computation, 218(16), 80298038.
Sergeyev Ya.D. (2011) Higher order numerical differentiation on the Infinity Computer, Optimization Letters, 5(4), 575585.
D’Alotto L. (2015) A classification of onedimensional cellular automata using infinite computations, Applied Mathematics and Computation, 255, 1524.
Sergeyev Ya. D., Garro A. (2015) The Grossone methodology perspective on Turing machines, in "Automata, Universality, Computation", A. Adamatzky (ed.), Springer Series "Emergence, Complexity and Computation", Vol. 12, pp. 139169.
D’Alotto L. (2013) A classification of twodimensional cellular automata using infinite computations, Indian Journal of Mathematics, 55, 143158.
Sergeyev Ya. D., Garro A. (2013) Singletape and multitape Turing machines through the lens of the Grossone methodology, Journal of Supercomputing, 65(2), 645663.
D’Alotto L. (2012) Cellular Automata Using Infinite Computations, Applied Mathematics and Computation, 218(16), 80778082.
Sergeyev Ya. D., Garro A. (2010) Observability of Turing Machines: a refinement of the theory of computation, Informatica, 21(3), 425454.
Falcone A., Garro A., Mukhametzhanov M.S., Sergeyev Ya.D. (2022) Simulation of hybrid systems under Zeno behavior using numerical infinitesimals, Communications in Nonlinear Science and Numerical Simulation, 111, article number 106443.
Iavernaro F., Mazzia F., Mukhametzhanov M.S., Sergeyev Y.D. (2021) Computation of higher order Lie derivatives on the Infinity Computer, Journal of Computational and Applied Mathematics, 383, article number 113135.
Amodio P., Brugnano L., Iavernaro F., Mazzia F. (2020) On the use of the Infinity Computer architecture to set up a dynamic precision floatingpoint arithmetic, Soft Computing, 24, 1758917600.
Falcone A., Garro A., Mukhametzhanov M.S., Sergeyev Y.D. (2020) Representation of grossonebased arithmetic in Simulink for scientific computing, Soft Computing, 24, 1752517539.
Iavernaro F., Mazzia F., Mukhametzhanov M.S., Sergeyev Ya.D. (2020) Conjugatesymplecticity properties of Euler–Maclaurin methods and their implementation on the Infinity Computer, Applied Numerical Mathematics, 155, 5872.
Amodio, P., Iavernaro, F., Mazzia, F., Mukhametzhanov, M.S., Sergeyev, Ya.D. (2017) A generalized Taylor method of order three for the solution of initial value problems in standard and infinity floatingpoint arithmetic, Mathematics and Computers in Simulation, 141, 24–39.
Mazzia F., Sergeyev Ya. D., Iavernaro F., Amodio P., and Mukhametzhanov M. S. (2016) Numerical methods for solving ODEs on the infinity computer, AIP Conference Proceedings 1776, 090033.
Sergeyev Ya.D., Mukhametzhanov M.S., Mazzia F., Iavernaro F., Amodio P. (2016) Numerical methods for solving initial value problems on the Infinity Computer, International Journal of Unconventional Computing, 12(1), 3–23.
Sergeyev Ya.D. (2013) Solving ordinary differential equations by working with infinitesimals numerically on the Infinity Computer, Applied Mathematics and Computation, 219(22), 10668–10681.
Caldarola F., Maiolo M. (2020) On the topological convergence of multirule sequences of sets and fractal patterns, Soft Computing, 24, 1773717749.
Antoniotti L., Caldarola F., and Maiolo M. (2020) Infinite Numerical Computing Applied to Hilbert’s, Peano’s, and Moore’s Curves, Mediterranean Journal of Mathematics, 17(3), article 99, 119.
Caldarola F. (2018) The exact measures of the Sierpiński ddimensional tetrahedron in connection with a Diophantine nonlinear system, Communications in Nonlinear Science and Numerical Simulation, 63, 228238.
Caldarola F. (2018) The Sierpinski curve viewed by numerical computations with infinities and infinitesimals, Applied Mathematics and Computation, 318, 321–328.
Margenstern M. (2016) Infinigons of the hyperbolic plane and grossone, Applied Mathematics and Computation, 278, 45–53.
Sergeyev Ya.D. (2016) The exact (up to infinitesimals) infinite perimeter of the Koch snowflake and its finite area, Communications in Nonlinear Science and Numerical Simulation, 31(1–3):21–29.
Margenstern M. (2015) Fibonacci words, hyperbolic tilings and grossone, Communications in Nonlinear Science and Numerical Simulation, 21(1–3), 311.
Iudin D.I., Sergeyev Ya.D. Hayakawa M. (2015) Infinity computations in cellular automaton forestfire model, Communications in Nonlinear Science and Numerical Simulation, 20(3), 861870.
Vita M.C., S. De Bartolo, C. Fallico, M. Veltri (2012) Usage of infinitesimals in the Menger’s Sponge model of porosity, Applied Mathematics and Computation, 218(16), 81878196.
Margenstern M. (2012) An application of Grossone to the study of a family of tilings of the hyperbolic plane, Applied Mathematics and Computation, 218(16), 80058018.
Iudin D.I., Ya.D. Sergeyev, M. Hayakawa (2012) Interpretation of percolation in terms of infinity computations, Applied Mathematics and Computation, 218(16), 80998111.
Sergeyev Ya.D. (2011) Using blinking fractals for mathematical modelling of processes of growth in biological systems, Informatica, 2011, 22(4), 559–576.
Sergeyev Ya.D. (2009) Evaluating the exact infinitesimal values of area of Sierpinski's carpet and volume of Menger's sponge, Chaos, Solitons & Fractals, 42, 3042–3046.
Sergeyev Ya.D. (2007) Blinking fractals and their quantitative analysis using infinite and infinitesimal numbers, Chaos, Solitons & Fractals, vol. 33(1), 5075.
Pepelyshev A., Zhigljavsky A. (2020) Discrete uniform and binomial distributions with infinite support, Soft Computing, 24, 1751717524.
Calude C. S., Dumitrescu M. (2020) Infinitesimal Probabilities Based on Grossone, SN Comput. Sci.1, 36.
Caldarola F., Maiolo M., Solferino V. (2020) A new approach to the Ztransform through infinite computation, Communications in Nonlinear Science and Numerical Simulation, 82, 105019.
Rizza D. (2018) A Study of Mathematical Determination through Bertrand’s Paradox, Philosophia Mathematica, 26(3), 375–395.
Sergeyev Ya.D. (2018) Numerical infinities applied for studying Riemann series theorem and Ramanujan summation, AIP Conference Proceedings 1978, 020004; doi: 10.1063/1.5043649
Sergeyev Ya.D. (2016) The difficulty of prime factorization is a consequence of the positional numeral system, International Journal of Unconventional Computing, Vol. 12 (56), 453–463.
A. Zhigljavsky (2012) Computing sums of conditionally convergent and divergent series using the concept of grossone, Applied Mathematics and Computation, 218, 8064–8076.
Sergeyev Ya.D. (2011) On accuracy of mathematical languages used to deal with the Riemann zeta function and the Dirichlet eta function, pAdicNumbers, Ultrametric Analysis and Applications, 3(2), 129148.
Sergeyev Ya.D. (2009) Numerical point of view on Calculus for functions assuming finite, infinite, and infinitesimal values over finite, infinite, and infinitesimal domains, Nonlinear Analysis Series A: Theory, Methods & Applications, 71(12), e1688e1707.
Cococcioni M., Fiaschi L., Lambertini L. (2021) Nonarchimedean zerosum games, Journal of Computational and Applied Mathematics, 393, 113483.
D’Alotto L. (2020) Infinite games on finite graphs using grossone, Soft Computing, 24, 1750917515.
Rizza D. (2019) Numerical methods for infinite decisionmaking processes, International Journal of Unconventional Computing, 14(2), 139158.
Fiaschi L., Cococcioni M. (2018) Numerical asymptotic results in Game Theory using Sergeyev's Infinity Computing, International Journal of Unconventional Computing, 14(1), 125.
Rizza, D. (2018) How to make an infinite decision, Bulletin of Symbolic Logic, 24(2), p.227.
Rizza D. (2016) Supertasks and numeral systems, AIP Conference Proceedings 1776, 090005.
Sergeyev Ya.D. (2015) The Olympic medals ranks, lexicographic ordering and numerical infinities, The Mathematical Intelligencer, 37(2), 48.
Nasr L. (2023) Students’ resolutions of some paradoxes of infinity in the lens of the grossone methodology. Informatics and Education, 38(1), 83–91. DOI: 10.32517/023404532023381
Mazzia F. (2022) A computational point of view on teaching derivatives, Informatics and education, 37(1), 7986.
Nasr L. (2022) The effect of Arithmetic of Infinity Methodology on students’ beliefs of infinity, Mediterranean Journal for Research in Mathematics Education, 19, 519.
Antoniotti L., Caldarola F., d’Atri G., Pellegrini M. (2020) New Approaches to Basic Calculus: An Experimentation via Numerical Computation, Lecture Notes in Computer Science, LNCS 11973, 329342.
Ingarozza F., Adamo M.T., Martino M., Piscitelli A. (2020) A GrossoneBased Numerical Model for Computations with Infinity: A Case Study in an Italian High School, Lecture Notes in Computer Science, LNCS 11973, 451462.
Iannone P., Rizza D., Thoma A. (2018) Investigating secondary school students’ epistemologies through a class activity concerning infinity, in E. Bergqvist, M. Österholm, C. Granberg, & L. Sumpter (Eds.). Proceedings of the 42nd Conference of the International Group for the Psychology of Mathematics Education (Vol. 3, 131138). Umeå, Sweden: PME.
Lepellere M.A., Piccinini L.C., Taverna M. (2018) From linguistic representation to fuzzy mathematics in grown up people, Proc. Int. Conf. “Society. Integration. Education”. Vol. III, May 25th 26th, 2018. 555565.