THE RECOVERY OF COMPREHENSIBLE MATHEMATICS
DOI:
https://doi.org/10.17770/sie2019vol5.3737Keywords:
Fields Medal, Optimal Mass Transport, Linear Programming, Stepping Stones, DualityAbstract
The main objective is to get over the gap that exists between mathematics and common people, especially grown up people. Apart mathematical details, the problem lies in a good choice of notices (curiosity) and nice problems (play). Some historical notes about great mathematicians are presented and discussed, with explicit reference to the cases when the boundary between Nobel prize and mathematics was broken. Favourable fields are probability and operations research. Since probability tends to an excess of theory, operations research seemed to be a good choice. The Fields Medal, a kind of Nobel prize for Mathematics, was also considered, since in 2018 it was achieved by the Italian mathematician Figalli, former student of Scuola Normale Superiore di Pisa. He started from an important field in the frame of Operations Research, namely Optimal Transport. This sector allows to summarize a very nice procedure for its solution, non at all obvious to be trasferred to the computer. Since mathematics is forgotten in the course of life, except for those few parts of current use, to bring the adult back into the interest of mathematics, topics related to everyday life should be presented. Operations research, and especially network optimization, provide significant but pleasing problems.
Downloads
References
Ackoff, R.L., & Sasieni, M.W. (1968). Fundamentals of operations research. New York: John Wiley.
Ambrosio, L. (2003). Lecture notes on optimal transport problems. In Mathematical Aspects of Evolving Interfaces, Lecture Notes in Mathematics 1812 (1-52). Berlin/New York: Springer-Verlag.
Ambrosio, L. (2008). Ennio De Giorgi e la moderna teoria geometrica della misura. In Ambrosio, L., Forti, M., Marino, A., & Spagnolo, S. Scripta volant, verba manent. Ennio De Giorgi matematico e filosofo (67-80) a cura di V. Letta Pisa ETS.
Ambrosio, L. (2009). Recenti sviluppi della teoria del trasporto ottimo di massa Lecture notes of Scuola Normale Superiore. Pisa, SNS, 1-33.
Andreatta, G., Mason, F., & Romanin Jacur, G. (1990). Ottimizzazione su reti Padova: Libreria Progetto chap.5.7.
Bombieri, E., De Giorgi, E., & Giusti, E. (1969). Minimal Cones and the Bernstein Problem, Invent. Math., 7, 243-268.
Bombieri, E., De Giorgi, E., & Miranda, M. (1969). Una maggiorazione a priori per le superfici minimali non parametriche, Arch. Rational Mech. Anal., 32, 255-267.
Chang, T.F.M., Piccinini, L.C., Iseppi, L., & Lepellere, M.A. (2013). The Black Box of Economic Interdependence in the Process of Structural Change, Italian Journal of Pure and Applied Mathematics, 31, 285-306.
Dantzig, G.B. (1963). Linear Programming and Extensions Princeton University Press.
De Giorgi, E. (1953). Definizione ed espressione analitica del perimetro di un insieme, Atti Acc. Naz. Lincei Cl SCI, 8, 390-393.
De Giorgi, E. (1954). Su una teoria generale della misura (r-1)-dimensionale in uno spazio a r dimensioni, Ann. di matematica, 36, 191-213.
De Giorgi, E. (1957). Sulla differenziabilità e l’analiticità delle estremali degli integrali multipli regolari Mem. Accad. Sc. Torino, 3, 25-43, English translation On the differentiability and the analyticity of extremals of regular multiple integrals, in Ennio De Giorgi Selected Papers, (1996) Berlin-Heidelberg. 149-166.
De Giorgi, E. (1958). Sulla proprietà isoperimetrica dell’ipersfera, Atti Acc. Naz. Lincei Mem. Scienze 5, 33-44.
De Giorgi, E., Colombini, F., & Piccinini, L.C. (1972). Frontiere orientate di misura minima e questioni collegate, Pisa, Scuola Normale Superiore, classe di Scienze.
De Philippis, G. & Figalli, A. (2014). The Monge Ampére equation and its link to optimal transportation. Bull. Am. Math. Soc. 51, 527-580.
Figalli, A. (2018). Free boundary regularity in obstacle problems, Journées EDP 2018, to appear.
Hillier, F.S., & Lieberman, G.J. (2005). Introduction to Operations Research. Boston MA: McGraw-Hill, 8th. (International) Edition.
Kantorovic, L.V. (1939). Matematiceskie metody organizacii i planrovanija projzvodsva American Translation (1960) Management Science 6 (4). 366-422.
Knuth, D.E. (1968). Fundamental algorithms, volume 1 of The art of computing Addison-Wesley.
Leontieff, W. (1966). Input-Output Economics, Oxford University Press.
Lovasz, L., & Plummer, M. (1986). Matching Theory. Budapest: Academic Press.
Miller, C. (1887-1916). Tabula Peutingeriana, ed. Conrad Millerg, Segmenta II-XII.
Monge, G. (1781). Mémoire sur la Théorie des Déblais et des Remblais. Hist. de l’Acad. Des Sciences de Paris, 666–704.
Moser, J. (1960). A new proof of De Giorgi’s theorem concerning the Regularity Problem for Elliptic Partial Differential Equations, Comm. Pure and Appl. Math. 13, 457-468.
Nash, J. (1958). Continuity of solutions of parabolic and elliptic equations Amer. J. Math., 80, 931-953.
Newell, A., Shaw, J.C., & Simon, H.A. (1957). Empirical Explorations of the Logic Joint Computer Conference, n.11.
Parlangeli, A. (2015-2019). Uno spirito puro: Ennio De Giorgi, Lecce: Milella. English translation: A Pure Soul: Ennio De Giorgi, A Mathematical Genius, Springer.
Piccinini, L.C. (1973). De Giorgi’s Measure and thin obstacles. In (Ed.) Bombieri, E., Geometric Measure Theory and Minimal Surfaces Roma: Cremonese, 223-230.
Piccinini, L.C. (2016). Al suo grande maestro Ennio De Giorgi, a cura di V. Valzano Biliotti e G. Sartor Zanzotto Lecce, Edizioni Milella.
Piccinini, L.C., & Lepellere, M.A. (2018). The Mathematical Teaching of De Giorgi and its Design Reality, Il mosaico paesistico-culturale: Convegno Venezia 2017; Udine, IPSAPA, 279-291.
Rachev, S.T., & Rueschendorf, L. (1989). Mass transportation problems, Berlin- Heidelberg: Springer Verlag.
Simon, H.A. (1995). Models of my Life, New York: Basic.
Villani, C. (2009). Optimal Transport, Old and New, Grundlehren der Mathematischen Wissenschaften.Vol. 338. Berlin: Springer-Verlag.