E pluribus unum From Complexity, Universality

• Published in: The Best Writing on Mathematics 2013 Vol. 4; pp. 32 - 46
• Main Author: Tao, Terence
• Format: Book Chapter
• Language: English
• Published: United States Princeton University Press 19.01.2014
• Subjects: Applied mathematics; Central limit theorem; Concept of being; Counting numbers; Discrete mathematics; Election forecasting; Formal logic; Integers; Lattice theory; Law of large numbers; Line spectra; Logic; Logical topics; Mathematical analysis; Mathematical lattices; Mathematical logic; Mathematical models; Mathematical set theory; MATHEMATICS; Metaphysics; Microphysics; Molecular physics; Molecular properties; Molecular spectra; Number theory; Numbers; Ontological properties; Ontology; Philosophy; Physical sciences; Physics; Political elections; Political processes; Political science; Politics; Polls; Popular science; Prime numbers; Pure mathematics; Rational numbers; Real numbers; Statistical theories; Statistics; Universality
• ISBN: 9780691160412; 0691160414
• DOI: 10.1515/9781400847990-005

Modern mathematics is a powerful tool to model any number of real-world situations, whether they be natural—the motion of celestial bodies, for example, or the physical and chemical properties of a material—or man-made: for example, the stock market or the voting preferences of an electorate.¹ In principle, mathematical models can be used to study even extremely complicated systems with many interacting components. However, in practice, only simple systems (ones that involve only two or three interacting agents) can be solved precisely. For instance, the mathematical derivation of the spectral lines of hydrogen, with its single electron orbiting the