Solving wigner’s mystery: The reasonable (though perhaps limited) effectiveness of mathematics in the natural sciences

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[1]  Ivor Grattan-Guinness,et al.  The mathematics of the past: distinguishing its history from our heritage , 2004 .

[2]  P. Simons,et al.  Reviews-The Applicability of Mathematics as a Philosophical Problem , 1998 .

[3]  Sundar Sarukkai Revisiting the 'unreasonable effectiveness' of mathematics , 2005 .

[4]  Ivor Grattan-Guinness,et al.  Joseph Fourier, 1768-1830 , 1973 .

[5]  G. Pólya Mathematics and Plausible Reasoning , 1958 .

[6]  Vela Ela Velupillai The unreasonable ineffectiveness of mathematics in economics , 2005 .

[7]  M. Beller Matrix Theory before Schrodinger: Philosophy, Problems, Consequences , 1983, Isis.

[8]  E. Wigner Gruppentheorie und ihre Anwendung auf die Quantenmechanik der Atomspektren , 1931 .

[9]  Ignacio Matte-Blanco The unconscious as infinite sets : an essay in bi-logic , 1975 .

[10]  Jean-Luc Chabert,et al.  A History of Algorithms , 1999 .

[11]  I. Grattan-Guinness Convolutions in French Mathematics, 1800–1840 , 1990 .

[12]  Otto Toeplitz,et al.  The Calculus: A Genetic Approach , 1964 .

[13]  Ivor Grattan-Guinness,et al.  Companion encyclopedia of the history and philosophy of the mathematical sciences , 1994 .

[14]  E. Knobloch Analogy and the Growth of Mathematical Knowledge , 2000 .

[15]  L. Corry,et al.  Recensioni/Reviews-Modern Algebra and the Rise of Mathematical Structures , 1996 .

[16]  Ivor Grattan-Guinness Structure-Similarity as a Cornerstone of the Philosophy of Mathematics , 1992 .

[17]  J. Thomison,et al.  Compared to what? , 1990, Journal of the Tennessee Medical Association.

[18]  Ivor Grattan-Guinness,et al.  Joseph Fourier, 1768-1830; a survey of his life and work, based on a critical edition of his monograph on the propagation of heat, presented to the Institut de France in 1807 , 1972 .

[19]  Is our mathematics natural? The case of equilibrium statistical mechanics , 1988 .

[20]  Mark Colyvan,et al.  The Miracle of Applied Mathematics , 2001, Synthese.

[21]  I. Blanco,et al.  The Unconscious as Infinite Sets: An Essay in Bi-logic , 1975 .

[22]  Peter Medawar,et al.  The art of the soluble , 2021, Nature.

[23]  J. Henshaw Does Measurement Measure Up?: How Numbers Reveal and Conceal the Truth , 2006 .

[24]  G. Pólya Mathematical Methods in Science , 1998 .

[25]  John J. Roche,et al.  The Mathematics of Measurement: A Critical History , 1999 .

[26]  E. Wigner The Unreasonable Effectiveness of Mathematics in the Natural Sciences (reprint) , 1960 .

[27]  Alison Tomlin,et al.  Where is the mathematics in measurement , 2003 .

[28]  B. West An Essay on the Importance of Being Nonlinear , 1985 .

[29]  H. Weyl,et al.  Philosophy of Mathematics and Natural Science , 1950 .

[30]  G. B. Dantzig,et al.  Reminiscences about the origins of linear programming , 1982, Operations Research Letters.

[31]  Archive for History of Exact Sciences , 1960, Nature.

[32]  Arthur M. Lesk,et al.  The unreasonable effectiveness of mathematics in molecular biology , 2000 .

[33]  A. Pais Symmetries and Reflections. Scientific Essays. Eugene P. Wigner. Indiana University Press, Bloomington, 1967. 288 pp., illus. $7.50 , 1967 .

[34]  Jack Schwartz,et al.  The Pernicious Influence of Mathematics on Science , 1992 .

[35]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[36]  Hans Wussing,et al.  The genesis of the abstract group concept , 1984 .

[37]  R. Hamming The Unreasonable Effectiveness of Mathematics. , 1980 .

[38]  I. Grattan-Guinness On the Early Work of William Thomson: Mathematical Physics and Methodology in the 1840s , 2008 .

[39]  Curtis A. Wilson Perturbations and solar tables from Lacaille to Delambre: the rapprochement of observation and theory, part I , 1980 .

[40]  John H. Holland,et al.  Adaptation in Natural and Artificial Systems: An Introductory Analysis with Applications to Biology, Control, and Artificial Intelligence , 1992 .

[41]  D. Kun Mathematics:The Unifying Thread in Science and Technology , 2006 .

[42]  Emily Grosholz,et al.  The Growth of Mathematical Knowledge , 2000 .

[43]  G. Mackey Harmonic analysis as the exploitation of symmetry–a historical survey , 1980 .

[44]  M. Kendall,et al.  The Logic of Scientific Discovery. , 1959 .

[45]  K. Popper,et al.  The Logic of Scientific Discovery , 1960 .

[46]  Differential equations and linearity in the 19th and early 20th centuries , 2008 .

[47]  Barry Smith,et al.  Parts and Moments: Studies in Logic and Formal Ontology. , 1985 .

[48]  Thomas Mormann,et al.  The Space of Mathematics , 1992 .

[49]  Silvanus P. Thompson,et al.  Calculus Made Easy , 1910 .

[50]  Patrick Suppes,et al.  Logic, Methodology and Philosophy of Science , 1963 .

[51]  Thomas Hawkins,et al.  Cauchy and the spectral theory of matrices , 1975 .

[52]  Antonio Guarnieri,et al.  WITH THE COLLABORATION OF , 2009 .

[53]  George B. Dantzig,et al.  Reminiscences about the origins of linear programming , 1982, Oper. Res. Lett..

[54]  I. Grattan-Guinness Scientific Revolutions as Convolutions? A Sceptical Enquiry , 1992 .

[55]  Ivor Grattan-Guinness Convolutions in French Mathematics, 1800–1840: From the Calculus and Mechanics to Mathematical Analysis and Mathematical Physics , 1990 .

[56]  G. Mackey The scope and history of commutative and noncommutative harmonic analysis , 1992 .

[57]  Jean-Luc Chabert,et al.  A history of algorithms: from the pebble to the microchip , 1999 .

[58]  Steven French,et al.  The Reasonable Effectiveness of Mathematics: Partial Structures and the Application of Group Theory to Physics , 2004, Synthese.

[59]  Eugene P. Wigner,et al.  Symmetries and Reflections: Scientific Essays , 1968 .

[60]  J. Gray CAUCHY AND THE CREATION OF COMPLEX FUNCTION THEORY , 1999 .