Discrete Mathematical Chemistry: Social Aspects of its Emergence and Reception

We first show some successes of discrete mathematical chemistry (DMC), a branch of theoretical chemistry born in the 1960s and 1970s. Then we explore the social context in which the emergence of DMC took place, ini- tiated mainly in East European countries. The availability of knowledge, espe- cially of mathematical knowledge, and the lack of research funds were the main conditions that helped get DMC started. We also explore the reception of DMC in the chemical and mathematical circles, being flat rejection in chemistry and slow acceptance in mathematics. Finally, we discuss some defi- nitions of the subject and propose a new one stating that mathematical chem- istry is the realization of mathematical thinking in chemistry, understood as functional thinking defined by Felix Klein in the Erlangen Program.

[1]  Walter Kohn,et al.  Nobel Lecture: Electronic structure of matter-wave functions and density functionals , 1999 .

[2]  Alan L. Goodson.  Graph-Based Chemical Nomenclature. 2. Incorporation of Graph-Theoretical Principles into Taylor's Nomenclature Proposal , 1980, J. Chem. Inf. Comput. Sci..

[3]  Adalbert Kerber.  The diagram lattice as structural principle in mathematics , 1978 .

[4]  D. M. Hutton,et al.  Handbook of Discrete and Combinatorial Mathematics , 2001 .

[5]  Johann Gasteiger,et al.  Handbook of Chemoinformatics , 2003 .

[6]  Milan Randić,et al.  Molecular bonding profiles , 1996 .

[7]  Guillermo Restrepo,et al.  Lemont B. Kier: a bibliometric exploration of his scientific production and its use. , 2013, Current computer-aided drug design.

[8]  Arnold B. Arons,et al.  The Edge of Objectivity , 1960 .

[9]  G. Pólya,et al.  Combinatorial Enumeration Of Groups, Graphs, And Chemical Compounds , 1988 .

[10]  C. A. Coulson,et al.  Present State of Molecular Structure Calculations , 1960 .

[11]  Milan Randić,et al.  The nature of chemical structure , 1990 .

[12]  L B Kier,et al.  Molecular connectivity. I: Relationship to nonspecific local anesthesia. , 1975, Journal of pharmaceutical sciences.

[13]  Roberto Todeschini,et al.  Molecular descriptors for chemoinformatics , 2009 .

[14]  H Weyl.  THE MATHEMATICAL WAY OF THINKING. , 1940, Science.

[15]  E. Ruch,et al.  Algebraic aspects of the chirality phenomenon in chemistry , 1972 .

[16]  Harriet Martineau,et al.  The Positive Philosophy of Auguste Comte , 2008 .

[17]  E. Ruch,et al.  Das stereochemische Strukturmodell, ein mathematisches Modell zur gruppentheoretischen Behandlung der dynamischen Stereochemie , 1966 .

[18]  Milan Randic,et al.  A Comparative Study of Proteomics Maps Using Graph Theoretical Biodescriptors , 2002, J. Chem. Inf. Comput. Sci..

[19]  A. C. Esq.,et al.  XXVIII. On the theory of the analytical forms called trees , 1857 .

[20]  Guillermo Restrepo,et al.  Topological Study of the Periodic System , 2004, J. Chem. Inf. Model..

[21]  H. Wiener.  Structural determination of paraffin boiling points. , 1947, Journal of the American Chemical Society.

[22]  Alan L. Goodson.  Graph-Based Chemical Nomenclature. 1. Historical Background and Discussion , 1980, J. Chem. Inf. Comput. Sci..

[23]  Milan Randic,et al.  A novel 2-D graphical representation of DNA sequences of low degeneracy , 2001 .

[24]  G. Restrepo.  To mathematize, or not to mathematize chemistry , 2013 .

[25]  Nenad Trinajstić – Pioneer of Chemical Graph Theory , 2004 .

[26]  Ivar Ugi,et al.  Die Vandermondesche Determinante als Näherungsansatz für eine Chiralitätsbeobachtung, ihre Verwendung in der Stereochemie und zur Berechnung der optischen Aktivität , 1967 .

[27]  Guillermo Restrepo,et al.  Chemistry, a lingua philosophica , 2011 .

[28]  Ernst Ruch,et al.  Theorie der ChiralitÄtsfunktionen , 1970 .

[29]  W. H. Powell,et al.  A guide to IUPAC nomenclature of organic compounds : recommendations 1993 , 1994 .

[30]  I. Gutman,et al.  Mathematical Chemistry * , 2003 .

[31]  Alexandru T. Balaban,et al.  Reflections About Mathematical Chemistry , 2005 .

[32]  Milan Randic,et al.  On 3‐D Graphical Representation of DNA Primary Sequences and Their Numerical Characterization. , 2001 .

[33]  M. Randic.  Novel molecular descriptor for structure—property studies , 1993 .

[34]  Douglas J. Klein,et al.  Diamond-graphite hybrids , 1994 .

[35]  Béla Bollobás,et al.  Graphs of Extremal Weights , 1998, Ars Comb..

[36]  E. Cayley,et al.  Ueber die analytischen Figuren, welche in der Mathematik Bäume genannt werden und ihre Anwendung auf die Theorie chemischer Verbindungen , 1875 .

[37]  Roberto Todeschini,et al.  Handbook of Molecular Descriptors , 2002 .

[38]  G. Restrepo,et al.  A Network Study of Chemical Elements: From Binary Compounds to Chemical Trends , 2012 .

[39]  R. Brereton,et al.  Handbook of chemoinformatics: from data to knowledge, edited by Johann Gasteiger, Volumes 1–4. Wiley‐VCH, Weinheim, 2003, ISBN 3527306803, €485 , 2004 .

[40]  Arthur Cayley,et al.  The Collected Mathematical Papers: On the Theory of the Analytical Forms called Trees , 2009 .

[41]  Douglas J. Klein,et al.  Mathematical Chemistry! Is It? And if so, What Is It? , 2013 .

[42]  Milan Randić,et al.  Aromaticity of Polycyclic Conjugated Hydrocarbons , 2003 .

[43]  Adalbert Kerber,et al.  Applied finite group actions , 1999 .

[44]  H. Hosoya.  The Topological Index Z Before and After 1971 , 2003 .

[45]  G. Restrepo,et al.  Mathematical Thinking in Chemistry , 2012 .