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"Every attempt to employ mathematical methods in the study of chemical questions must be considered profoundly irrational and contrary to the spirit of chemistry. If mathematical analysis should ever hold a prominent place in chemistry – an aberration which is happily almost impossible – it would occasion a rapid and widespread degeneration of that science." Auguste Comte (1830) [1]
"Important investigations by physicists on the foundations of mechanics are at hand; I refer to the writings of Mach, Hertz, Boltzmann and Volkmann. It is therefore very desirable that the discussion of the foundations of mechanics be taken up by mathematicians also." David Hilbert (1900) [2]
"Every mathematician knows it is impossible to understand an elementary course in thermodynamics." Vladimir I. Arnold (1989)[3]

Here are details of mathematical tools that have applications in classical thermodynamics, statistical mechanics and computer simulation techniques.


Functions and distributions[edit]


Integrals and quadrature[edit]



Computer assisted mathematics[edit]

Packages Program or library Notes License
BLAS routines Basic Linear Algebra Subprograms free source
CGAL library Computational Geometry Algorithms Library free, Open Source
FreeMat program free (GNU General Public License)
IMSL Numerical Libraries library
LAPACK routines Linear Algebra PACKage free source
ScaLAPACK library Scalable LAPACK free source
Maple program commercial
Mathematica program commercial
Math Kernel Library library
MATLAB program commercial
Maxima program free (General Public License)
NAG routines Numerical Algorithms Group commercial
Numerical Recipes routines
Octave program free (GNU)
QUADPACK routines free
SAGE program free (General Public License)
Scilab program free, Open Source

Interesting reading[edit]


  1. Auguste Comte"Cours de philosophie positive" (Tome 3) 35e Leçon. Considérations philosophiques sur l'ensemble de la chimie (1830)
  2. David Hilbert, excerpt from problem VI of his lecture "Sur les problèmes futurs des Mathématiques", Second International Congress of Mathematicians, pp. 58-114 Paris (1900)
  3. Vladimir I. Arnold "Contact geometry: The geometrical method of Gibbs' thermodynamics," in Proceedings of the Gibbs Symposium, Yale University, May 15-17, 1989 Ed. D. G. Caldi and G. D. Mostow, American Mathematical Society (1990) ISBN 978-0-8218-0157-4 p. 163.

External links[edit]