Georges Matheron

Professor Georges Matheron (1930 - 2000)

A life devoted to probabilistic modelling

Professor Georges Matheron, the founder of geostatistics, passed away August 7, 2000.

He developed his skills in mathematics, physics and probability at the Ecole Polytechnique (X49), and then at the École des Mines de Paris (engineer of the Corps des Mines, a structure gathering high-rank civil servants at the Ministry of Industry). One of his professors was Paul Levy, an authority in probabilities, whose influence is present throughout Georges Matheron's works.

From 1954 to 1963, during his visit to the Bureau de Recherches Géologiques et Minières (Bureau of Geological and Mining Research) in Algeria and in France, he discovered the pioneering works of the South African school (Krige, Sichel, de Wijs) devoted to the Witwatersrand gold mines and developed then the key concepts of geostatistics, a theory for the estimation of natural resources. These early works find their culmination with the publication of two books (Mémoires du BRGM) :

  • The monumental Traité de géostatistique appliquée (Treaty of applied geostatistics) (Editions Technip, France, 1962-63), where the basic tools of linear geostatistics are defined : variography, estimation variance and dispersion variance, kriging, so called from the contributions of the South African engineer Danie Krige (paper in the Encyclopedia Universalis devoted to this theory).
  • A more theoretical book, his thesis, entitled : Les variables régionalisées et leur estimation : une application de la théorie des functions aléatoires aux sciences de la nature (The regionalized variables and their estimation : an application of the theory of random functions to natural sciences), published by Masson in 1965.

From 1964 to 1968, G. Matheron worked on the mathematical characterization of forms and created, in collaboration with Jean Serra, a new discipline, mathematical morphology, today one of the essential components of image processing. At the same time, he also worked in hydrodynamics and published in 1967 a book entitled Éléments pour une théorie des milieux poreux (Elements for a theory of porous media) (Masson).

After having developed teaching in probability and geostatistics at the Ecole des Mines de Nancy, G. Matheron joined the Ecole des Mines de Paris and in 1968 took charge of a research centre newly created on the site of Fontainebleau, the Centre of Mathematical Morphology (Centre de Morphologie Mathématique - CMM). Due to the diversity of its applications, the centre was renamed the Centre for Geostatistics and Mathematical Morphology (Centre de Géostatitique et de Morphologie Mathématique - CGMM) in 1979, and divided in two new structures in 1986, with J. Serra as the director of the new Centre for Mathematical Morphology and G. Matheron as the director of the Centre for Geostatistics (CG). The well-known Issue 5 of the Cahiers du Centre de Morphologie Mathématique de Fontainebleau, entitled La théorie des variables régionalisées, et ses applications (The Theory of regionalized variables and its applications) (Matheron, 1970) is the geostatistical bible of several students and researchers.

In Fontainebleau, G. Matheron showed an amazing creativity by developing with a team of colleagues (André Journel, Alain Maréchal, Pierre Delfiner, Jean-Paul Chilès being a few long-standing collaborators) the concepts of nonlinear geostatistics and non stationary geostatistics, while keeping a strong interest in other mining problems (such as the optimization of open pits) and in Mathematical Morphology. He published in 1975 Random sets and integral geometry (Wiley), an essential contribution to the theory of random sets.

G. Matheron, whose whole life was devoted to research, has published more than 250 notes, mostly internal to the centres of Fontainebleau, and five books. His work is full of ideas, concepts and models that will inspire us, engineers and researchers.

A recurring topic can be identified through this eclectic and prolific output : the use of probabilistic models. G. Matheron showed an exceptional ability to confront so-called unsolvable problems, to reduce them to simpler questions he solved with appropriate models. Thus, the methods and concepts he developed are still current : they respond to real problems.

The best proof is the remarkable variety of the applications of geostatistics : formerly confined to mining applications, geostatistics is now used in oil industry, forestry, agronomy, oceanography, meteorology, halieutics, environment, etc.

This accumulation of experiments for the modelling of unique natural phenomena by a probabilistic approach led G. Matheron to write in 1978 Estimer et choisir : un essai sur les probabilités appliquées, that anyone interested in probabilities must read. As A.M. Hasofer wrote in the preface to the English translation (Estimating and Choosing: An Essay on Probability in Practice, Springer, 1989) :

To read the work of Matheron is an illumination. We find a coherent developed framework leading to purely objective a use of probabilistic models for describing unique phenomena. Through his unifying vision, Matheron was able to eliminate from the practice of probabilities all philosophical considerations that had made it obscure and confused for decades. He proposes us a guideline to determine the suitability and the limitations of probabilistic modelling.

Beyond his outstanding scientific abilities, G. Matheron was literally a master : how many students or professionals have not had their careers launched or changed by his teaching, his publications, or by exchanges with him ?

The disappearance of Georges Matheron marks the end of an era: in addition to his many writings, he lefts behind him two growing disciplines, the Geostatistics and the Mathematical Morphology. We must now follow his path and advance his ideas.