**Grigore Moisil**'s father, Constantin Moisil, was a historian and member of the Romanian Academy. Grigore was named after his grandfather, Constantin's father, who had been a clergyman but died a few years before his grandson was born. Constantin was married to Elena who was an elementary school teacher in Tulcea, but later she became the director of the "Maidanul Dulapului" school in Bucharest. Marcus, in [14], describes what Grigore, the subject of this biography, was like as a child:-

The child Grigore enjoyed to look around, to give free expression to his curiosity and wonder, to ask questions, to read books of a large diversity from science and literature and from practical jobs to philosophy. He felt always the need to react to what he was seeing, listening and reading. His diary is an excellent mirror of this fact. His main pleasure was always of an intellectual nature, he was not attracted to play with other children or to practice various sports of games. His mother taught him to count and to make calculations and only as a second step to read and write. The most important part of the learning process took place at his home, with his parents and sometimes with his brothers and his sister, all of them becoming intellectuals.

Certainly learning at home was important, but Grigore attended primary school in Bucharest, where his family had moved. He entered high school in 1916, first in Vaslui, then at the "Spiru Haret" high school in Bucharest. Mathematics was the most important subject for him during his school years but his great passion for the subject did not stop him enjoying and excelling in all the other subjects he studied at school. He graduated from high school in 1922 and in 1923 he entered the Faculty of Mathematics University of Bucharest. His parents, however, believed that someone as devoted to mathematics as Grigore was, surely must take up engineering. They pressed him to study that subject at the Polytechnic University and so in 1924 he enrolled as a student. Although he progressed well in the engineering courses, this was not a topic which he enjoyed. Mathematics, on the other hand, gave him nothing but the greatest of joy. He was greatly influenced by his lecturers at the University of Bucharest, particularly Gheorghe Țițeica and Dimitrie Pompeiu. Moisil submitted his doctoral thesis *Analytical Mechanics of Continuous Systems* in 1929 and the examining committee was lead by Țițeica, with Pompeiu and other mathematicians also on the committee. He never completed his engineering degree at the Polytechnic University, however, and he dropped out in 1929.

Moisil then went to Paris to study for the year 1930-31 where he worked with a number of mathematicians including Élie Cartan and Jacques Hadamard. While working there he wrote the paper *On a class of systems of equations with partial derivatives from mathematical physics.* He returned to Romania at the end of his studies in France and was appointed to the Mathematics Department of the University of Iasi in 1931. He left shortly after being appointed to spent another year abroad, this time in Rome, supported by a Rockefeller scholarship, where he spent 1931-32 working with Vito Volterra. After Rome he spent a short while back in Paris before returning to Iasi where he was appointed provisional associate professor on 1 November 1932.

An important event in Moisil's mathematical life was when he read Van der Waerden's famous work *Moderne Algebra* which had been published in 1930. Before reading this work Moisil had worked on differential equations, the theory of functions and mechanics. Van der Waerden's treatise fascinated him, however, and he published his first paper on algebra in 1934. In fact on 1 January 1935 he was appointed as Associate Professor of Algebra at the University of Iasi. His interest in algebra certainly did not mean that he stopped working on the other areas that interested him, he just simply added another to the list of topics on which he was undertaking research. He was appointed as Professor of Differential and Integral Calculus on 1 November 1936 at Iasi, then as Professor of Calculus in 1939. Algebra was not the only new research topic for Moisil during these years, for he became interested in logic after reading a paper by Jan Łukasiewicz. Marcus writes in [14]:-

Moisil spent ten years at Iasi University(1931 - 1941). It was a period in which he alternated his old interests in continuous mathematics with applications to mechanics and physics with his new interests in discrete mathematics, mainly in algebra and logic.

His first paper on algebra and logic was *Recherches sur l'algèbra de la logique* (1935). However, it was in the paper *Recherches sur les logiques non-chrysippiennes* (1940) that Moisil first defined 3-valued and 4-valued Łukasiewicz algebras. These algebras are now called Łukasiewicz-Moisil algebras or L-M algebras. First we must comment on the title of this paper, in particular the term non-chrysippiennes used by Moisil in the title. By non-chrysippian logic he means multivalued logic (non-aristotelian). Moisil feels that the strictest standpoint in classical (formal) logic is represented by Chrysippus rather than Aristotle. Hence "non-chrysippian" should be more accurate than "non-aristotelian". The authors of [10] explain that, in introducing these algebras, Moisil's:-

... goal was to algebrize Łukasiewicz's logic. Boolean algebras, algebraic models of classical logic, are particular cases of the new structures.

To show the breadth of Moisil's research, let us note that in 1940 he also published *Sur les petits mouvements des corps élastiques* and *Sur les géodésiques des espaces de Riemann singuliers.* In the second of these papers he investigates the properties of singular Riemann spaces.

A position of professor at Bucharest University became available in 1941 and Moisil put himself forward for the position. However, Vrănceanu, Barbilian and Miron Nicolescu also applied for the post and Moisil was the youngest of these four, very well qualified, applicants. Not surprisingly Vrănceanu was appointed but then came a quite twist. Moisil approached the ministry of education explaining what a great opportunity it would be for mathematics in Romania if all of them were to be appointed as professors in Bucharest. It looks like a long shot, but Moisil must have known what he was doing for indeed the ministry of education appointed them all to chairs. Moisil took up his new professorship at Bucharest University at the start of the 1941-42 academic year.

In 1942 he introduced *n*-valued L-M algebras generalising the 3-valued and 4-valued ones he had introduced two years earlier [10]:-

Moisil invented L-M algebras in order to create an algebraic structure playing the same role with respect to multiple-valued logic as Boolean algebras play with respect to classical, bivalent logic. However, as shown by the example of A Rose[1956], this only happens for the cases n =3and n =4.

Through the 1950 Moisil applied his ideas to the theory of switching circuits. In 1959 he published the book *The algebraic theory of switching circuits* (Romanian) which and an excellent summary is given by E F Moore in a review. We quote a part of that review:-

More than fifty papers by Moisil, and many additional papers by Ioanin, Nedelcu, Mariana, and others, have developed a distinctive Rumanian approach to switching circuit theory, which remains little known and rarely referred to outside of Romania, despite the fact that most of these papers have been reviewed in Mathematical Reviews. This book gives a very detailed coverage of this approach, starting on a very elementary level, not even presupposing familiarity with the integers modulo n. ...

The most distinctive characteristic of this approach is the very strong use that is made of Galois fields. Tables for multiplication, addition, and exponentiation, for GF(3^{3})and GF(5^{2})are inserts which fold out from the book, and similar tables for GF(p)^{n}whenever p25^{n}<, are printed in the text of the book. The p(^{n}states of a circuit having n relays, each of which has p positions, are represented by the elements of GFp)^{n}. Lagrangian interpolation polynomials are used in these finite fields, to permit finding algebraic formulas for functions which take on arbitrary values at each state of the circuit. Time is usually assumed to take on only discrete values. Extensive use is also made of n-valued logic.

Among Moisil's other books we mention: *Associated matrices of systems of partial differential equations. Introduction to the study of the investigations of I N Lopatinskii* (Romanian) (1950); *Introduction to algebra. I. Rings and ideals* (Romanian) (1954); *Time sequential operation of circuits with ideal relays* (Romanian) (1960); *Essays old and new on non-classical logic* (Romanian) (1965); *Algebraic theory of schemes with contacts and relays* (Romanian) (1965); and *Actual functioning of relay switching circuits. I* (Romanian) (1965).

Moisil was also involved in the introduction of computers into Romania. In 1957 he assisted in setting up the first Romanian computer in the Institute of Atomic Physics and he encouraged mathematics students to learn computer programming, essentially setting up the first Romanian computer science course.

Eight years after his death, the Faculty of Mathematics of Bucharest University organised a conference on 10 January 1981 on the occasion of Moisil's 75^{th} birthday. The conference was dedicated to his life and work and many spoke of their appreciation for his outstanding contributions. C Andreian Cazacu delivered the opening address in which he said:-

Prof Gr C Moisil has fought with all his energy and perseverance in order to open the way to the understanding of mathematics in our country now and in the future. He has been aware of the importance of informatics, cybernetics and automata theory. He has created centres of computation.

Other speakers included P P Teodorescu who said::

Professor Moisil has cultivated with great pleasure and passion the boundary sciences and has created various schools - mechanics, automata theory, etc. He has contributed to different literary journals. He has had his column 'Science and Humanism' at the 'Contemporanul'.

Moisil was elected to the Romanian Academy of Sciences in 1948, the Academy of Sciences in Bologna and to the International Institute of Philosophy. He was honoured posthumously for his contributions to computing when the IEEE Computer Society awarded him their "Computer Pioneer" prize in 1996, twenty-three years after his death. In 2002 Viorica Moisil, Grigore Moisil's widow, published her husband's diary so giving the world a deeper look into the character of this outstanding mathematician.

**Article by:** *J J O'Connor* and *E F Robertson*