Grigore Constantin Moisil (; 10 January 1906 – 21 May 1973) was a

Romania Romania ( ; ro, România ) is a country located at the crossroads of Central Europe, Central, Eastern Europe, Eastern, and Southeast Europe, Southeastern Europe. It borders Bulgaria to the south, Ukraine to the north, Hungary to the west, S ...

mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematical problems. Mathematicians are concerned with numbers, data, quantity, structure, space, models, and change. History On ...

computer A computer is a machine that can be programmed to Execution (computing), carry out sequences of arithmetic or logical operations (computation) automatically. Modern digital electronic computers can perform generic sets of operations known as C ...

pioneer, and titular member of the Romanian Academy. His research was mainly in the fields of

mathematical logic Mathematical logic is the study of logic, formal logic within mathematics. Major subareas include model theory, proof theory, set theory, and recursion theory. Research in mathematical logic commonly addresses the mathematical properties of for ...

(

Łukasiewicz–Moisil algebra Łukasiewicz–Moisil algebras (LM''n'' algebras) were introduced in the 1940s by Grigore Moisil (initially under the name of Łukasiewicz algebras) in the hope of giving algebraic semantics for the ''n''-valued Łukasiewicz logic. However, in 195 ...

algebraic logic In mathematical logic, algebraic logic is the reasoning obtained by manipulating equations with free variables. What is now usually called classical algebraic logic focuses on the identification and algebraic description of models appropriate for ...

MV-algebra In abstract algebra, a branch of pure mathematics, an MV-algebra is an algebraic structure with a binary operation \oplus, a unary operation \neg, and the constant 0, satisfying certain axioms. MV-algebras are the algebraic semantics of Łukasie ...

, and

differential equations In mathematics, a differential equation is an equation that relates one or more unknown functions and their derivatives. In applications, the functions generally represent physical quantities, the derivatives represent their rates of change, an ...

. He is viewed as the father of

computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

in Romania. Moisil was also a member of the

Academy of Sciences of Bologna The Academy of Sciences of the Institute of Bologna (''Accademia delle Scienze dell'Istituto di Bologna'') is an academic society in Bologna, Italy, that was founded in 1690 and prospered in the Age of Enlightenment. Today it is closely associated ...

and of the International Institute of Philosophy. In 1996, the

IEEE Computer Society The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operati ...

awarded him posthumously the ''Computer Pioneer'' Award.

Biography

Grigore Moisil was born in 1906 in Tulcea into an

intellectual An intellectual is a person who engages in critical thinking, research, and reflection about the reality of society, and who proposes solutions for the normative problems of society. Coming from the world of culture, either as a creator or a ...

family. His great-grandfather, Grigore Moisil (1814–1891), a

clergyman Clergy are formal leaders within established religions. Their roles and functions vary in different religious traditions, but usually involve presiding over specific rituals and teaching their religion's doctrines and practices. Some of the ter ...

, was one of the founders of the first Romanian high school in

Năsăud Năsăud (; german: Nassod, ''Nußdorf''; hu, Naszód) is a town in Bistrița-Năsăud County in Romania located in the historical region of Transylvania. The town administers two villages, Liviu Rebreanu (until 1958 ''Prislop''; ''Priszlop'') a ...

. His father,

Constantin Moisil Constantin C. Moisil (December 8, 1876–October 22, 1958) was an Austro-Hungarian-born Romanian archivist, historian, numismatist and schoolteacher. Born in Năsăud, in the Transylvania region, his grandfather Grigore Moisil was a priest; h ...

(1876–1958), was a history professor,

archaeologist Archaeology or archeology is the scientific study of human activity through the recovery and analysis of material culture. The archaeological record consists of artifacts, architecture, biofacts or ecofacts, sites, and cultural landscap ...

and

numismatist A numismatist is a specialist in numismatics ("of coins"; from Late Latin ''numismatis'', genitive of ''numisma''). Numismatists include collectors, specialist dealers, and scholars who use coins and other currency in object-based research. Altho ...

; as a member of the

Romanian Academy The Romanian Academy ( ro, Academia Română ) is a cultural forum founded in Bucharest, Romania, in 1866. It covers the scientific, artistic and literary domains. The academy has 181 active members who are elected for life. According to its byl ...

, he filled the position of Director of the Numismatics Office of the Academy. His mother, Elena (1863–1949), was a teacher in Tulcea, later the director of "Maidanul Dulapului" school in

Bucharest Bucharest ( , ; ro, București ) is the capital and largest city of Romania, as well as its cultural, industrial, and financial centre. It is located in the southeast of the country, on the banks of the Dâmbovița River, less than north of ...

(now "

Ienăchiță Văcărescu Ienăchiță Văcărescu (; 1740 – 11 July 1797) was a Wallachian Romanian poet, historian, philologist, and boyar belonging to the Văcărescu family. A polyglot, he was able to speak Ancient and Modern Greek, Old Church Slavonic, Arabic, P ...

" school). Grigore Moisil attended

primary school A primary school (in Ireland, the United Kingdom, Australia, Trinidad and Tobago, Jamaica, and South Africa), junior school (in Australia), elementary school or grade school (in North America and the Philippines) is a school for primary e ...

in Bucharest, then high school in

Vaslui Vaslui (), a city in eastern Romania, is the seat of Vaslui County, in the historical region of Western Moldavia. The city administers five villages: Bahnari, Brodoc, Moara Grecilor, Rediu, and Viișoara. History Archaeological surveys indicate ...

and Bucharest (at "

Spiru Haret Spiru C. Haret (; 15 February 1851 – 17 December 1912) was a Romanian mathematician, astronomer, and politician. He made a fundamental contribution to the ''n''-body problem in celestial mechanics by proving that using a third degree approx ...

" High School) between 1916 and 1922. In 1924 he was admitted to the Civil Engineering School of the

Polytechnic University of Bucharest Politehnica University of Bucharest ( ro, Universitatea Politehnica din București) is a technical university in Bucharest, Romania. 200 years of activity have been celebrated lately, as the university was founded in 1818.University of Bucharest The University of Bucharest ( ro, Universitatea din București), commonly known after its abbreviation UB in Romania, is a public university founded in its current form on by a decree of Prince Alexandru Ioan Cuza to convert the former Princel ...

. He showed a stronger interest in mathematics, so he quit the Polytechnic University in 1929, despite already having passed all the third-year exams. In 1929 he defended his

Ph.D. A Doctor of Philosophy (PhD, Ph.D., or DPhil; Latin: or ') is the most common degree at the highest academic level awarded following a course of study. PhDs are awarded for programs across the whole breadth of academic fields. Because it is ...

thesis, ''La mécanique analytique des systemes continus'' (Analytical mechanics of continuous systems), before a commission led by

Gheorghe Țițeica Gheorghe Țițeica (; 4 October 1873 – 5 February 1939) publishing as George or Georges Tzitzéica) was a Romanian mathematician who made important contributions in geometry. He is recognized as the founder of the Romanian school of differentia ...

, with

Dimitrie Pompeiu Dimitrie D. Pompeiu (; – 8 October 1954) was a Romanian mathematician, professor at the University of Bucharest, titular member of the Romanian Academy, and President of the Chamber of Deputies. Biography He was born in 1873 in Broscăuți, ...

and

Anton Davidoglu Anton Davidoglu (June 30, 1876–May 27, 1958) was a Romanian mathematician who specialized in differential equations. He was born in 1876 in Bârlad, Vaslui County, the son of Profira Moțoc and Doctor Cleante Davidoglu. His older brother was G ...

as members. The thesis was published the same year by the Gauthier-Villars publishing house in

Paris Paris () is the capital and most populous city of France, with an estimated population of 2,165,423 residents in 2019 in an area of more than 105 km² (41 sq mi), making it the 30th most densely populated city in the world in 2020. S ...

, and received favourable comments from

Vito Volterra Vito Volterra (, ; 3 May 1860 – 11 October 1940) was an Italian mathematician and physicist, known for his contributions to mathematical biology and integral equations, being one of the founders of functional analysis. Biography Born in Anc ...

Tullio Levi-Civita Tullio Levi-Civita, (, ; 29 March 1873 – 29 December 1941) was an Italian mathematician, most famous for his work on absolute differential calculus (tensor calculus) and its applications to the theory of relativity, but who also made significa ...

, and Paul Lévy. In 1930 Moisil went to the

University of Paris , image_name = Coat of arms of the University of Paris.svg , image_size = 150px , caption = Coat of Arms , latin_name = Universitas magistrorum et scholarium Parisiensis , motto = ''Hic et ubique terrarum'' (Latin) , mottoeng = Here and a ...

for further study in mathematics, which he finalized the next year with the paper ''On a class of systems of equations with partial derivatives from mathematical physics''. In 1931 he returned to Romania, where he was appointed in a teaching position at the Mathematics School of the

University of Iași The Alexandru Ioan Cuza University (Romanian: ''Universitatea „Alexandru Ioan Cuza"''; acronym: UAIC) is a public university located in Iași, Romania. Founded by an 1860 decree of Prince Alexandru Ioan Cuza, under whom the former Academia Mih ...

. Shortly after, he left for a one-year

Rockefeller Foundation The Rockefeller Foundation is an American private foundation and philanthropic medical research and arts funding organization based at 420 Fifth Avenue, New York City. The second-oldest major philanthropic institution in America, after the Carneg ...

scholarship to study in

Rome , established_title = Founded , established_date = 753 BC , founder = King Romulus (legendary) , image_map = Map of comune of Rome (metropolitan city of Capital Rome, region Lazio, Italy).svg , map_caption ...

. In 1932 he returned to

Iași Iași ( , , ; also known by other alternative names), also referred to mostly historically as Jassy ( , ), is the second largest city in Romania and the seat of Iași County. Located in the historical region of Moldavia, it has traditionally ...

, where he remained for almost 10 years, developing a close relationship with professor Alexandru Myller. He taught the first

modern algebra In mathematics, more specifically algebra, abstract algebra or modern algebra is the study of algebraic structures. Algebraic structures include group (mathematics), groups, ring (mathematics), rings, field (mathematics), fields, module (mathe ...

course in Romania, named ''Logic and theory of proof'', at the University of Iași. During that time, he started writing a series of papers based on the works of

Jan Łukasiewicz Jan Łukasiewicz (; 21 December 1878 – 13 February 1956) was a Polish logician and philosopher who is best known for Polish notation and Łukasiewicz logic His work centred on philosophical logic, mathematical logic and history of logic. He ...

multi-valued logic Many-valued logic (also multi- or multiple-valued logic) refers to a propositional calculus in which there are more than two truth values. Traditionally, in Aristotle's logical calculus, there were only two possible values (i.e., "true" and "false ...

. His research in mathematical logic laid the foundation for significant work done afterwards in Romania, as well as

Argentina Argentina (), officially the Argentine Republic ( es, link=no, República Argentina), is a country in the southern half of South America. Argentina covers an area of , making it the second-largest country in South America after Brazil, th ...

Yugoslavia Yugoslavia (; sh-Latn-Cyrl, separator=" / ", Jugoslavija, Југославија ; sl, Jugoslavija ; mk, Југославија ;; rup, Iugoslavia; hu, Jugoszlávia; rue, label=Pannonian Rusyn, Югославия, translit=Juhoslavija ...

Czechoslovakia , rue, Чеськословеньско, , yi, טשעכאסלאוואקיי, , common_name = Czechoslovakia , life_span = 1918–19391945–1992 , p1 = Austria-Hungary , image_p1 ...

, and

Hungary Hungary ( hu, Magyarország ) is a landlocked country in Central Europe. Spanning of the Carpathian Basin, it is bordered by Slovakia to the north, Ukraine to the northeast, Romania to the east and southeast, Serbia to the south, Croatia a ...

. While in Iași, he completed research remarkable for the many new ideas and for his way of finding and using new connections between concepts from different areas of mathematics. He was promoted to Full Professor in November 1939. In 1941, a position of professor at the

University of Bucharest The University of Bucharest ( ro, Universitatea din București), commonly known after its abbreviation UB in Romania, is a public university founded in its current form on by a decree of Prince Alexandru Ioan Cuza to convert the former Princel ...

opened up, and Moisil applied for it. However, Gheorghe Vrânceanu, Dan Barbilian, and

Miron Nicolescu Miron Nicolescu (; August 27, 1903 – June 30, 1975) was a Romanian mathematician, best known for his work in real analysis and differential equations. He was President of the Romanian Academy and Vice-President of the International Mathematical ...

also applied for the position, and Vrânceanu got it. Moisil approached the Ministry of Education, arguing that it would be a great opportunity for mathematics in Romania if all four could be appointed. As a result of his appeal, all four mathematicians were hired. Moisil moved to

, where he became a Professor in the School of Mathematics (later the School of Mathematics and Computer Science) at the University of Bucharest, on 30 December 1941. From 1946 to 1948, Moisil took a leave of absence, being named

plenipotentiary A ''plenipotentiary'' (from the Latin ''plenus'' "full" and ''potens'' "powerful") is a diplomat who has full powers—authorization to sign a treaty or convention on behalf of his or her sovereign. When used as a noun more generally, the word ...

envoy to

Ankara Ankara ( , ; ), historically known as Ancyra and Angora, is the capital of Turkey. Located in the central part of Anatolia, the city has a population of 5.1 million in its urban center and over 5.7 million in Ankara Province, maki ...

. While in

Turkey Turkey ( tr, Türkiye ), officially the Republic of Türkiye ( tr, Türkiye Cumhuriyeti, links=no ), is a list of transcontinental countries, transcontinental country located mainly on the Anatolia, Anatolian Peninsula in Western Asia, with ...

, he gave several series of mathematics lectures at

Istanbul University , image = Istanbul_University_logo.svg , image_size = 200px , latin_name = Universitas Istanbulensis , motto = tr, Tarihten Geleceğe Bilim Köprüsü , mottoeng = Science Bridge from Past to the Future , established = 1453 1846 1933 ...

and

Istanbul Technical University Istanbul Technical University ( tr, İstanbul Teknik Üniversitesi, commonly referred to as ITU or The Technical University) is an international technical university located in Istanbul, Turkey. It is the world's third-oldest technical university ...

. In 1948, he resumed teaching at the University of Bucharest. That same year, he was elected to the Romanian Academy, and a member of the

Institute of Mathematics of the Romanian Academy The "Simion Stoilow" Institute of Mathematics of the Romanian Academy is a research institute in Bucharest, Romania. It is affiliated with the Romanian Academy, and it is named after Simion Stoilow, one of its founders. History On December 2 ...

. After 1965, one of his students, George Georgescu, worked closely with him on multi-valued logics, and after the

Romanian Revolution The Romanian Revolution ( ro, Revoluția Română), also known as the Christmas Revolution ( ro, Revoluția de Crăciun), was a period of violent civil unrest in Romania during December 1989 as a part of the Revolutions of 1989 that occurred i ...

of 1989, became a Professor of Mathematics and Logic at the same university and department as Moisil in 1991. His student also published extensive, original work on

algebra Algebra () is one of the broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathematics. Elementary a ...

algebraic topology Algebraic topology is a branch of mathematics that uses tools from abstract algebra to study topological spaces. The basic goal is to find algebraic invariant (mathematics), invariants that classification theorem, classify topological spaces up t ...

, categories of

category theory Category theory is a general theory of mathematical structures and their relations that was introduced by Samuel Eilenberg and Saunders Mac Lane in the middle of the 20th century in their foundational work on algebraic topology. Nowadays, cate ...

and

Work

Moisil published papers on

mechanics Mechanics (from Ancient Greek: μηχανική, ''mēkhanikḗ'', "of machines") is the area of mathematics and physics concerned with the relationships between force, matter, and motion among physical objects. Forces applied to objects r ...

mathematical analysis Analysis is the branch of mathematics dealing with continuous functions, limit (mathematics), limits, and related theories, such as Derivative, differentiation, Integral, integration, measure (mathematics), measure, infinite sequences, series (m ...

geometry Geometry (; ) is, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

and

. He developed a multi-dimensional extension of Pompeiu's

areolar derivative Loose connective tissue, sometimes called areolar tissue, is a cellular connective tissue with thin and relatively sparse collagen fibers. Its ground substance occupies more volume than the fibers do. It has a viscous to gel-like consistenc ...

, and studied

monogenic function A monogenic function is a complex function with a single finite derivative. More precisely, a function f(z) defined on A \subseteq \mathbb is called monogenic at \zeta \in A , if f'(\zeta) exists and is finite, with: f'(\zeta) = \lim_\frac ...

s of one hypercomplex variable with applications to mechanics. Moisil also introduced some many-valued algebras, which he called Łukasiewicz algebras (now also named Łukasiewicz–Moisil algebras), and used them in logic and the study of

automata theory Automata theory is the study of abstract machines and automata, as well as the computational problems that can be solved using them. It is a theory in theoretical computer science. The word ''automata'' comes from the Greek word αὐτόματο� ...

. He created new methods to analyze

finite automata A finite-state machine (FSM) or finite-state automaton (FSA, plural: ''automata''), finite automaton, or simply a state machine, is a mathematical model of computation. It is an abstract machine that can be in exactly one of a finite number o ...

, and had many contributions to the field of automata theory in algebra. Whereas Moisil's early contributions were in mathematics, he later devoted his scientific activity to

and

. He was a professor of mathematical logic and computer science at the

, and he also taught

Boolean logic In mathematics and mathematical logic, Boolean algebra is a branch of algebra. It differs from elementary algebra in two ways. First, the values of the variable (mathematics), variables are the truth values ''true'' and ''false'', usually denote ...

at the

Politehnica University of Bucharest Politehnica University of Bucharest ( ro, Universitatea Politehnica din București) is a technical university in Bucharest, Romania. 200 years of activity have been celebrated lately, as the university was founded in 1818.computer science Computer science is the study of computation, automation, and information. Computer science spans theoretical disciplines (such as algorithms, theory of computation, information theory, and automation) to Applied science, practical discipli ...

in Romania, and in raising the first generations of Romanian computer scientists. Furthermore, several of Moisil’s books had an impact on the beginning of computer science: ''Încercări Vechi și Noi în Logica Neoclasică'' ew and Old Approaches in Neoclassic Logic 1953; ''Teoria Algebrică a Mecanismelor Automate'' lgebraic Theory of Automata 1959; and ''Circuite cu Tranzistori'' ransistorized Circuits 1961. These books were translated into several languages, including

Russian Russian(s) refers to anything related to Russia, including: *Russians (, ''russkiye''), an ethnic group of the East Slavic peoples, primarily living in Russia and neighboring countries *Rossiyane (), Russian language term for all citizens and peo ...

and

Czech Czech may refer to: * Anything from or related to the Czech Republic, a country in Europe ** Czech language ** Czechs, the people of the area ** Czech culture ** Czech cuisine * One of three mythical brothers, Lech, Czech, and Rus' Places * Czech, ...

. He furthermore gave lectures at various universities in Europe and North America. Moisil was a titular member of the

and a member of the Academy of Bologna. In 1996, he was awarded by exception posthumously the

Computer Pioneer Award The Computer Pioneer Award was established in 1981 by the Board of Governors of the IEEE Computer Society to recognize and honor the vision of those people whose efforts resulted in the creation and continued vitality of the computer industry. T ...

by the

Institute of Electrical and Electronics Engineers The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operation ...

Computer Society The Institute of Electrical and Electronics Engineers (IEEE) is a 501(c)(3) professional association for electronic engineering and electrical engineering (and associated disciplines) with its corporate office in New York City and its operation ...

Notes

Selected publications

* ''Logique modale'', Disquisit. Math. Phys. 2 (1942), 3–98. * ''Introducere in algebră. I. Inele și ideale'' ntroduction to algebra. I. Rings and ideals Editura Academiei Republicii Popular Române, Bucharest, 1954. * ''Teoria algebrică a mecanismelor automate'' lgebraic theory of automatic machines Academia Republicii Popular Romîne, Editura Tehnică, Bucharest, 1959. * ''Circuite cu tranzistori'' ransistor Circuits Editura Academiei Republicii Popular Romîne, Bucharest, 1961–62. * ''Théorie structurelle des automates finis'', Gauthier-Villars, Paris, 1967. * ''The algebraic theory of switching circuits'',

Pergamon Press Pergamon Press was an Oxford-based publishing house, founded by Paul Rosbaud and Robert Maxwell, that published scientific and medical books and journals. Originally called Butterworth-Springer, it is now an imprint of Elsevier. History The cor ...

, Oxford, New York, 1969.

Books and articles on Moisil

* George Georgescu, Afrodita Iorgulescu, Sergiu Rudeanu
"Grigore C. Moisil (1906–1973) and his School in Algebraic Logic"
International Journal of Computers, Communications & Control, vol. 1 (2006), no.1, 81–99. *

Solomon Marcus Solomon Marcus (; 1 March 1925 – 17 March 2016) was a Romanian mathematician, member of the Mathematical Section of the Romanian Academy (full member from 2001) and emeritus professor of the University of Bucharest's Faculty of Mathematics. H ...

"Grigore C. Moisil: A life becoming a myth"International Journal of Computers, Communications & Control
vol. 1 (2006), no. 1, 73–79. * Viorica Moisil, "Once upon a time... Grigore Moisil" (''A fost odată... Grigore Moisil''), Bucharest: Curtea Veche, 2002. * Sergiu Rudeanu, Afrodita Iorgulescu, George Georgescu and Cătălin Ioniţă, "G. C. Moisil memorial issue", ''Multiple-Valued Logic'' 6 (2001), no. 1-2.

Gordon and Breach Taylor & Francis Group is an international company originating in England that publishes books and academic journals. Its parts include Taylor & Francis, Routledge, F1000 Research or Dovepress. It is a division of Informa plc, a United Kin ...

, Yverdon, 2001.

External links