Emanuels Donats Frīdrihs Jānis Grinbergs (1911–1982, westernized as Emanuel Grinberg) was a

Latvia Latvia, officially the Republic of Latvia, is a country in the Baltic region of Northern Europe. It is one of the three Baltic states, along with Estonia to the north and Lithuania to the south. It borders Russia to the east and Belarus to t ...

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, mathematical structure, structure, space, Mathematica ...

, known for

Grinberg's theorem In graph theory, Grinberg's theorem is a necessary condition for a planar graph to contain a Hamiltonian cycle, based on the lengths of its face cycles. If a graph does not meet this condition, it is not Hamiltonian. The result has been widely use ...

on the Hamiltonicity of

planar graph In graph theory, a planar graph is a graph (discrete mathematics), graph that can be graph embedding, embedded in the plane (geometry), plane, i.e., it can be drawn on the plane in such a way that its edges intersect only at their endpoints. ...

s....

Biography

Grinbergs was born on January 25, 1911, in

St. Petersburg Saint Petersburg, formerly known as Petrograd and later Leningrad, is the second-largest city in Russia after Moscow. It is situated on the River Neva, at the head of the Gulf of Finland on the Baltic Sea. The city had a population of 5,601, ...

, the son of a

Lutheran Lutheranism is a major branch of Protestantism that emerged under the work of Martin Luther, the 16th-century German friar and Protestant Reformers, reformer whose efforts to reform the theology and practices of the Catholic Church launched ...

bishop from Latvia. Latvia became independent from Russia in 1917, and on the death of his father in 1923, Grinbergs' family returned to

Riga Riga ( ) is the capital, Primate city, primate, and List of cities and towns in Latvia, largest city of Latvia. Home to 591,882 inhabitants (as of 2025), the city accounts for a third of Latvia's total population. The population of Riga Planni ...

, taking Grinbergs with them. In 1927, he won a high school mathematics competition, the prize for which was to study in

Lille Lille (, ; ; ; ; ) is a city in the northern part of France, within French Flanders. Positioned along the Deûle river, near France's border with Belgium, it is the capital of the Hauts-de-France Regions of France, region, the Prefectures in F ...

France France, officially the French Republic, is a country located primarily in Western Europe. Overseas France, Its overseas regions and territories include French Guiana in South America, Saint Pierre and Miquelon in the Atlantic Ocean#North Atlan ...

. He then studied mathematics at the

University of Latvia University of Latvia (, shortened ''LU'') is a public research university located in Riga, Latvia. The university was established in 1919. History The University of Latvia, initially named as the Higher School of Latvia () was founded on Se ...

beginning in 1930. On graduating in 1934, he won a prize that again funded study in France; he did graduate studies in 1935 and 1936 at the

École Normale Supérieure École or Ecole may refer to: * an elementary school in the French educational stages normally followed by Secondary education in France, secondary education establishments (collège and lycée) * École (river), a tributary of the Seine flowing i ...

Paris Paris () is the Capital city, capital and List of communes in France with over 20,000 inhabitants, largest city of France. With an estimated population of 2,048,472 residents in January 2025 in an area of more than , Paris is the List of ci ...

, during which he published his first paper, in geometry. He returned to the University of Latvia as a ''

privatdozent ''Privatdozent'' (for men) or ''Privatdozentin'' (for women), abbreviated PD, P.D. or Priv.-Doz., is an academic title conferred at some European universities, especially in German-speaking countries, to someone who holds certain formal qualifi ...

'' in 1937, and joined the faculty as a

dozent The term "docent" is derived from the Latin word , which is the third-person plural present active indicative of ('to teach, to lecture'). Becoming a docent is often referred to as habilitation or doctor of science and is an academic qualifica ...

in 1940. His lectures at that time covered subjects including

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

probability theory Probability theory or probability calculus is the branch of mathematics concerned with probability. Although there are several different probability interpretations, probability theory treats the concept in a rigorous mathematical manner by expre ...

, and

group theory In abstract algebra, group theory studies the algebraic structures known as group (mathematics), groups. The concept of a group is central to abstract algebra: other well-known algebraic structures, such as ring (mathematics), rings, field ( ...

. While there, he defended a thesis in geometry at the University of Latvia in 1943, entitled ''On Oscillations, Superoscillations and Characteristic Points''. In the meantime, the

Soviet Union The Union of Soviet Socialist Republics. (USSR), commonly known as the Soviet Union, was a List of former transcontinental countries#Since 1700, transcontinental country that spanned much of Eurasia from 1922 until Dissolution of the Soviet ...

had annexed Latvia in 1940, and the army of

Nazi Germany Nazi Germany, officially known as the German Reich and later the Greater German Reich, was the German Reich, German state between 1933 and 1945, when Adolf Hitler and the Nazi Party controlled the country, transforming it into a Totalit ...

had occupied it and incorporated it into the

Reichskommissariat Ostland The (RKO; ) was an Administrative division, administrative entity of the Reich Ministry for the Occupied Eastern Territories of Nazi Germany from 1941 to 1945. It served as the German Civil authority, civilian occupation regime in Lithuania, La ...

. Grinbergs was drafted into the

Latvian Legion The Latvian Legion () was a formation of the Nazi German Waffen-SS during World War II. Created in 1943, it consisted primarily of ethnic Latvians.Gerhard P. Bassler, ''Alfred Valdmanis and the politics of survival'', 2000, p150 Mirdza Kate Balta ...

, part of the German military, in 1944. After the war, because of his service as a German soldier, he was held prisoner in a camp in

Kutaisi Kutaisi ( ; ka, ქუთაისი ) is a city in the Imereti region of the Georgia (country), Republic of Georgia. One of the List of oldest continuously inhabited cities, oldest continuously inhabited cities in the world, it is the List o ...

Georgia Georgia most commonly refers to: * Georgia (country), a country in the South Caucasus * Georgia (U.S. state), a state in the southeastern United States Georgia may also refer to: People and fictional characters * Georgia (name), a list of pe ...

, until 1946; he lost his university position, and his doctorate (awarded during the German occupation) was annulled. Grinbergs returned to Latvia, where he became a factory worker in the Radiotehnika radio factory, while continuing to be interrogated regularly by the KGB. He developed mathematical models of electrical circuits, which he wrote up as a second thesis, ''Problems of analysis and synthesis of simple linear circuits'', his defense of which earned him a

candidate A candidate, or nominee, is a prospective recipient of an award or honor, or a person seeking or being considered for some kind of position. For example, one can be a candidate for membership in a group (sociology), group or election to an offic ...

degree. In 1954, Grinbergs was allowed to return to the University of Latvia faculty. In 1956, he joined the Institute of Physics of the

Latvian Academy of Sciences The Latvian Academy of Sciences (, ) is the official science academy of Latvia and is an association of the country's foremost scientists. The academy was founded as the ''Latvian SSR Academy of Sciences'' (). It is located in Riga. The curren ...

, and in 1960, he began working at the Computer Center of the University of Latvia, where he remained for the rest of his career, eventually becoming Chief Scientist there.

Research

Grinbergs' initial research interests were in geometry, and later shifted to graph theory. With professors Arins and Daube at the University of Latvia, Grinbergs was one of the first to work in applied mathematics and computer science in Latvia. Grinbergs and his collaborators wrote many papers on the design of electrical circuits and

electronic filter Electronic filters are a type of signal processing filter in the form of electrical circuits. This article covers those filters consisting of lumped-element model, lumped electronic components, as opposed to distributed-element filters. That ...

s, stemming from his radio work. He earned the State Prize of the Latvian SSR in 1980 for his research on nonlinear electronic circuit theory. Another early line of research by Grinbergs at the Computer Center concerned the automated design of ship hulls, and the computations with

spline curve In mathematics, a spline is a Function (mathematics), function defined piecewise by polynomials. In interpolation, interpolating problems, spline interpolation is often preferred to polynomial interpolation because it yields similar results, eve ...

s and surfaces needed in this design. The goal of this research was to calculate patterns for cutting and then bending flat steel plates so that they could be welded together to form ship hulls without the need for additional machining after the bending step; the methods developed by Grinbergs were later used throughout the Soviet Union. In graph theory, Grinbergs is best known for

, a necessary condition for a

to have a

Hamiltonian cycle In the mathematics, mathematical field of graph theory, a Hamiltonian path (or traceable path) is a path (graph theory), path in an undirected or directed graph that visits each vertex (graph theory), vertex exactly once. A Hamiltonian cycle (or ...

that has been frequently used to find non-Hamiltonian planar graphs with other special properties.. His researches in graph theory also concerned

graph coloring In graph theory, graph coloring is a methodic assignment of labels traditionally called "colors" to elements of a Graph (discrete mathematics), graph. The assignment is subject to certain constraints, such as that no two adjacent elements have th ...

graph isomorphism In graph theory, an isomorphism of graphs ''G'' and ''H'' is a bijection between the vertex sets of ''G'' and ''H'' : f \colon V(G) \to V(H) such that any two vertices ''u'' and ''v'' of ''G'' are adjacent in ''G'' if and only if f(u) and f(v) a ...

, cycles in directed graphs, and a counterexample to a conjecture of András Ádám on the number of cycles in

tournaments A tournament is a competition involving at least three competitors, all participating in a sport or game. More specifically, the term may be used in either of two overlapping senses: # One or more competitions held at a single venue and concentr ...

. Other topics in Grinbergs' research include

Steiner triple system 250px, thumbnail, The Fano plane is a Steiner triple system S(2,3,7). The blocks are the 7 lines, each containing 3 points. Every pair of points belongs to a unique line. In combinatorial mathematics, a Steiner system (named after Jakob Steiner) ...

magnetohydrodynamics In physics and engineering, magnetohydrodynamics (MHD; also called magneto-fluid dynamics or hydromagnetics) is a model of electrically conducting fluids that treats all interpenetrating particle species together as a single Continuum ...

operations research Operations research () (U.S. Air Force Specialty Code: Operations Analysis), often shortened to the initialism OR, is a branch of applied mathematics that deals with the development and application of analytical methods to improve management and ...

, and the mathematical modeling of

hydrocarbon exploration Hydrocarbon exploration (or oil and gas exploration) is the search by petroleum geologists and geophysicists for hydrocarbon deposits, particularly petroleum and natural gas, in the Earth's crust using petroleum geology. Exploration methods ...

References

{{DEFAULTSORT:Grinbergs, Emanuels 1911 births 1982 deaths University of Latvia alumni Academic staff of the University of Latvia Graph theorists Latvian Waffen-SS personnel 20th-century Latvian mathematicians Soviet mathematicians