Ivo Lah
Encyclopedia
Slovenia
Slovenia , officially the Republic of Slovenia , is a country in Central and Southeastern Europe touching the Alps and bordering the Mediterranean. Slovenia borders Italy to the west, Croatia to the south and east, Hungary to the northeast, and Austria to the north, and also has a small portion of...
n mathematician
Mathematician
A mathematician is a person whose primary area of study is the field of mathematics. Mathematicians are concerned with quantity, structure, space, and change....
and actuary
Actuary
An actuary is a business professional who deals with the financial impact of risk and uncertainty. Actuaries provide expert assessments of financial security systems, with a focus on their complexity, their mathematics, and their mechanisms ....
, best known for his discovery of the Lah number
Lah number
In mathematics, Lah numbers, discovered by Ivo Lah in 1955, are coefficients expressing rising factorials in terms of falling factorials.Unsigned Lah numbers have an interesting meaning in combinatorics: they count the number of ways a set of n elements can be partitioned into k nonempty linearly...
s in 1955.
Lah attended elementary school in St. Vid nad Cerknico and in Ljubljana
Ljubljana
Ljubljana is the capital of Slovenia and its largest city. It is the centre of the City Municipality of Ljubljana. It is located in the centre of the country in the Ljubljana Basin, and is a mid-sized city of some 270,000 inhabitants...
. Later he enrolled in the Klasicna gymnasium in Ljubljana where he graduated top of the class in 1915. He spent 1918 at the University of Vienna
University of Vienna
The University of Vienna is a public university located in Vienna, Austria. It was founded by Duke Rudolph IV in 1365 and is the oldest university in the German-speaking world...
and seven semesters at the University of Zagreb
University of Zagreb
The University of Zagreb is the biggest Croatian university and the oldest continuously operating university in the area covering Central Europe south of Vienna and all of Southeastern Europe...
in the period 1919-1922. He completed his studies of mathematics and physics in Zagreb on April 28, 1925. At the same time he was studying at the School of Commerce and Traffic in Zagreb
Zagreb
Zagreb is the capital and the largest city of the Republic of Croatia. It is in the northwest of the country, along the Sava river, at the southern slopes of the Medvednica mountain. Zagreb lies at an elevation of approximately above sea level. According to the last official census, Zagreb's city...
with a state exam on March 3, 1923. Before finishing high school Ivo Lah volunteered for the Austro-Hungarian army
Austro-Hungarian Army
The Austro-Hungarian Army was the ground force of the Austro-Hungarian Dual Monarchy from 1867 to 1918. It was composed of three parts: the joint army , the Austrian Landwehr , and the Hungarian Honvédség .In the wake of fighting between the...
to defend the western borders of Slovenia. In the years 1915-1918 he was a Lieutenant in the Austria
Austria
Austria , officially the Republic of Austria , is a landlocked country of roughly 8.4 million people in Central Europe. It is bordered by the Czech Republic and Germany to the north, Slovakia and Hungary to the east, Slovenia and Italy to the south, and Switzerland and Liechtenstein to the...
n army on the front against Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
.
After World War I
World War I
World War I , which was predominantly called the World War or the Great War from its occurrence until 1939, and the First World War or World War I thereafter, was a major war centred in Europe that began on 28 July 1914 and lasted until 11 November 1918...
he served as a volunteer in the Koroska Legion defending and shaping the Yugoslavian border with Austria. From April to June 1921 he was an Assistant for Mathematics at the Forestry Faculty of the University of Zagreb. From then until 1950 he was employed at the Social Security Foundation in Ljubljana, Zagreb and Belgrade
Belgrade
Belgrade is the capital and largest city of Serbia. It is located at the confluence of the Sava and Danube rivers, where the Pannonian Plain meets the Balkans. According to official results of Census 2011, the city has a population of 1,639,121. It is one of the 15 largest cities in Europe...
, after which he was worked at the Yugoslavian Federal Statistical Office in Belgrade until his retirement on December 31, 1956.
The Adriatic Insurance Company (Riunione Adriatica di Sicurita) based in Trieste
Trieste
Trieste is a city and seaport in northeastern Italy. It is situated towards the end of a narrow strip of land lying between the Adriatic Sea and Italy's border with Slovenia, which lies almost immediately south and east of the city...
sent him to Vienna
Vienna
Vienna is the capital and largest city of the Republic of Austria and one of the nine states of Austria. Vienna is Austria's primary city, with a population of about 1.723 million , and is by far the largest city in Austria, as well as its cultural, economic, and political centre...
in the years 1927-1928 to study personal insurance. As a representative of the Society of Actuaries of the Kingdom of Yugoslavia he attended the International Congress of Actuaries
International Congress of Actuaries
The International Congress of Actuaries is a conference held under the auspices of the International Actuarial Association every four years...
in Rome
Rome
Rome is the capital of Italy and the country's largest and most populated city and comune, with over 2.7 million residents in . The city is located in the central-western portion of the Italian Peninsula, on the Tiber River within the Lazio region of Italy.Rome's history spans two and a half...
(1934) and in Paris
Paris
Paris is the capital and largest city in France, situated on the river Seine, in northern France, at the heart of the Île-de-France region...
(1937).
In 1943 he was invited to Rome as an Assistant Dean of the Faculty of Statistical, Demographic and Actuarial Sciences where he stayed only a month due to World War II
World War II
World War II, or the Second World War , was a global conflict lasting from 1939 to 1945, involving most of the world's nations—including all of the great powers—eventually forming two opposing military alliances: the Allies and the Axis...
. From 1933 until 1941 he was an active member of the Society of Actuaries of Yugoslavia. In the years 1937-1941 he was the founding editor of the Journal Glasnik udruzenja aktuarjev Kraljevine Jugoslavije. Due to his scientific publications Ivo Lah became a correspondent of member of several international institutions from Portugal
Portugal
Portugal , officially the Portuguese Republic is a country situated in southwestern Europe on the Iberian Peninsula. Portugal is the westernmost country of Europe, and is bordered by the Atlantic Ocean to the West and South and by Spain to the North and East. The Atlantic archipelagos of the...
, Switzerland
Switzerland
Switzerland name of one of the Swiss cantons. ; ; ; or ), in its full name the Swiss Confederation , is a federal republic consisting of 26 cantons, with Bern as the seat of the federal authorities. The country is situated in Western Europe,Or Central Europe depending on the definition....
, Belgium
Belgium
Belgium , officially the Kingdom of Belgium, is a federal state in Western Europe. It is a founding member of the European Union and hosts the EU's headquarters, and those of several other major international organisations such as NATO.Belgium is also a member of, or affiliated to, many...
, Italy
Italy
Italy , officially the Italian Republic languages]] under the European Charter for Regional or Minority Languages. In each of these, Italy's official name is as follows:;;;;;;;;), is a unitary parliamentary republic in South-Central Europe. To the north it borders France, Switzerland, Austria and...
, Germany
Germany
Germany , officially the Federal Republic of Germany , is a federal parliamentary republic in Europe. The country consists of 16 states while the capital and largest city is Berlin. Germany covers an area of 357,021 km2 and has a largely temperate seasonal climate...
and France
France
The French Republic , The French Republic , The French Republic , (commonly known as France , is a unitary semi-presidential republic in Western Europe with several overseas territories and islands located on other continents and in the Indian, Pacific, and Atlantic oceans. Metropolitan France...
.
Since 1932 when Ivo Lah became in charge of Statistics of Social Security in Slovenia he connected his work with studies at the University of Ljubljana. Students were able to prepare Seminars and other projects in Statistics. Based on the Statistics of Social Security several Doctoral Theses were written. Ivo Lah worked in practical Demographics and Statistics. Based on demographic tables he was able to prepare the so-called "computational bases" for personal life insurance and retirement insurance of employees.
His main work is a trilingual book Racunske osnovice zivotnog osiguranja written in Croatian, Russian and French and published in Zagreb in 1947. Because of a quote in Latin: Natura non facit saltus (Nature does not make leaps) the book was proclaimed "antimarxist", taken out of circulation and later, in 1951, was mostly destroyed. Ivo Lah was able to save some copies of the book. It is a tragic irony that he was later serving as a member of the Yugoslav delegation negotiating treaties with Italy, Hungary, Austria and West and East Germany. Racunske osnovice withstood the criticism of actuaries during the negotiations in Rome, Bonn and Vienna and he was able to get full Social Security compensation for Yugoslavia from these countries. Ivo Lah was a prolific writer and he published several hundred newspaper articles.
His scientific bibliography contains about 120 items covering a wide spectrum of topics from Mathematics to Statistics, Demographics, etc. For instance one can find 10 items in Maths Reviews, and 19 items in Zentralblatt für Mathematik. His most important mathematical result, published in 1955, is the so-called "Lah identity" where he shows how the rising powers can be expressed in terms of falling powers. The reviewer of his paper was a leading combinatorialist of that time, John Riordan
John Riordan
John Riordan was an American mathematician and the author of major early works in combinatorics, particularly Introduction to Combinatorial Analysis and Combinatorial Identities.- Life :...
.