Anders Lindstedt (27 June 1854 – 16 May 1939) was a Swedish

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 ...

, astronomer, and actuarial scientist, known for the Lindstedt-Poincaré method.

Life and work

Lindstedt was born in a small village in the district of Sundborns, Dalecarlia a province in central Sweden.
Hvar 8 dag, 10:de Årg, No 11, 13 december 1908, sid. 162
'.Memoir Anders Lindstedt 27 June 1854-16 May 1939, Journal of the Institute of Actuaries, 70 (1939) p. 269

/ref> He obtained a PhD from the

University of Lund Lund University () is a public research university in Sweden and one of Northern Europe's oldest universities. The university is located in the city of Lund in the Swedish province of Scania. The university was officially founded in 1666 on the ...

aged 32 and was subsequently appointed as a lecturer in astronomy. He later went on to a position at the University of Dorpat (then belonging to Russia, now

University of Tartu The University of Tartu (UT; ; ) is a public research university located in the city of Tartu, Estonia. It is the national university of Estonia. It is also the largest and oldest university in the country.

in Estonia) where he worked for around seven years on theoretical astronomy. He combined practical astronomy with an interest in theory, developing especially an interest in the

three-body problem In physics, specifically classical mechanics, the three-body problem is to take the initial positions and velocities (or momenta) of three point masses orbiting each other in space and then calculate their subsequent trajectories using Newton' ...

This work was to influence Poincaré whose work on the three-body problem led to the discovery that there can be orbits which are nonperiodic, and yet not forever increasing nor approaching a fixed point, the beginning of what we now know as '

chaos theory Chaos theory is an interdisciplinary area of Scientific method, scientific study and branch of mathematics. It focuses on underlying patterns and Deterministic system, deterministic Scientific law, laws of dynamical systems that are highly sens ...

'. His papers on

celestial mechanics Celestial mechanics is the branch of astronomy that deals with the motions of objects in outer space. Historically, celestial mechanics applies principles of physics (classical mechanics) to astronomical objects, such as stars and planets, to ...

written during that period include a technique for uniformly approximating periodic solutions to

ordinary differential equations In mathematics, an ordinary differential equation (ODE) is a differential equation (DE) dependent on only a single independent variable. As with any other DE, its unknown(s) consists of one (or more) function(s) and involves the derivatives ...

when regular perturbation approaches fail. This was later developed by

Henri Poincaré Jules Henri Poincaré (, ; ; 29 April 185417 July 1912) was a French mathematician, Theoretical physics, theoretical physicist, engineer, and philosophy of science, philosopher of science. He is often described as a polymath, and in mathemati ...

and is known today as the Lindstedt–Poincaré method. Lindstedt returned to Sweden in 1886 to take a post as professor at the

Royal Institute of Technology KTH Royal Institute of Technology (), abbreviated KTH, is a public research university in Stockholm, Sweden. KTH conducts research and education in engineering and technology and is Sweden's largest technical university. Since 2018, KTH consist ...

Stockholm Stockholm (; ) is the Capital city, capital and List of urban areas in Sweden by population, most populous city of Sweden, as well as the List of urban areas in the Nordic countries, largest urban area in the Nordic countries. Approximately ...

, where he was rector from 1903 to 1909. During his time at the institute, until 1909, he developed an interest in

actuarial science Actuarial science is the discipline that applies mathematics, mathematical and statistics, statistical methods to Risk assessment, assess risk in insurance, pension, finance, investment and other industries and professions. Actuary, Actuaries a ...

. He made contributions to the theory of

pension funds A pension fund, also known as a superannuation fund in some countries, is any program, fund, or scheme which provides retirement income. The U.S. Government's Social Security Trust Fund, which oversees $2.57 trillion in assets, is the world' ...

and worked as a member of government committees responsible for

insurance law Insurance law is the practice of law surrounding insurance, including insurance policies and claims. It can be broadly broken into three categories - regulation of the business of insurance; regulation of the content of insurance policies, especia ...

and

social insurance Social insurance is a form of Social protection, social welfare that provides insurance against economic risks. The insurance may be provided publicly or through the subsidizing of private insurance. In contrast to other forms of Welfare spend ...

. He became a corresponding member of the

Institute of Actuaries The Institute of Actuaries was one of the two professional bodies which represented actuaries in the United Kingdom. The institute was based in England, while the other body, the Faculty of Actuaries, was based in Scotland. While the Institute a ...

in London. He was for a time Kings Inspector of insurance companies. In 1909 he resigned his professorial position to work full-time on

insurance Insurance is a means of protection from financial loss in which, in exchange for a fee, a party agrees to compensate another party in the event of a certain loss, damage, or injury. It is a form of risk management, primarily used to protect ...

. From 1909 to 1916 Lindstedt was also a Justice of the

Supreme Administrative Court of Sweden The Supreme Administrative Court of Sweden (, before 2011 ''Regeringsrätten'', acronym ''RR'' or ''RegR'') is the supreme court and the third and final tier for administrative court cases in Sweden, and is located in Stockholm. It has a parall ...

. In 1912 Lindstedt constructed a

life table In actuarial science and demography, a life table (also called a mortality table or actuarial table) is a table which shows, for each age, the probability that a person of that age will die before their next birthday ("probability of death"). In ...

for

annuities In investment, an annuity is a series of payments made at equal intervals based on a contract with a lump sum of money. Insurance companies are common annuity providers and are used by clients for things like retirement or death benefits. Examples ...

using data from Swedish population experience and for each age was able to extrapolate the sequence of annual

probability Probability is a branch of mathematics and statistics concerning events and numerical descriptions of how likely they are to occur. The probability of an event is a number between 0 and 1; the larger the probability, the more likely an e ...

of death, namely the mortality profile. Probably, this work constitutes the earliest projection of age-specific functions.Pitcco, Ermnno, From Halley to Frailty: A Review of Survival Models for Actuarial Calculations

/ref> He directed the actuarial work which underpinned the state old age an invalidity pensions in Sweden introduced in 1913 as part of the ''National Pension Act'' (see Swedish welfare#History, Swedish welfare). Even after his retirement aged 70 he continued to take an active interest in actuarial activities both in Sweden and abroad, attending meetings of the Swedish Actuarial Society until shortly before his death in 1939.

Notes

{{DEFAULTSORT:Lindstedt, Anders 1854 births 1939 deaths 19th-century Swedish astronomers 19th-century Swedish mathematicians Academic staff of the KTH Royal Institute of Technology Rectors of KTH Royal Institute of Technology Lund University alumni Swedish actuaries Justices of the Supreme Administrative Court of Sweden 20th-century Swedish mathematicians 20th-century Swedish judges