Thorvald Nicolai Thiele

Thorvald Nicolai Thiele around 1860

Thorvald Nicolai Thiele (born December 24, 1838 in Copenhagen ; † September 26, 1910 there ) was an important Danish mathematician and astronomer and is now considered one of the founders of modern actuarial mathematics . Throughout his life he frequented the Danish royal court and founded both the mathematical society and the actuaries' association of his country.

Life

Thiele was born on Christmas Eve 1838 as the son of Just Mathias Thiele , the royal librarian and head of the royal printing house. It was named after his godfather, the sculptor Bertel Thorvaldsen , a friend of the family.

After his school education he began studying astronomy at the University of Copenhagen , which he graduated in 1860 at the age of 21. After six more years, he obtained a doctorate with his dissertation on the movement of double stars and married Marie Martine Trolle the following year, with whom he had six children. In 1878 he was appointed director of the university observatory , which he directed until his retirement in 1907. In 1900 he was the rector of the university.

In addition to his teaching and research activities, Thiele always worked as an actuary for an insurance company and was ultimately co-founder of the Hafnia Insurance (now part of the Danish Codan insurance), for which he worked as the responsible actuary until his death. He was also a founding member of the Danish Mathematical Society (1873) and the first Danish chess club (1865).

plant

The focus of his research activities were the three-body problem in astronomy, in whose research he was significantly involved, as well as the statistics of time series . In his 1880 published work Om Anvendelse mindste Kvadraters af method i nogle tilfaelde, hvor en complication af visse Slags uensartede tilfældige Fejlkilder giver Fejlene en 'systematisk' Karakter ( On the application of the least squares method in cases where certain varieties of random errors giving the errors a "systematic" character ) he anticipated many statistical phenomena ( moving average , correlated errors, cumulants ), which were only systematically examined again much later. Today this work is also considered to be the first mathematical work in which a Brownian movement occurs - 25 years before it was statistically investigated by Albert Einstein .

One of Thiele's best-known contributions to actuarial mathematics is the differential equation attributed to him today , which describes the course of the premium reserve over time:

${\displaystyle {\frac {dV_{t}}{dt}}=\pi +\delta V_{t}-m_{t}(1-V_{t})}$,

where is the reserve, the death rate and the contribution amount. Thiele himself did not publish this result, but through his colleague Jørgen Pedersen Gram the formula was made public and is still one of the most important tools in life insurance mathematics today. ${\displaystyle V_{t}}$ ${\displaystyle m_{t}}$ ${\displaystyle \pi }$

Number theory: Thieles parquet

Quadratic remainders modulo 12 + 13i (Gaussian prime number). The zero and associated whole Gaussian numbers are marked in blue

Thiele also dealt professionally with number theory : He examined square residues in the rings of Gaussian integers and Eisenstein integers . In his work Om Talmønstre (On Number Patterns) published in 1894 , he discovered that the square residues in quotient rings of the above rings give symmetrical patterns on the Gaussian plane of numbers . A contemporary witness reports that the tiled stove in Thiele's private house was tiled according to such a pattern, and the entrance hall at the headquarters of the Hafnia insurance company also received a tile pattern made from square remains. However, it was not until 2002 that the mathematics professor Steffen Lauritzen from Aalborg and a group of students succeeded in deciphering the parquet: These are square remains modulo 71, the age of Thiele in 1910 when the building was opened. ${\displaystyle \mathbb {Z} +i\mathbb {Z} \subset \mathbb {C} }$ ${\displaystyle \mathbb {Z} +i\omega \mathbb {Z} \subset \mathbb {C} ,\;\omega ={\frac {1-{\sqrt {-3}}}{2}}}$

Thiele's legacy

In honor of his former lecturer, the University of Copenhagen is holding the TN Thiele Symposium , an international series of lectures on actuarial topics, and the University of Aarhus set up an applied mathematics research center in 2004 called the Thiele Center . The asteroid (1586) Thiele is named after him.

Web links

• Thiele Center of Aarhus University
• Paper about Thiele's tiling (Danish, pdf) (360 kB)
• Publications by TN Thiele in the Astrophysics Data System
• C. Burrau: Notification of the death of Thorvald Nicolai Thiele. Astronomische Nachrichten, Vol. 186 (1910), p. 63

Individual evidence

1. ^ Dictionary of Minor Planet Names, Volume 1 in the Google Book Search