Friedrich Robert Helmert (31 July 1843 – 15 June 1917) was a German geodesist and

statistician A statistician is a person who works with Theory, theoretical or applied statistics. The profession exists in both the private sector, private and public sectors. It is common to combine statistical knowledge with expertise in other subjects, a ...

with important contributions to the

theory of errors In statistics, propagation of uncertainty (or propagation of error) is the effect of variables' uncertainties (or errors, more specifically random errors) on the uncertainty of a function based on them. When the variables are the values of ex ...

Career

Helmert was born in

Freiberg Freiberg () is a university and former mining town in Saxony, Germany, with around 41,000 inhabitants. The city lies in the foreland of the Ore Mountains, in the Saxon urbanization axis, which runs along the northern edge of the Elster and ...

Kingdom of Saxony The Kingdom of Saxony () was a German monarchy in Central Europe between 1806 and 1918, the successor of the Electorate of Saxony. It joined the Confederation of the Rhine after the dissolution of the Holy Roman Empire, later joining the German ...

. After schooling in Freiberg and

Dresden Dresden (; ; Upper Saxon German, Upper Saxon: ''Dräsdn''; , ) is the capital city of the States of Germany, German state of Saxony and its second most populous city after Leipzig. It is the List of cities in Germany by population, 12th most p ...

, he entered the Polytechnische Schule, now Technische Universität, in Dresden to study engineering science in 1859. Finding him especially enthusiastic about geodesy, one of his teachers, , hired him while still a student to work on the of the

Ore Mountains The Ore Mountains (, or ; ) lie along the Czech–German border, separating the historical regions of Bohemia in the Czech Republic and Saxony in Germany. The highest peaks are the Klínovec in the Czech Republic (German: ''Keilberg'') at ab ...

and the drafting of the trigonometric network for Saxony. In 1863 Helmert became Nagel's assistant on the . After a year's study of mathematics and astronomy Helmert obtained his doctor's degree from the

University of Leipzig Leipzig University (), in Leipzig in Saxony, Germany, is one of the world's oldest universities and the second-oldest university (by consecutive years of existence) in Germany. The university was founded on 2 December 1409 by Frederick I, Electo ...

in 1867 for a thesis based on his work for Nagel. In 1870 Helmert became instructor and in 1872 professor at

RWTH Aachen RWTH Aachen University (), in German ''Rheinisch-Westfälische Technische Hochschule Aachen'', is a German public research university located in Aachen, North Rhine-Westphalia, Germany. With more than 47,000 students enrolled in 144 study prog ...

, the new Technical University in

Aachen Aachen is the List of cities in North Rhine-Westphalia by population, 13th-largest city in North Rhine-Westphalia and the List of cities in Germany by population, 27th-largest city of Germany, with around 261,000 inhabitants. Aachen is locat ...

. At Aachen he wrote ''Die mathematischen und physikalischen Theorieen der höheren Geodäsie'' (Part I was published in 1880 and Part II in 1884). This work laid the foundations of modern

geodesy Geodesy or geodetics is the science of measuring and representing the Figure of the Earth, geometry, Gravity of Earth, gravity, and Earth's rotation, spatial orientation of the Earth in Relative change, temporally varying Three-dimensional spac ...

. See

history of geodesy The history of geodesy ( /dʒiːˈɒdɪsi/) began during antiquity and ultimately blossomed during the Age of Enlightenment. Many early conceptions of the Earth held it to be flat, with the heavens being a physical dome spanning over it. Early ...

. Part I is devoted to the mathematical aspects of geodesy and contains a comprehensive summary of techniques for solving for

geodesics on an ellipsoid The study of geodesics on an ellipsoid arose in connection with geodesy specifically with the solution of triangulation networks. The figure of the Earth is well approximated by an '' oblate ellipsoid'', a slightly flattened sphere. A ''geod ...

. The method of

least squares The method of least squares is a mathematical optimization technique that aims to determine the best fit function by minimizing the sum of the squares of the differences between the observed values and the predicted values of the model. The me ...

had been introduced into geodesy by

Gauss Johann Carl Friedrich Gauss (; ; ; 30 April 177723 February 1855) was a German mathematician, astronomer, Geodesy, geodesist, and physicist, who contributed to many fields in mathematics and science. He was director of the Göttingen Observat ...

and Helmert wrote a fine book on least squares (1872, with a second edition in 1907) in this tradition, which became a standard text. In 1876 he discovered the

chi-squared distribution In probability theory and statistics, the \chi^2-distribution with k Degrees of freedom (statistics), degrees of freedom is the distribution of a sum of the squares of k Independence (probability theory), independent standard normal random vari ...

as the distribution of the sample variance for a

normal distribution In probability theory and statistics, a normal distribution or Gaussian distribution is a type of continuous probability distribution for a real-valued random variable. The general form of its probability density function is f(x) = \frac ...

. This discovery and other of his work was described in German textbooks, including his own, but was unknown in English, and hence later rediscovered by English statisticians – the chi-squared distribution by

Karl Pearson Karl Pearson (; born Carl Pearson; 27 March 1857 – 27 April 1936) was an English biostatistician and mathematician. He has been credited with establishing the discipline of mathematical statistics. He founded the world's first university ...

(1900), and the application to the sample variance by 'Student' and

Fisher Fisher is an archaic term for a fisherman, revived as gender-neutral. Fisher, Fishers or The Fisher may also refer to: Places Australia * Division of Fisher, an electoral district in the Australian House of Representatives, in Queensland *Elec ...

. From 1887 Helmert was professor of advanced geodesy at the

University of Berlin The Humboldt University of Berlin (, abbreviated HU Berlin) is a public research university in the central borough of Mitte in Berlin, Germany. The university was established by Frederick William III on the initiative of Wilhelm von Humbol ...

and director of the Geodetic Institute. In 1916 he had a stroke and died of its effects the following year in

Potsdam Potsdam () is the capital and largest city of the Germany, German States of Germany, state of Brandenburg. It is part of the Berlin/Brandenburg Metropolitan Region. Potsdam sits on the Havel, River Havel, a tributary of the Elbe, downstream of B ...

Honours

Helmert received many honours. He was president of the global

geodetic Geodesy or geodetics is the science of measuring and representing the geometry, gravity, and spatial orientation of the Earth in temporally varying 3D. It is called planetary geodesy when studying other astronomical bodies, such as planets ...

association of " Internationale Erdmessung", member of the

Prussian Academy of Sciences The Royal Prussian Academy of Sciences () was an academy established in Berlin, Germany on 11 July 1700, four years after the Prussian Academy of Arts, or "Arts Academy," to which "Berlin Academy" may also refer. In the 18th century, when Frenc ...

Berlin Berlin ( ; ) is the Capital of Germany, capital and largest city of Germany, by both area and List of cities in Germany by population, population. With 3.7 million inhabitants, it has the List of cities in the European Union by population withi ...

, was elected a member of the

Royal Swedish Academy of Sciences The Royal Swedish Academy of Sciences () is one of the Swedish Royal Academies, royal academies of Sweden. Founded on 2 June 1739, it is an independent, non-governmental scientific organization that takes special responsibility for promoting nat ...

in 1905, and recipient of some 25 German and foreign decorations. The lunar crater

Helmert Friedrich Robert Helmert (31 July 1843 – 15 June 1917) was a German geodesist and statistician with important contributions to the theory of errors. Career Helmert was born in Freiberg, Kingdom of Saxony. After schooling in Freiberg and ...

was named in his honor, approved by the

IAU The International Astronomical Union (IAU; , UAI) is an international non-governmental organization (INGO) with the objective of advancing astronomy in all aspects, including promoting astronomical research, outreach, education, and developmen ...

in 1973.Helmert
Gazetteer of Planetary Nomenclature, International Astronomical Union (IAU) Working Group for Planetary System Nomenclature (WGPSN)

References

Works cited

General references

* Walther Fischer "Helmert, Friedrich Robert" ''Dictionary of Scientific Biography'' volume 7, pp. 239–241, New York: Scribners 1973. *O. B. Sheynin (1995). "Helmert's work in the theory of errors". ''Archive for History of Exact Sciences,'' 49, 73–104. *Die Genauigkeit der Formel von Peters zur Berechnung des wahrscheinlichen Fehlers director Beobachtungen gleicher Genauigkeit
''Astron. Nach.,'' 88, (1876), 192–218
An extract from the paper is translated and annotated in H. A. David & A. W. F. Edwards (eds.) ''Annotated Readings in the History of Statistics'', New York: Springer 2001. * *

External links

Royal Society citation 1908 (very succinct)
There is an obituary at

There is a photograph of Helmert at
Helmert
on th

page and three more at

See also

The first edition of Helmert's textbook on least squares is available at the GDZ site
''Die Ausgleichsrechnung nach der Methode der kleinsten Quadrate''
(''

Adjustment Computations Least-squares adjustment is a model for the solution of an overdetermined system of equations based on the principle of least squares of observation residuals. It is used extensively in the disciplines of surveying, geodesy, and photogrammetry—t ...

by the Method of Least Squares'') A partial scan of ''Die mathematischen und physikalischen Theorieen der höheren Geodäsie'' (Part I) is available on the site
Friedrich Robert Helmert (1841–1917)
English translations (by the Aeronautical Chart and Information Center, St. Louis) of Parts I and II of ''Die mathematischen und physikalischen Theorieen der höheren Geodäsie'' are available at
doi:10.5281/zenodo.32050doi:10.5281/zenodo.32051
There is an account of Helmert's work on the theory of errors in section 10.6 of
Oscar Sheynin Theory of Probability: A Historical Essay
For eponymous terms in statistics see

for the Abbe–Helmert criterion an

for the Helmert transformation. {{DEFAULTSORT:Helmert, Friedrich Robert 1843 births 1917 deaths German statisticians German geodesists People from the Kingdom of Saxony Leipzig University alumni Academic staff of RWTH Aachen University Academic staff of the Humboldt University of Berlin Members of the Prussian Academy of Sciences Members of the Royal Swedish Academy of Sciences Foreign members of the Royal Society Spatial statisticians