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Friedrich Robert Helmert (* July 31, 1843 in Freiberg, Saxonia; † June 15, 1917 in Potsdam) was a celebrated German geodesist and an important writer on the theory of errors.

After schooling in Freiberg and Dresden Helmert 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, August Nagel, hired him while still a student to work on the triangulation of the Erzgebirge and the drafting of the trigonometric network for Saxony. In 1863 Helmert became Nagel's assistant on the Central European Arc Measurement. After a year's study of mathematics and astronomy Helmert obtained his doctor's degree from the University of Leipzig in 1867 for a thesis based on his work for Nagel.

In 1870 Helmert became instructor and in 1872 professor at RWTH Aachen, the new Technical University in Aachen. At Aachen he wrote Die mathematischen und physikalischen Theorien der höheren Geodäsie (Part I was published in 1880 and Part II in 1884). This work laid the foundations of modern geodesy. See history of geodesy.

The method of least squares had been introduced into geodesy by Gauss and Helmert wrote a fine book on least squares (1872, with a second edition in 1907) in this tradition. Hald (p. 633) gives this assessment: "[It] is a pedagogical masterpiece; it became a standard text until it was superseded by expositions using matrix algebra." In 1876 Helmert published an article deriving the distribution of the sample variance for a normal population. The work was described in German textbooks, including his own, but the English statisticians 'Student' and Fisher did not know of it and re-derived the distribution.

From 1887 Helmert was professor of advanced geodesy at the University of Berlin and director of the Geodetic Institute. In 1916 he had a stroke and died of its effects the following year.

Helmert received many honours. He was president of the global geodetic association of "Internationale Erdmessung", member of the Prussian Academy of Sciences in Berlin and recipient of some 25 German and foreign decorations.

See also: Helmert transformation, coordinate system, Helmert-Wolf blocking, national survey, terrestrial gravity field

• Walther Fischer "Helmert, Friedrich Robert" Dictionary of Scientific Biography volume 7, pp. 239-241, New York: Scribners 1973.

• Anders Hald (1998) A History of Mathematical Statistics from 1750 to 1930 New York: Wiley.

• 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 directer 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.

• Royal Society citation 1908 (very succinct)

There is an obituary at

• MNRAS 78 (1918) 256

There is a photograph of Helmert at

• Helmert on the Portraits of Statisticians page

and three more at

• Helmert

See also

• memorial stone

The first edition of Helmert's textbook on least squares is available at the GDZ site

• Die Ausgleichsrechnung nach der Methode der kleinsten Quadrate

A partial scan of Die mathematischen und physikalischen Theorien der höheren Geodäsie (Part I) is available on the site

• Friedrich Robert Helmert (1841-1917)

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