Ferdinand von Lindemann
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Carl Louis Ferdinand von Lindemann (12 April 1852 – 6 March 1939) was a German
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 ...
, noted for his proof, published in 1882, that (pi) is a
transcendental number In mathematics, a transcendental number is a number that is not algebraic number, algebraic—that is, not the Zero of a function, root of a non-zero polynomial of finite degree with rational number, rational coefficients. The best known transcen ...
, meaning it is not a
root In vascular plants, the roots are the plant organ, organs of a plant that are modified to provide anchorage for the plant and take in water and nutrients into the plant body, which allows plants to grow taller and faster. They are most often b ...
of any
polynomial In mathematics, a polynomial is an expression (mathematics), expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addition, subtrac ...
with
rational Rationality is the Quality (philosophy), quality of being guided by or based on reasons. In this regard, a person Action (philosophy), acts rationally if they have a good reason for what they do or a belief is rational if it is based on strong e ...
coefficients.


Life and education

Lindemann was born in
Hanover Hanover (; german: Hannover ; nds, Hannober) is the capital and largest city of the German States of Germany, state of Lower Saxony. Its 535,932 (2021) inhabitants make it the List of cities in Germany by population, 13th-largest city in Germa ...
, the capital of the
Kingdom of Hanover The Kingdom of Hanover (german: Königreich Hannover) was established in October 1814 by the Congress of Vienna, with the restoration of George III of the United Kingdom, George III to his Hanoverian territories after the Napoleonic Wars, Napoleo ...
. His father, Ferdinand Lindemann, taught modern languages at a Gymnasium in Hanover. His mother, Emilie Crusius, was the daughter of the Gymnasium's headmaster. The family later moved to
Schwerin Schwerin (; Mecklenburgisch dialect, Mecklenburgian Low German: ''Swerin''; Latin: ''Suerina'', ''Suerinum'') is the Capital city, capital and List of cities and towns in Germany, second-largest city of the northeastern States of Germany, German ...
, where young Ferdinand attended school. He studied mathematics at Göttingen,
Erlangen Erlangen (; East Franconian German, East Franconian: ''Erlang'', Bavarian language, Bavarian: ''Erlanga'') is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative d ...
, and
Munich Munich ( ; german: München ; bar, Minga ) is the capital and most populous city of the States of Germany, German state of Bavaria. With a population of 1,558,395 inhabitants as of 31 July 2020, it is the List of cities in Germany by popu ...
. At Erlangen he received a doctorate, supervised by
Felix Klein Christian Felix Klein (; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work with group theory, complex analysis, non-Euclidean geometry, and on the associations between geometry and group ...
, on
non-Euclidean geometry In mathematics, non-Euclidean geometry consists of two geometries based on axioms closely related to those that specify Euclidean geometry. As Euclidean geometry lies at the intersection of metric geometry and affine geometry, non-Euclidean geo ...
. Lindemann subsequently taught in Würzburg and at the
University of Freiburg The University of Freiburg (colloquially german: Uni Freiburg), officially the Albert Ludwig University of Freiburg (german: Albert-Ludwigs-Universität Freiburg), is a public university, public research university located in Freiburg im Breisg ...
. During his time in Freiburg, Lindemann devised his proof that is a transcendental number (see
Lindemann–Weierstrass theorem In transcendental number theory, the Lindemann–Weierstrass theorem is a result that is very useful in establishing the transcendental number, transcendence of numbers. It states the following: In other words, the extension field \mathbb(e^, \ ...
). After his time in Freiburg, Lindemann transferred to the University of Königsberg. While a professor in
Königsberg Königsberg (, ) was the historic Prussian city that is now Kaliningrad, Russia. Königsberg was founded in 1255 on the site of the ancient Old Prussian settlement ''Twangste'' by the Teutonic Knights during the Northern Crusades, and was named ...
, Lindemann acted as supervisor for the doctoral theses of the mathematicians
David Hilbert David Hilbert (; ; 23 January 1862 – 14 February 1943) was a German mathematician, one of the most influential mathematicians of the 19th and early 20th centuries. Hilbert discovered and developed a broad range of fundamental ideas in many a ...
,
Hermann Minkowski Hermann Minkowski (; ; 22 June 1864 – 12 January 1909) was a German mathematician and professor at University of Königsberg, Königsberg, University of Zürich, Zürich and University of Göttingen, Göttingen. He created and developed the ge ...
, and
Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld, (; 5 December 1868 – 26 April 1951) was a Germans, German theoretical physicist who pioneered developments in atomic physics, atomic and quantum physics, and also educated and mentored many students for th ...
.


Transcendence proof

In 1882, Lindemann published the result for which he is best known, the transcendence of . His methods were similar to those used nine years earlier by
Charles Hermite Charles Hermite () Royal Society of London, FRS FRSE MIAS (24 December 1822 – 14 January 1901) was a French mathematician who did research concerning number theory, quadratic forms, invariant theory, orthogonal polynomials, elliptic functions, ...
to show that ''e'', the base of natural logarithms, is transcendental. Before the publication of Lindemann's proof, it was known that ''if'' was transcendental, with
Johann Heinrich Lambert Johann Heinrich Lambert (, ''Jean-Henri Lambert'' in French language, French; 26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, generally referred to as either Switzerland, Swiss or France, French, who made i ...
as the first to prove being irrational in the 1760s, along with the impossibility to
square the circle Squaring the circle is a problem in geometry first proposed in Greek mathematics. It is the challenge of constructing a square (geometry), square with the area of a circle by using only a finite number of steps with a compass and straighted ...
by
compass and straightedge In geometry, straightedge-and-compass construction – also known as ruler-and-compass construction, Euclidean construction, or classical construction – is the construction of lengths, angles, and other geometric figures using only an Idealiz ...
.


References


External links

* * * * Lindemann, F.
Über die Zahl
, ''Mathematische Annalen'' 20 (1882): pp. 213–225. {{DEFAULTSORT:Lindemann, Ferdinand von 1852 births 1939 deaths 19th-century German mathematicians 20th-century German mathematicians Squaring the circle Number theorists Scientists from Hanover People from the Kingdom of Hanover University of Göttingen alumni University of Erlangen-Nuremberg alumni Ludwig Maximilian University of Munich alumni University of Königsberg faculty