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 real or complex number that is not algebraic: that is, not the root of a non-zero polynomial with integer (or, equivalently, rational) coefficients. The best-known transcendental numbers are and . ...

, 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 bel ...

of any

polynomial In mathematics, a polynomial is a Expression (mathematics), mathematical expression consisting of indeterminate (variable), indeterminates (also called variable (mathematics), variables) and coefficients, that involves only the operations of addit ...

with

rational Rationality is the quality of being guided by or based on reason. In this regard, a person acts rationally if they have a good reason for what they do, or a belief is rational if it is based on strong evidence. This quality can apply to an ...

coefficient In mathematics, a coefficient is a Factor (arithmetic), multiplicative factor involved in some Summand, term of a polynomial, a series (mathematics), series, or any other type of expression (mathematics), expression. It may be a Dimensionless qu ...

Life and education

Lindemann was born in

Hanover Hanover ( ; ; ) is the capital and largest city of the States of Germany, German state of Lower Saxony. Its population of 535,932 (2021) makes it the List of cities in Germany by population, 13th-largest city in Germany as well as the fourth-l ...

, the capital of the

Kingdom of Hanover The Kingdom of Hanover () was established in October 1814 by the Congress of Vienna, with the restoration of George III to his Hanoverian territories after the Napoleonic Wars, Napoleonic era. It succeeded the former Electorate of Hanover, and j ...

. 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-Vorpommersch dialect, Mecklenburgisch-Vorpommersch Low German: ''Swerin''; Polabian language, Polabian: ''Zwierzyn''; Latin: ''Suerina'', ''Suerinum'') is the Capital city, capital and List of cities and towns in Germ ...

, where young Ferdinand attended school. He studied mathematics at

Göttingen Göttingen (, ; ; ) is a college town, university city in Lower Saxony, central Germany, the Capital (political), capital of Göttingen (district), the eponymous district. The River Leine runs through it. According to the 2022 German census, t ...

Erlangen Erlangen (; , ) is a Middle Franconian city in Bavaria, Germany. It is the seat of the administrative district Erlangen-Höchstadt (former administrative district Erlangen), and with 119,810 inhabitants (as of 30 September 2024), it is the smalle ...

, and

Munich Munich is the capital and most populous city of Bavaria, Germany. As of 30 November 2024, its population was 1,604,384, making it the third-largest city in Germany after Berlin and Hamburg. Munich is the largest city in Germany that is no ...

. At Erlangen he received a doctorate, supervised by

Felix Klein Felix Christian Klein (; ; 25 April 1849 – 22 June 1925) was a German mathematician and Mathematics education, mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and the associations betwe ...

, 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 ge ...

. Lindemann subsequently taught in

Würzburg Würzburg (; Main-Franconian: ) is, after Nuremberg and Fürth, the Franconia#Towns and cities, third-largest city in Franconia located in the north of Bavaria. Würzburg is the administrative seat of the Regierungsbezirk Lower Franconia. It sp ...

and at the

University of Freiburg The University of Freiburg (colloquially ), officially the Albert Ludwig University of Freiburg (), is a public university, public research university located in Freiburg im Breisgau, Baden-Württemberg, Germany. The university was founded in 1 ...

. 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 transcendence of numbers. It states the following: In other words, the extension field \mathbb(e^, \dots, e^) has transc ...

). After his time in Freiburg, Lindemann transferred to the

University of Königsberg The University of Königsberg () was the university of Königsberg in Duchy of Prussia, which was a fief of Poland. It was founded in 1544 as the world's second Protestant Reformation, Protestant academy (after the University of Marburg) by Duke A ...

. While a professor in

Königsberg Königsberg (; ; ; ; ; ; , ) is the historic Germany, German and Prussian name of the city now called Kaliningrad, Russia. The city was founded in 1255 on the site of the small Old Prussians, Old Prussian settlement ''Twangste'' by the Teuton ...

, 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 and philosopher of mathematics and one of the most influential mathematicians of his time. Hilbert discovered and developed a broad range of fundamental idea ...

Hermann Minkowski Hermann Minkowski (22 June 1864 – 12 January 1909) was a mathematician and professor at the University of Königsberg, the University of Zürich, and the University of Göttingen, described variously as German, Polish, Lithuanian-German, o ...

, and

Arnold Sommerfeld Arnold Johannes Wilhelm Sommerfeld (; 5 December 1868 – 26 April 1951) was a German Theoretical physics, theoretical physicist who pioneered developments in Atomic physics, atomic and Quantum mechanics, quantum physics, and also educated and ...

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 () 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, and algebra. Hermite p ...

to show that ''e'', the base of natural logarithms, is transcendental. Before the publication of Lindemann's proof, it was known that was irrational, as

Johann Heinrich Lambert Johann Heinrich Lambert (; ; 26 or 28 August 1728 – 25 September 1777) was a polymath from the Republic of Mulhouse, at that time allied to the Switzerland, Swiss Confederacy, who made important contributions to the subjects of mathematics, phys ...

proved was irrational in the 1760s.

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 German 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 Academic staff of the University of Königsberg