Ferdinand Gotthold Max Eisenstein (16 April 1823 – 11 October 1852) 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 ...

who made significant contributions to

number theory Number theory is a branch of pure mathematics devoted primarily to the study of the integers and arithmetic functions. Number theorists study prime numbers as well as the properties of mathematical objects constructed from integers (for example ...

and

analysis Analysis (: analyses) is the process of breaking a complex topic or substance into smaller parts in order to gain a better understanding of it. The technique has been applied in the study of mathematics and logic since before Aristotle (38 ...

. Born in Berlin, Prussia, to Jewish parents who converted to Protestantism before his birth, Eisenstein displayed exceptional mathematical talent from a young age.

Early life and education

Despite suffering from health problems, including

meningitis Meningitis is acute or chronic inflammation of the protective membranes covering the brain and spinal cord, collectively called the meninges. The most common symptoms are fever, intense headache, vomiting and neck stiffness and occasion ...

, Eisenstein excelled academically. At 14, he attended Friedrich Werder Gymnasium. By age 15, he had mastered the mathematics curriculum. His teachers recognized his mathematical abilities, one quoted as saying: He then turned to the works of Leonhard Euler and

Joseph-Louis Lagrange Joseph-Louis Lagrange (born Giuseppe Luigi Lagrangiadifferential calculus In mathematics, differential calculus is a subfield of calculus that studies the rates at which quantities change. It is one of the two traditional divisions of calculus, the other being integral calculus—the study of the area beneath a curve. ...

. While still a student, Eisenstein began attending lectures by

Peter Gustav Lejeune Dirichlet Johann Peter Gustav Lejeune Dirichlet (; ; 13 February 1805 – 5 May 1859) was a German mathematician. In number theory, he proved special cases of Fermat's last theorem and created analytic number theory. In analysis, he advanced the theory o ...

and others 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 ...

. In 1843, he met

William Rowan Hamilton Sir William Rowan Hamilton (4 August 1805 – 2 September 1865) was an Irish astronomer, mathematician, and physicist who made numerous major contributions to abstract algebra, classical mechanics, and optics. His theoretical works and mathema ...

Dublin Dublin is the capital and largest city of Republic of Ireland, Ireland. Situated on Dublin Bay at the mouth of the River Liffey, it is in the Provinces of Ireland, province of Leinster, and is bordered on the south by the Dublin Mountains, pa ...

, who introduced him to

Niels Henrik Abel Niels Henrik Abel ( , ; 5 August 1802 – 6 April 1829) was a Norwegian mathematician who made pioneering contributions in a variety of fields. His most famous single result is the first complete proof demonstrating the impossibility of solvin ...

's proof of the impossibility of solving fifth-degree polynomials, sparking his interest in mathematical research.

Contributions to mathematics (1843-1848)

Upon returning to Berlin in 1843, Eisenstein passed his graduation exams and enrolled in the University. Within a year, he presented his first work on cubic forms in two variables to the Berlin Academy. He also gained the patronage of

Alexander von Humboldt Friedrich Wilhelm Heinrich Alexander von Humboldt (14 September 1769 – 6 May 1859) was a German polymath, geographer, natural history, naturalist, List of explorers, explorer, and proponent of Romanticism, Romantic philosophy and Romanticism ...

, who secured grants to support Eisenstein's financial needs. During this period, Eisenstein published numerous papers in Crelle's Journal, including two proofs of the law of

quartic reciprocity Quartic or biquadratic reciprocity is a collection of theorems in elementary and algebraic number theory that state conditions under which the congruence ''x''4 ≡ ''p'' (mod ''q'') is solvable; the word "reciprocity" comes from the form ...

and analogous laws for cubic and quartic reciprocity. He also visited

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

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 ...

and received an

honorary doctorate An honorary degree is an academic degree for which a university (or other degree-awarding institution) has waived all of the usual requirements. It is also known by the Latin phrases ''honoris causa'' ("for the sake of the honour") or '' ad hon ...

from the University of Breslau. In 1847, Eisenstein habilitated at the University of Berlin and began teaching there.

Challenges and continued research

Despite his revolutionary activities in Berlin, which led to a brief imprisonment in 1848, Eisenstein continued his mathematical research. He made significant contributions to quadratic partitions of

prime number A prime number (or a prime) is a natural number greater than 1 that is not a Product (mathematics), product of two smaller natural numbers. A natural number greater than 1 that is not prime is called a composite number. For example, 5 is prime ...

s and the reciprocity laws. His work was recognized by his election to the Academy of Göttingen and

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 ...

in 1851 and 1852, respectively.

Illness and death

Unfortunately, Eisenstein's health deteriorated, and he succumbed to

tuberculosis Tuberculosis (TB), also known colloquially as the "white death", or historically as consumption, is a contagious disease usually caused by ''Mycobacterium tuberculosis'' (MTB) bacteria. Tuberculosis generally affects the lungs, but it can al ...

at the age of 29.

, a lifelong supporter, accompanied his remains to the cemetery.

Publications

*
Weil's review

Eponym concepts

Eisenstein's criterion In mathematics, Eisenstein's criterion gives a sufficient condition for a polynomial with integer coefficients to be irreducible over the rational numbers – that is, for it to not be factorizable into the product of non-constant polynomials wit ...

* Eisenstein ideal *

Eisenstein integer In mathematics, the Eisenstein integers (named after Gotthold Eisenstein), occasionally also known as Eulerian integers (after Leonhard Euler), are the complex numbers of the form : z = a + b\omega , where and are integers and : \omega = \frac ...

* Eisenstein prime * Eisenstein reciprocity * Eisenstein sum *

Eisenstein series Eisenstein series, named after German mathematician Gotthold Eisenstein, are particular modular forms with infinite series expansions that may be written down directly. Originally defined for the modular group, Eisenstein series can be generalize ...

* Eisenstein's theorem * Eisenstein triple * Eisenstein–Kronecker number * Real analytic Eisenstein series

References

External links

* *
The life of Gotthold Ferdinand Eisenstein
'' by M.Schmitz ( PDF format) *
Ferdinand Eisenstein
' by Larry Freeman (2005), Fermat's Last Theorem Blog. {{DEFAULTSORT:Eisenstein, Ferdinand Gotthold Max 1823 births 1852 deaths 19th-century German mathematicians German number theorists Humboldt University of Berlin alumni Academic staff of the Humboldt University of Berlin German people of Jewish descent German Protestants Mathematicians from Berlin 19th-century deaths from tuberculosis Mathematicians from the Kingdom of Prussia Tuberculosis deaths in Germany