Martin Eichler
Encyclopedia
Martin Eichler was a German number theorist
.
Eichler received his Ph.D. from the Martin Luther University of Halle-Wittenberg in 1936.
Eichler once stated that there were five fundamental operations of mathematics
: addition
, subtraction
, multiplication
, division
, and modular forms. He is linked with Goro Shimura
in the development of a method to construct elliptic curve
s from
certain modular forms. The converse notion that every elliptic curve has a corresponding
modular form would later be the key to the proof of Fermat's last theorem
.
Number theory
Number theory is a branch of pure mathematics devoted primarily to the study of the integers. Number theorists study prime numbers as well...
.
Eichler received his Ph.D. from the Martin Luther University of Halle-Wittenberg in 1936.
Eichler once stated that there were five fundamental operations of mathematics
Mathematics
Mathematics is the study of quantity, space, structure, and change. Mathematicians seek out patterns and formulate new conjectures. Mathematicians resolve the truth or falsity of conjectures by mathematical proofs, which are arguments sufficient to convince other mathematicians of their validity...
: addition
Addition
Addition is a mathematical operation that represents combining collections of objects together into a larger collection. It is signified by the plus sign . For example, in the picture on the right, there are 3 + 2 apples—meaning three apples and two other apples—which is the same as five apples....
, subtraction
Subtraction
In arithmetic, subtraction is one of the four basic binary operations; it is the inverse of addition, meaning that if we start with any number and add any number and then subtract the same number we added, we return to the number we started with...
, multiplication
Multiplication
Multiplication is the mathematical operation of scaling one number by another. It is one of the four basic operations in elementary arithmetic ....
, division
Division (mathematics)
right|thumb|200px|20 \div 4=5In mathematics, especially in elementary arithmetic, division is an arithmetic operation.Specifically, if c times b equals a, written:c \times b = a\,...
, and modular forms. He is linked with Goro Shimura
Goro Shimura
is a Japanese mathematician, and currently a professor emeritus of mathematics at Princeton University.Shimura was a colleague and a friend of Yutaka Taniyama...
in the development of a method to construct elliptic curve
Elliptic curve
In mathematics, an elliptic curve is a smooth, projective algebraic curve of genus one, on which there is a specified point O. An elliptic curve is in fact an abelian variety — that is, it has a multiplication defined algebraically with respect to which it is a group — and O serves as the identity...
s from
certain modular forms. The converse notion that every elliptic curve has a corresponding
modular form would later be the key to the proof of Fermat's last theorem
Fermat's Last Theorem
In number theory, Fermat's Last Theorem states that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two....
.