How Do You Spell ERNST KUMMER?

1. Ernst Kummer was a German mathematician born on January 29, 1810, in Sorau, Brandenburg, and died on May 14, 1893, in Berlin. He made significant contributions to the fields of algebraic number theory and quadratic forms.

   In algebraic number theory, Kummer is famous for his work on Fermat's Last Theorem, which states that there are no three positive integers a, b, and c that satisfy the equation a^n + b^n = c^n for any integer value of n greater than 2. Although Kummer did not prove the general case of Fermat's Last Theorem, he was able to demonstrate its validity for regular primes in 1843. He introduced the concept of ideals, which are subsets of integers within a number field, to overcome the limitations of unique factorization for non-regular primes. Kummer's ideal theory paved the way for later mathematicians, such as Richard Dedekind and Ernst Eduard Selling, to develop a more comprehensive understanding of algebraic number fields.

   Furthermore, Kummer also made important contributions to the study of quadratic forms, forms with variables of degree 2. He developed algorithms to count the number of properly equivalent classes within specific types of quadratic forms, laying the foundation for the further development of this branch of mathematics.

   Ernst Kummer's work greatly contributed to the advancement of algebraic number theory and quadratic forms, leaving a lasting impact on the field of mathematics.

The term "Ernst Kummer" does not have an etymology since it is not a common word or phrase in the English language. However, "Ernst Kummer" refers to a person named Ernst Eduard Kummer (1810-1893), a German mathematician who made significant contributions to the field of number theory.