MathNodes Validator and Dev Team

Paul Erdős (March 26, 1913 – September 20, 1996) was a prominent Hungarian mathematician. He was an extremely prolific writer (he wrote around 1,500 mathematical papers) and is famous for his excellent work in discrete mathematics, graph theory, number theory, mathematical analysis, approximation theory, set theory, and probability theory. He also contributed to the Ramsey theory. 

Goro Shimura born on 23 February 1930 in  Hamamatsu, Japan and is one of the most important mathematicians of the 20th century. He studied under the famous Iwasawa and is most known for his conjecture, the Taniyama-Shimura Conjecture which was the foundation in Andrew Wile’s proof of Fermat’s Last Theorem. Vaguely, the conjecture (now Theorem) surmised that every elliptic curve is modular. A bold claim that proved extremely fruitful 40 years later. 

His work in algebraic geometry is what our node is named after, particularly the Shimura Variety. It was said of Shimura that:

… his important and extensive work on arithmetical geometry and automorphic forms; concepts introduced by him were often seminal, and fertile ground for new developments, as witnessed by the many notations in number theory that carry his name and that have long been familiar to workers in the field.

Igor was born on 3 June 1923 in  Zhytomyr, Ukraine. Hailed as the foremost Russian mathematician of the 20th century, Igor had many other interests besides mathematics. Up until the age of 12, Igor fell passionately in love with history and classic literature – which continued thorughout his life. It was only until he turned 12 years old that signs of a gifted mathematician were eminent. 

Shafarevich made fundamental contributions to several parts of mathematics including algebraic number theory, algebraic geometry and arithmetic algebraic geometry. In algebraic number theory, the Shafarevich–Weil theorem extends the commutative reciprocity map to the case of Galois groups, which are extensions of abelian groups by finite groups.

He also was also active in Soviet politics and belonged to the same activist group that the infamous Aleksandr Solzhenitsyn lead. His political interests caused undue stress during the middle-later years of his life.

The node is named after the Galois cohomology group which illuminates properties of elliptic curves over p-adic number fields.