It is arguable that Frege is the greatest logician since Aristotle. His revolutionary Begriffsschrift (Concept Script ) from 1879 marked the beginning of a new epoch in the history of logic.
Frege invented propositional and predicate calculi which, with improved notation, are still taught today. The quantification so essential to Bertrand Russell's theory of descriptions, and to Russell and Alfred North Whitehead's Principia Mathematica, was also due to Frege. His work was largely unrecognized in his own day, and his ideas spread chiefly through those he influenced, particularly Giuseppe Peano and Russell. Ludwig Wittgenstein and Edmund Husserl were among the other philosophical notables strongly influenced by Frege.
Frege was the first major proponent of logicism[?] -- the view that mathematics is reducible to logic. His Grundgesetze der Arithmetik was an attempt to explicitly derive the laws of arithmetic from logic. After the first volume was published (at the author's expense), Russell discovered the paradox which bears his name, and that the axioms of the Grundgesetze led to this contradiction; he wrote to Frege, who acknowledged the contradiction in an appendix to volume two of the Grundgesetze, noting what he perceived to be the faulty axiom. Frege never did manage to amend his axioms to his satisfaction, however; and after Frege's death, Kurt Gödel's incompleteness theorems showed that Frege's logicist program was impossible.
He started studying at the University of Jena[?] in 1869 and moved to Göttingen after two years, where he received his Ph.D. in 1873. After returning to Jena two years later, he became lecturer of mathematics. In 1879, he was made associate professor and in 1896 became professor of mathematics.
His principal works are:
Frege intended these last three papers to be published in a book to be called Logical Investigations; in 1975 they were posthumously published (in English translation, at least) under this title.