Friedrich Ludwig Gottlob Frege (1848–1925) was born in Wismar, Germany. He studied mathematics, physics, and philosophy at the Universities of Jena and Göttingen, completing his doctoral dissertation on geometry in 1873 and his habilitation on the concept of quantity in 1874. Frege spent most of his academic career at the University of Jena, where he taught mathematics and, later, logic. He retired in 1918 and spent his final years in Bad Kleinen, passing away in 1925.

Frege’s early work established him as a pioneering thinker in logic and the philosophy of mathematics. His most important works include Begriffsschrift (“Concept-Script”, 1879), Die Grundlagen der Arithmetik (“The Foundations of Arithmetic”, 1884), and his magnum opus, Grundgesetze der Arithmetik (“The Basic Laws of Arithmetic”, 1893/1903).

Frege revolutionized modern logic by creating the first fully formal system of polyadic logic in Begriffsschrift. His work overcame the limitations of Aristotelian syllogistic logic and provided the foundation not only for contemporary formal logic but also for the development of modern linguistics and computer science.

In Die Grundlagen der Arithmetik and Die Grundgesetze der Arithmetik, Frege sought to show that arithmetic (which he understood broadly, including number theory and real and complex analysis) can be derived from pure logic. He introduced precise formal methods for defining the natural numbers and derived the basic laws of arithmetic from what he considered purely logical principles. After more than twenty years of work on this logicist program, a letter from Bertrand Russell revealed to Frege in 1902 that the logical system of Grundgesetze was inconsistent. While his project proved unfeasible in its original form, Frege continued his research into the foundations of mathematics until the end of his life, and many of his ideas continue to inspire philosophers of mathematics today.

Frege also made significant contributions to the philosophy of language. He introduced the distinction between sense and reference and developed the fundamental tools for analyzing predication, quantification, definite descriptions and other features of natural language in a compositional fashion. These insights profoundly shaped analytic philosophy, influencing thinkers such as Bertrand Russell, Rudolf Carnap and Ludwig Wittgenstein, and continue to guide contemporary research in semantics and the study of meaning.