Mathematician and logician, born in Wismar, Germany. He studied at Jena and Göttingen, and became professor of mathematics at Jena (1896). His Begriffsschrift (1879, Concept-script) outlined the first complete system of symbolic logic. The technical difficulties involved gave rise to his distinctive philosophical doctrines, forcefully set out in his Grundlagen der Arithmetik (1884, The Foundations of Arithmetic). His Grundgesetze der Arithmetik (1893--1903, Basic Laws of Arithmetic) contained a postscript acknowledging that Russell had spotted a contradiction in his thinking. Depressed by the poor reception of his ideas, he wrote little after 1903.
