 Frege's "conceptual notation", however, can represent such inferences.The analysis of logical concepts and the machinery of formalization that is essential to "Principia Mathematica" (3 vols., 1910–13, by Bertrand Russell, 1872–1970, and Alfred North Whitehead, 1861–1947), to Russell's theory of descriptions, to Kurt Gödel's (1906–78) incompleteness theorems, and to Alfred Tarski's (1901–83) theory of truth, is ultimately due to Frege.One of Frege's stated purposes was to isolate genuinely logical principles of inference, so that in the proper representation of mathematical proof, one would at no point appeal to "intuition".