Commenting upon his analysis of experimental results from in-laboratory soap film formations, Courant believed that the existence of a physical solution does not obviate the need for mathematical proof. Here is a quote from Courant on his mathematical perspective:
"Empirical evidence can never establish mathematical existence--nor can the mathematician's demand for existence be dismissed by the physicist as useless rigor. Only a mathematical existence proof can ensure that the mathematical description of a physical phenomenon is meaningful." - Richard Courant
Richard Courant (January 8, 1888 – January 27, 1972) was a German mathematician. He is best known by the general public for the book What is Mathematics?, co-written with Herbert Robbins, which was praised by Albert Einstein, stating, "A lucid representation of the fundamental concepts and methods of the whole field of mathematics...Easily understandable."
Courant was born in Lublinitz, in the Prussian Province of Silesia. His parents were Siegmund Courant and Martha Courant née Freund of Oels. During his youth his parents moved often, including to Glatz, then to Breslau and in 1905 to Berlin. He stayed in Breslau and entered the university there, then continued his studies at the University of Zürich and the University of Göttingen. He became David Hilbert's assistant in Göttingen and obtained his doctorate there in 1910. He was obliged to serve in World War I but was wounded shortly after enlisting and dismissed from the military. He continued his research in Göttingen and then engaged a two-year period at the University of Münster as professor of mathematics. There he founded the Mathematical Institute, which he headed as director from 1928 until 1933.
In 1936, after one year at Cambridge Courant accepted a professorship at New York University in New York City. There he founded an institute for graduate studies in applied mathematics. The Courant Institute of Mathematical Sciences (as it was renamed in 1964) is now one of the most respected research centers in applied mathematics.
Courant and David Hilbert authored the influential textbook Methoden der mathematischen Physik which, with its revised editions, is still current and widely used since its publication in 1924. With Herbert Robbins he coauthored a popular overview of higher mathematics, intended for the general public, titled What is Mathematics?.
Courant's name is also attached to the finite element method, with his numerical treatment of the plain torsion problem for multiply-connected domains, published in 1943. This method is now one of the ways to solve partial differential equations numerically. Courant is a namesake of the Courant–Friedrichs–Lewy condition and the Courant minimax principle.
Courant died in New Rochelle, New York.
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