Joseph Ritt

Joseph Fels Ritt (August 23, 1893 – January 5, 1951) was an American mathematician at Columbia University in the early 20th century. He was born and died in New York.

Joseph Ritt
Born	(1893-08-23)August 23, 1893 New York City, U.S.
Died	January 5, 1951(1951-01-05) (aged 57) New York City, U.S.
Alma mater	Columbia University
Known for	Differential algebra
Scientific career
Fields	Mathematics
Institutions	Columbia University
Thesis	On a General Class of Linear Homogeneous Differential Equations of Infinite Order with Constant Coefficients Preceded by a Note on the Resolution into Partial Fractions of the Reciprocal of an Entire Function of Genus Zero  (1917)
Doctoral advisor	Edward Kasner
Doctoral students	Ellis Kolchin Howard Levi Edgar Lorch

Biography

After beginning his undergraduate studies at City College of New York, Ritt received his B.A. from George Washington University in 1913. He then earned a doctorate in mathematics from Columbia University in 1917 under the supervision of Edward Kasner. After doing calculations for the war effort in World War I, he joined the Columbia faculty in 1921. He served as department chair from 1942 to 1945, and in 1945 became the Davies Professor of Mathematics.^[1][2] In 1932, George Washington University honored him with a Doctorate in Science,^[3] and in 1933 he was elected to join the United States National Academy of Sciences.^[1][2] He has 905 academic descendants listed in the Mathematics Genealogy Project, mostly through his student Ellis Kolchin, as of May 2024.^[4] Ritt was an Invited Speaker with talk Elementary functions and their inverses at the ICM in 1924 in Toronto and a Plenary Speaker at the ICM in 1950 in Cambridge, Massachusetts.^[5]

Ritt founded differential algebra theory, which was subsequently much developed by him and his student Ellis Kolchin.^[6]

He is known for his work on characterizing the indefinite integrals that can be solved in closed form, for his work on the theory of ordinary differential equations and partial differential equations, for beginning the study of differential algebraic groups,^[1][2] and for the method of characteristic sets used in the solution of systems of polynomial equations.

Despite his great achievements, he was never awarded any prize for his work, a fact which he resented, as he felt he was underappreciated. He once composed the following epitaph for himself:^[7]

Here at your feet J. F. Ritt lies;

He never won the Bôcher prize.

Selected works

• Differential equations from the algebraic standpoint, New York, American Mathematical Society 1932^[8]
• Theory of Functions, New York 1945, 1947^[9]
• Integration in finite terms: Liouville's Theory of Elementary Methods, Columbia University Press 1948^[10]
• Differential Algebra, American Mathematical Society 1950,^[11] Dover 1966

See also

• Ritt characteristic set
• Ritt theorem
• Ritt's polynomial decomposition theorem

References

1. O'Connor, John J.; Robertson, Edmund F., "Joseph Ritt", MacTutor History of Mathematics Archive, University of St Andrews
2. Smith, Paul A. (1956), Joseph Fels Ritt 1893–1951: A Biographical Memoir (PDF), United States National Academy of Sciences.
3. Lorch, E. R. (1951), "Obituary : Joseph Fels Ritt", Bulletin of the American Mathematical Society, 57 (4): 307–318, doi:10.1090/S0002-9904-1951-09529-4.
4. Joseph Ritt at the Mathematics Genealogy Project
5. Ritt, J. F. (1950). "Differential groups" (PDF). In: Proceedings of the International Congress of Mathematicians, Cambridge, Massachusetts, U.S.A., August 30–September 6, 1950. Vol. 1. pp. 207–208. Archived from the original (PDF) on December 30, 2013. Retrieved December 4, 2017.
6. Kondratieva, M. V. (1998). Differential and Difference Dimension Polynomials. Springer Science & Business Media. p. vii (preface). ISBN 978-0-7923-5484-0.
7. Peter L. Duren; Richard Askey; Uta C. Merzbach; Harold M. Edwards (1989). A Century of Mathematics in America, Part III. American Mathematical Society. p. 158. ISBN 978-0-8218-0136-9.
8. Thomas, J. M. (1934). "Review: Differential Equations from the Algebraic Standpoint by J. F. Ritt" (PDF). Bull. Amer. Math. Soc. 40 (3): 197–200. doi:10.1090/s0002-9904-1934-05808-7.
9. Cohen, L. W. (1950). "Review: J. F. Ritt, Theory of functions". Bull. Amer. Math. Soc. 56 (2): 209–211. doi:10.1090/s0002-9904-1950-09395-1.
10. Lorch, E. R. (1948). "Review: Integration in finite terms by J. F. Ritt" (PDF). Bull. Amer. Math. Soc. 54, Part 1 (11): 1090–1092. doi:10.1090/S0002-9904-1948-09105-4.
11. van der Waerden, B. L. (1950). "Review: Differential Algebra by J. F. Ritt" (PDF). Bull. Amer. Math. Soc. 56 (6): 521–523. doi:10.1090/s0002-9904-1950-09434-8.