**Born:** March 1, 1879, Goodwater, Alabama

**Died:** May 2, 1967, Merriam, Kansas

Robert Daniel Carmichael was a University of Illinois mathematics professor, textbook author, and editor.

## Presidency: 1923

During his presidency, Carmichael published reviews in the *American Mathematical Monthly*, and his textbook *Diophantine Analysis* (1915) and other works were discussed in mathematical journals. Carmichael and A.J. Kempner taught at the University of Illinois betwen 1915 and 1925.

Carmichael gave his retiring presidential address, "The Present State of the Difference Calculus and the Prospect for the Future" on December 27, 1923, at the national meeting.

## Education and Career

1898 Lineville College, A.B.

1909-1911 Princeton University, Ph.D., advised by G.D. Birkhoff

Between completing his bachelor's degree and beginning graduate work, Carmichael accumulated 170 publications in the *Monthly* and 13 papers in research journals, and he was a professor of mathematics at the Presbyterian College for Men in Anniston, Alabama, for three years.

Upon earning his Ph.D., Carmichael joined Indiana University. In 1915, he moved to the University of Illinois. There he served as head of the department (1929-34) and dean of the graduate school (1933-47). He retired in 1947.

Carmichael is known for the Carmichael numbers: odd composite numbers *n* that satisfy *x*^{n-1} = 1 mod *n* for every *x* relatively prime to *n*. Carmichael's conjecture that there are infinitely many Carmichael numbers originally appeared as an exercise in his textbook *The Theory of Numbers* (1914), but he later found a flaw in his proof. The conjecture was finally proven in 1994.

In the MAA, Carmichael was a charter member, a member of the first publications committee, vice president (1921-22), editor-in-chief of the *American Mathematical Monthly* (1918), and a member of the board of governors (1920, 1924-29, 1939-41). He was also a vice president of the American Association for the Advancement of Science (1934), a member of the American Mathematical Society council (1916-18, 1920, 1924, 1925-27), and a member of the National Research Council (1929-32).

## External Resources

MacTutor History of Mathematics Archive biography

Robert D. Carmichael Papers, 1905-64

The Mathematics Genealogy Project