The fading amateur: William Lenhart and 19th-century American mathematics (Q917537)

The article, which is mainly built upon the letters and printed work of William Lenhart (1787-1840), describes the mathematical activity of this last mathematical amateur to be counted among the leading American mathematicians. His achievement, though reckoned by certain contemporaries on a par with that of Gauß, Lagrange and Euler, is shown to be better described by his own words: ``if not ingenious, at least novel and exceedingly curious''. Concerned as Lenhart was with specific solutions and specific problems in Diophantine analysis, and not familiar with the new, general methods introduced by Gauß into number theory, his mathematics is shown to be typical of the highly gifted amateur with limited knowledge. Lenhart's relation to the field is finally used, in contrast with the attitudes of Benjamin Peirce the champion of scientific professionalization and fellow number theorist, to highlight the mid-nineteenth shift in the style and organization of American science. The article is provided with the most necessary biographic details, but is not biographic in orientation.