Mathematician of the week: Paul Guldin


Paul Guldin spend much of his teaching career at Jesuit colleges in Rome and Graz, Austria. He is remembered for Guldin’s Theorem: If any plane figure revolve about an external axis in its plane, the volume of the solid body so generated is equal to the product of the area of the figure and the distance traveled by the center of gravity of the figure.

Guldin published this result in his De centro gravitatis (1635-1641), and the result is more widely referred to as Pappus’s Theorem, having been anticipated by Pappus of Alexandria circa 320 CE.

Ivor Bulmer-Thomas writes about the question of whether Guldin had known of Pappus’s work in an article in Isis (vol 75, 1984).  He argues convincingly that Guldin is almost certain to have read Pappus’s work in translation in 1618, and probably unconsciously plagiarized it some 20 years later when completing his own work on centers of gravity.  Bulmer-Thomas’s article debunks a longstanding error in historiography:  Moncula’s 1758 history of mathematics erroneously stated that Pappus’s Theorem had been omitted from the first Latin translation of his work, and consequently Guldin’s discovery must have been arrived at independently.  Moncula corrected this error in the second edition of his history (1799), but the incorrect account has gotten wider dissemination (from Paul Ver Eecke [editor of a modern collection of Pappus’s writings], Carl Boyer’s History of Mathematics, and even the Dictionary of Scientific Biography‘s entry for Guldin, for example).

Moral:  as much as possible, check and recheck the claims of your secondary sources, even if they are highly regarded and generally known to be sound.

Mathematicians with birth or death anniversaries during the week of June 8 through June 14:

June 8: Birthdays of Giovanni Cassini [1625] (discovered Cassini gap in Saturn’s rings; introduced use of Jovian moon observations to determine longitude), Caspar Wessel [1745] (“Argand” diagram), and Charlotte Angas Scott [1858] (algebraic geometer; first head of math dept at Bryn Mawr)

June 9: Birthday of John Littlewood [1885] (worked with Hardy on theory of functions); death anniversaries of John Machin [1751] (use of series to compute over 100 digits of π) and Vivienne Malone-Mayes [1995] (asymptotic analysis; fifth African-American woman to earn a PhD in mathematics [in 1966])

June 10: birthdays of Mohammad Abu’l-Wafa [940] (introduction of tangent function; mathematical astronomy) and Pierre Duhem [1861] (mathematical physics); deaths of André-Marie Ampère [1836] (PDEs, chemistry, and physics) and Antonio Cremona [1903] (introduced use of graphical methods in study of statics)

June 11: Birthday of Hilda Hudson [1881] (algebraic geometry); death of Wilhelm Meyer [1934] (invariant theory)

June 12: Birthdays of Paul Guldin [1577] (Guldin’s Theorem) and Vladimir Arnold [1937] (solution of Hilbert’s 13th problem; 2001 recipient of the Wolf Prize); death of Jean Frenet [1900] (differential geometry)

June 13: Birthdays of James Clerk Maxwell [1831] (study of electricity and magnetism), Ernst Steinitz [1871] (abstract algebra), William Gosset [1876] (“Student”‘s t-distribution), and John Nash [1928] (game theory)

June 14: Birthdays of Nilakantha Somayaji [1444] (mathematical astronomy, series for arctangent), Andrei Andreyevich Markov [1856] (probability theory), Alonzo Church [1903] (computability; lambda calculus), and Atle Selberg [1917] (zeta function); death of Colin Maclaurin [1746] (analysis)

Sources:  Ivor Bulmer-Thomas, “Guldin’s Theorem-Or Pappus’s?”  Isis 75 (1984) 348-352 (for information on Guldin’s Theorem and the controversy over its provenance);   the MacTutor History of Mathematics website (for dates and biographical data generally; for the image of Paul Gulden)

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