Mathematical Manuscript Notebooks

The Only Known Mathematical Manuscript of Alfred North Whitehead [Whitehead, Alfred North]. Mathmatical Manuscript Notebooks. Whitehead (1861-1947) Writing in manuscript. [Unsigned and undated, circa: 1900]. Two composition notebooks. Quarto (202 x 160 mm). 50 ff each, written primarily on rectos in black ink, with a few notes on versos, each page with approx. 15-20 lines of manuscript. Ruled paper self-wrappers, first and last leaves toned and worn,some chipping to edges,corners worn, lower right corner of last 2 ff in vol.I missing with some loss to text. Fragile. Two sequential notebooks, divided into three sections as follows: Part 1: 21 pp, on ff 1r-20r of first notebook. In black ink, written on versos. Treating Karl Weierstrass's 1858 "Über ein die homogenen Functionen zweiter Grades betreffen des Theorem." Part 2: 64 pp, on ff 24r-50r of first notebook, and 1r-32r of second notebook. Treating Karl Weierstrass's 1868 "Zu theorie der bilinearen und quadratischen Formen." Part 3: 15 pp, on ff 34r-47r of second notebook. Treating Fredinand Georg Frobenius' proof of Karl Weierstrass' theorem. WITH: WHITEHEAD, J[essie) M[arie). Autograph notebook signed, ("J.M. Whitehead"), 60 pp. Cloth-backed flexible boards. Being class notes for librarian/archivist school, majority written in short-hand. The three housed together in a full calf clamshell. The only knownsurviving mathematical manuscript by Alfred North Whitehead.Manuscript material by Whitehead has never come to public auction, and in fact, any manuscript material by him is of the utmost rarity, with even institutional holdings being very minimal. It is common academic tradition to leave one'sNachlassto a favored graduate student or in a scholarly archive so that it may be available to future scholars. Leibniz, Wittgenstein, Nietzsche, and Gauss are just a few examples of scholars who left behind extensiveNachlässe. Whitehead chose to eschew this long tradition, and upon his death, "His widow destroyed all of his manuscripts, as he had expressly desired." (ODNB) Whitehead had an almost fanatical belief in the individuals' right to privacy, which explains his wishes to have his papers destroyed; he rarely even wrote letters to friends or colleagues. In 2011, a 6-page letter from Whitehead was donated to the Library of Congress from the estate of Whitehead's former assistant. In honor of this most rare item, the Library of Congress held a symposium focusing "on the historical context of the letter and on Whitehead and his intellectual focus in a number of fields. Whitehead seldom corresponded with anyone, and a receipt of a letter by his friends or colleagues was described as 'rare and cause of a communal celebration'. Further, Whitehead's family carried out his instructions and destroyed his papers." ("Experts to Discuss Famed Mathematician and Philosopher Alfred North Whitehead and a Rare Piece of Correspondence at Symposium on Feb. 17," Library of Congress News). In the present manuscript, likely written ca 1900, possibly in early preparation for his magnus opus, Principia Mathematica, Whitehead takes a deep look at several issues in mathematics, primarily in regards to bilinear forms, homogeneous functions, and quadratic forms, as discussed in the work of mathematicians Karl Weierstrass and Ferdinand Georg Frobenius, and citing the work of several other mathematicians, most notably George Salmon. Widely known as the "father of modern analysis" Weierstrass was a German mathematician who was one of the founders of the modern theory of functions. Very interested in the soundness of calculus, he made great contributions to the theories of periodic, elliptic, and Abelian functions, functions of real variables, the calculus of variations, and as in the second work analyzed in the present manuscript, bilinear and quadratic forms. The first section, titled "Weierstrass Monatsberichte der Königl. Akad. zu Berlin. 1858" and subtitled "Über ein die homogenen Functionen zweiter Grad. …