HILBERT, DAVID.

Ueber die Darstellung definiter Formen als Summen von Formenquadraten.

Leipzig, B.G. Teubner, 1888. 8vo. Original printed wrappers, no backstrip. In "Mathematische Annalen. Begründet durch Rudolf Friedrich Alfred Clebsch. XXXII. [32] Band. 3. Heft." Entire issue offered. [Hilbert:] Pp. 342-50. [Entire issue: Pp. 309-456].

First publication of Hilbert's fundamental and exceedingly important paper on real algebraic geometry. "In 1888, David Hilbert published an influential paper [the present] which became fundamental for real algebraic geometry, and which remains an inspiring source for research even today." (Pfister & Scheiderer).

David Hilbert, one of the most influential mathematicians of the 19th and early 20th centuries, is probably best known for the "Hilbert Problems" - a list of twenty-three problems in mathematics all unsolved at the time, and several of them were very exceedingly influential for 20th century mathematics.
He is regarded as one of the founders of proof theory and mathematical logic, as well as for being among the first to distinguish between mathematics and metamathematics.
"Hermann Weyl described his teacher Hilbert's style: "It is as if you were on a swift walk through a sunny open landscape; you look freely around, demarcation lines and connecting roads are pointed out to you, before you must brace yourself to climb the hill; then the path goes straight up." (Princeton Companion to Mathematics).

Order-nr.: 44427