Mathematics began with the earliest records of attempts to quantify time. The Ishango Bone, a notched talley stick discovered at Ishango in the Congo (Zaire) in 1960 by Jean de Heinzelin de Braucourt, and now preserved in the Royal Belgian Institute of Natural Sciences, represents, according to Alexander Marschak, a six-month lunar calendar. It is one of the oldest known objects containing logical or mathematical carvings. Other lunar calendars from about the same date have been discovered on other bones such as the Isturitz Baton, and possibly in cave paintings in Lascaux and elsewhere.
In 1970 Alexander Marshack published his innovative Notation dans les gravures du Paléolithique Supérieur. He argued that talley marks on certain bones represented a system of proto-writing, and proposed the controversial theory that notches and lines carved on certain Upper Paleolithic bone plaques were in fact notation systems, specifically lunar calendars notating the passage of time. Using microscopic analysis, Marshack showed that seemingly random or meaningless notches on bone were sometimes interpretable as structured series of numbers. Marshack expanded upon these ideas in his book, The Roots of Civilization (1972).