In 1844, Grassmann published his masterpiece, his "Die Lineale Ausdehnungslehre, ein neuer Zweig der Mathematik" Theory of Linear Extension, a New Branch of Mathematics, hereinafter denoted A1 and commonly referred to as the "Ausdehnungslehre", which translates as "theory of extension" or "theory of extensive magnitudes". Since A1 proposed a new foundation for all of mathematics, the work began with quite general definitions of a philosophical nature. Grassmann then showed that once geometry is put into the algebraic form he advocated, the number three has no privileged role as the number of spatial dimensions; the number of possible dimensions is in fact unbounded.