History of mathematics By jan2jan Period: 1875 to 1940 Axiomatisation of Linear Algebra 1887 Peano introduced n-tuples as vectors 1888 Peano: Axiomatic approach for vectors in geometry 1898 Peano: Geometry defined by vectors 1904 Hamel basis over the reals 1904 Hilbert first mentioned Hilbert spaces 1918 Weyl on axioms for finite vector spaces 1920 Banarch: Normed vector space 1920 Wiener: Normed vector spaces 1922 Hahn: Normed vector space 1925 Fréchet response to Banarch spaces 1927 Von Neumann on Hilbert spaces 1932 Banarch on linear functionals 1941 A Survey of Modern Algebra (Birkhoff & Mac Lane) A first general axiomatized description of linear algebra