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Index using Historical Classification Systems

Here are the top-level areas of mathematics and related fields classified according to two systems used earlier in this century.

The first is the system used in the "Catalogue of Scientific Papers 1800-1900" published by the Royal Society of London in 1908; they continued using this classification system for another decade or so as Schedule A (Pure Mathematics) of the International Catalogue of Scientific Literature. The system often subdivides these roughly 200 headings into unnumbered subheadings, not shown.

The second is the set of about a hundred headings used by the "Jahrbuch über die Fortschritte der Mathematik" near the time it slowed publication about 1931. (Publication began about 1880, and ended around 1945.)

These systems are included primarily for historical interest; many of the most active fields of research during the twentieth century correspond to no field in these schemes. However, traces of these systems can be seen in the Mathematics Subject Classification (MSC) scheme developed several decades later and, with modifications, still used to classify current publications. The MSC is the basis for the organization of materials at this site. (In addition, the Library of Congress scheme includes several passages nearly identical to portions of the Royal Society schedules.)

Not shown in the Royal Society Scheme are the classifications of topics in applied mathematics, such as mechanics. (But no classification existed for Mathematical Logic, Ring Theory, Algebraic Topology, Numerical Analysis, Quantum Theory, and all the other fields of today's mathematics which were at the time at best minor or isolated topics!)

The headings in the Royal Society system are

Finer divisions within the headings above were enumerated; these are shown at the end of this document. The system used by the Jahrbuch used the following headings:

Here are the numbered subdivisions of the Royal Society system:

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Last modified 1999/05/12 by Dave Rusin. Mail: feedback@math-atlas.org