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I am interested in the way scientific and mathematical subject areas developed (and are still developing). One of the great visual tools that can help us gain insight in how these areas developed is by creating a "genealogy".

For the case of mathematics: I already asked about it here (on Quora). Although there is a genealogy of mathematicians, (take a look over here), to my knowledge there is no such thing for mathematical subject areas. There are a few so-called "mind-maps" that show how some (certainly not all) mathematical areas are connected, but they don't take into account the historical developments that are relevant (another example is the Mathematical Atlas made by Dave Rusin, which unfortunately currently can't be viewed online).

So, to come back to the question: do you know of any (annotated) genealogies of scientific and/or mathematical subject areas? I think those can be great to help one gain a broad perspective on the history of science and mathematics, however crude it may be.

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History of Mathematics Classification

To see how the classification of mathematics has developed historically, compare the ancient classification of mathematics:

  • Arithmetic (discrete math)
  • Geometry (continuous math)

to that of Descartes' era:

  • Analytic Geometry
    • Arithmetic (discrete math)
    • Geometry (continuous math)

to the 1868 classification in Jahrbuch über die Fortschritte der Mathematik:

  • History and Philosophy
  • Algebra
  • Number Theory
  • Probability
  • Series
  • Differential and Integral Calculus
  • Theory of Functions
  • Analytic Geometry
  • Synthetic Geometry
  • Mechanics
  • Mathematical Physics
  • Geodesy and Astronomy
  • (+ 38 subcategories)

to the modern zbMATH or MSC2010 classifications of mathematics.

History of Physics Classification

For physics, cf. my question "Classification of experimentally-determined physics laws?"

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  • $\begingroup$ Hello Geremia. Your answer regarding mathematics is mostly a classification of current mathematical areas. I am more interested in a diagram or genealogy that shows how these mathematical areas developed through time, roughly like the question you posted regarding physical experiments. $\endgroup$
    – Max Muller
    Jun 17, 2016 at 12:52
  • $\begingroup$ @MaxMuller As I mentioned here, C. S. Peirce (1839-1914), the greatest American philosopher-scientist IMHO, did some excellent work on the classification of the modern sciences (cf. this), including mathematics, but I don't think it's as detailed as you are looking for. Perhaps searching for a history of the classification of the sciences will help. $\endgroup$
    – Geremia
    Jun 17, 2016 at 14:42
  • $\begingroup$ @MaxMuller Mathematics used to be classified very simply (cf. my answer here): arithmetic (discrete math) and geometry (continuous math). By the time of Descartes, these two main branches merged into analytic geometry. Also, even Archimedes did combinatorics (cf. Archimedes Codex by Netz & Noel), which could be considered a "child" of discrete math. $\endgroup$
    – Geremia
    Jun 17, 2016 at 15:01

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