How Mathematics Has Got Broader With Time

How Mathematics has got broader with time
Early Mathematics: Study of Quantities and Shapes
    • Areas: Number System, Algebra, Number Theory, Geometry
    • Foundational work by Euclid (Elements) and Pythagoras



  • Mathematics of change
  • Still the study of quantities, but changing ones
  • 17th century invention
  • Newton and Leibniz



  • Mathematics of chance
  • 17th century invention
  • Fermat, Pascal & Others


Analysis [Link]

  • Generalization of the ideas of Calculus – limit, continuity, differentiability, etc.


Abstract Algebra [Link]

  • Generalization of Classical Algebra
  • Study of Algebraic Structures
  • Mathematics of symmetry (Not just calculation of “quantities”)
  • Flourished in 19th & 20th Century


Extensions of geometry


Automata, Languages, Computability – Discrete Mathematics 

  • 20th century
  • Advent of Computers – finite state machine
  • Interest in Number Theory, Combinatorics, Graph Theory exploded

Network Science [Link]

  • Dynamic graph
  • Work begun in earnest in the late 20th and into the 21st century
  • Proliferation of Computer, Telecommunications and Social Networks.

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