Pure & Applied Mathematics Foundation
OVERVIEW
Mathematics is the study of quantity 
, structure , space , and change . Mathematicians seek out patterns ,[1a][1b] formulate new conjectures , and establish truth by rigorous deduction from appropriately chosen axioms and definitions .[1c] There is debate over whether mathematical objects such as numbers and points exist naturally or are human creations. The mathematician Benjamin Peirce called mathematics “the science that draws necessary conclusions.” [1d] Albert Einstein , on the other hand, stated that “as far as the laws of mathematics refer to reality, they are not certain; and as far as they are certain, they do not refer to reality.” [1]
Historically, applied mathematics consisted principally of applied analysis , most notably differential equations ; approximation theory (broadly construed, to include representations , asymptotic methods, variational methods , and numerical analysis ) and applied probability . These areas of mathematics were intimately tied to the development of Newtonian physics , and in fact the distinction between mathematicians and physicists was not sharply drawn before the mid-19th century. This history left a legacy as well: until the early 20th century subjects such as classical mechanics were often taught in applied mathematics departments at American universities rather than in physics departments, and fluid mechanics may still be taught in applied mathematics departments.[2a] As well as physics, engineering and computer science have traditionally made use of applied mathematics.[2]
