Digital computing is intimately tied to the representation of numbers. But long before abstractions like the number arose, there were mathematical concepts to serve the purposes … See more

Mathematical statements need not be abstract only; when a statement can be illustrated with actual numbers, the numbers can be communicated and a community can arise. This allows the repeatable, verifiable statements which are the hallmark of … See more

Starting with known special cases, the calculation of logarithms and trigonometric functions can be performed by looking up numbers in a See more

By the late 1960s, computer systems could perform symbolic algebraic manipulations well enough to pass college-level calculus courses. See more

Eventually, the concept of numbers became concrete and familiar enough for counting to arise, at times with sing-song mnemonics to teach sequences to others. All known human … See more

The "brain" [computer] may one day come down to our level [of the common people] and help with our income-tax and book-keeping calculations. But this is speculation and … See more

The numerical solution of differential equations, notably the Navier-Stokes equations was an important stimulus to computing, with See more