John Wallis mathematics |

## Infinite and infinitesimal

In 1635, Bonaventura Cavalieri
introduced infinitesimals,
which he called indivisibles,
as a means of calculating areas and volumes.
John Wallis’s treatise on conic sections
clarified Decartes’ work on analytic geometry
and introduced the symbol ∞ for infinity
and the symbol 1/∞ for the infinitesimal.
Wallis’s work *Arithmetica
Infinitorum*
finds the area under a curve by integration
and established the principle of interpolation
to derive the value of π.
Thus Wallis, James Gregory, and Isaac Barrow
contributed to the development of integral calculus
put to use by Isaac Newton and given
modern notation by Gottfried Wilhelm Leibniz.

## Infinity symbol

The infinity symbol, ∞, the digit 8 on its side, traces a closed path without an end. More could be said approaching the symbol but not what it symbolizes unless turning into itself.

## Negative numbers

John Wallis introduced the number line and interpreted negative numbers as values greater than infinity rather than as less than nothing. Me, I think of negative numbers as mere arithmetic conveniences and I’ve learned there are positive infinities greater than infinity.

James Gregory stated and proved the fundamental theorem of calculus for a special class of curves; Isaac Barrow proved the fundamental theorem in general, showing that differentiation and integration are inverses of each other. Isaac Newton was a student of Isaac Barrow.

See also in

The book of science:Zero—BrahmaguptaNumber system—Leonardo Pisano Bigollo (Fibonacci)Fundamental theorem of calculus—James Gregory, Isaac BarrowCalculus—Isaac Newton, Gottfried Wilhelm LeibnizPrincipia Mathematica—Isaac NewtonPi—Johann Heinrich Lambert, Ferdinand von LindemannReadings in wikipedia: