GOTTFRIED LEIBNIZ (1646-1716)

1684 – Germany

‘A new method for maxima and minima, as well as tangents … and a curious type of calculation’

Newton invented calculus (fluxions) as early as 1665, but did not publish his major work until 1687. The controversy continued for years, but it is now thought that each developed calculus independently.
Terminology and notation of calculus as we know it today is due to Leibniz. He also introduced many other mathematical symbols: the decimal point, the equals sign, the colon (:) for division and ratio, and the dot for multiplication.

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LEONHARD EULER (1707- 83)

1755 – Switzerland

‘Analytical calculus – the study of infinite processes and their limits’

Swiss mathematician. His notation is even more far-reaching than that of LEIBNIZ and much of the mathematical notation that is in use to-day may be credited to Euler.

The number of theorems, equations and formulae named after him is enormous.
Euler made important discoveries in the analytic geometry of surfaces and the theory of differential equations.

Euler popularised the use of the symbols  Π (Pi);  e , for the base of the natural logarithm; and  i , for the imaginary unit.
Euler is credited with contributing the useful notations   f (x) , for the general function of  x ; and   Σ , to indicate a general sum of terms.

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