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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OSBORNE REYNOLDS (1842-1912)

1883 – UK

‘The ratio of pressure forces to viscosity forces in a fluid flow’

The Reynolds number is a dimensionless quantity (that is, it has no units). The number has great importance in fluid dynamics.

The number depends upon the speed, density, viscosity and linear dimensions (such as the diameter of a pipe or height of a building) of the flow. Fluid flow is described as ‘Turbulent’ when the number is greater than 2000. It is considered ‘Laminar’ (steady) when the value is less than 2000.

Reynolds presented the concept of a number to determine the type of fluid flow in a paper –
‘An experimental investigation of the circumstances which determine whether motion of water shall be direct or sinuous and of the law of resistance in parallel channels’
– in the Philosophical Transactions of the Royal Society.

He observed that the tendency of water to eddy becomes much greater as the temperature rises –
he associated temperature rise with a decrease in viscosity (the resistance of a fluid to flow).

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[To] mechanical progress there is apparently no end: for as in the past so in the future, each step in any direction will remove limits and bring in past barriers which have till then blocked the way in other directions; and so what for the time may appear to be a visible or practical limit will turn out to be but a bend in the road.
— Osborne Reynolds
Opening address to the Mechanical Science Section, Meeting of the British Association, Manchester. In Nature (15 Sep 1887), 36, 475.