A quote from Euler

Yesterday I paid tribute here to a great mathematician. Today I offer a quote from him.

"To those who ask what the infinitely small quantity in mathematics is, we answer that it is actually zero. Hence there are not so many mysteries hidden in this concept as there are usually believed to be."

The significance of that observation may not be obvious outside of some consideration of the history of math, the development of calculus in particular. But once we do a little grappling with that history, we see that Euler is making a point here that takes us back to ancient Greece. Back to Zeno, Achilles and tortoise. If Achilles is to catch up with the tortoise there must be a moment at which the difference between them is zero. One way of looking at the problem is to ask what is the next lower number -- one really really close to zero but still a positive number!

Euler here is saying "That is the wrong way of looking at it." Or, "don't create mysteries beyond necessity."

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