Carl Friedrich Gauss - Function Quotes

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The function just found cannot, it is true, express rigorously the probabilities of the errors: for since the possible errors are in all cases confined within certain limits, the probability of errors exceeding those limits ought always to be zero, while our formula always gives some value. However, this defect, which every analytical function must, from its nature, labor under, is of no importance in practice, because the value of our function decreases so rapidly... that it can safely be considered as vanishing. Besides, the nature of the subject never admits of assigning with absolute rigor the limits of error.

Carl Friedrich Gauss

One should not forget that the functions, like all mathematical constructions, are only our own creation, and that when the definition with which one begins ceases to make sense, one should not ask, what is, but what is convenient to assume in order that it [remain] significant.

Carl Friedrich Gauss