Rigor and Vigor in Mathematics

I just started reading Frequency Analysis, Modulation and Noise by Stanford Goldman. The writing is strikingly elegant and clear. Here is a paragraph from the introduction.

Rigorous mathematics has a rightful place of honor in human thought. However, it has wisely been said that vigor is more important than rigor in the use of mathematics by the average man. In the particular case of this volume, the amount of rigor will be used that is necessary for a thorough understanding of the subject at hand by a radio engineer; but when it appears that rigor will confuse rather than clarify the subject for an engineer, we shall trust in the correctness of the results established by rigorous methods by the pure mathematicians and use them without the background of a rigorous proof.

The back of the book says  “Professor Goldman’s exposition is both mathematically and physically enlightening and it is unusually well written.” So far I agree.

(I found the 1967 Dover paperback reprint of the original 1948 hardback at a used book store. I looked at Dover’s site while writing this and it doesn’t seem to be in print.)

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