In German textbooks one sometimes finds the term "tiefliegendes Ergebnis" for theorems whose proofs require strong methods. The literal translation would be "deep lying result" but I'm pretty sure that I have never read this phrase in any English textbook.

So does anyone know a correct translation?

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    $\begingroup$ I don't know that there is one universally preferred phrase. "Deep result" would be fairly typical. Should say "deep laying" is not good usage. "Deep seated" would be better English, but I think just "deep" works. $\endgroup$
    – lulu
    Dec 12, 2020 at 12:44
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    $\begingroup$ "deep laying" should be "deep lying" (or just "deep"). $\endgroup$ Dec 12, 2020 at 12:56
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    $\begingroup$ @DavidC.Ullrich Thanks I've edited the question $\endgroup$ Dec 12, 2020 at 13:30

2 Answers 2


The word 'profound' works for both the figurative and literal meaning of 'tiefliegend':

1a : having intellectual depth and insight
  b : difficult to fathom or understand
2a : extending far below the surface
  b : coming from, reaching to, or situated at a depth

(source: Merriam Webster)

So 'profound result' may be what you're looking for.

  • $\begingroup$ Thank you. I will go for this translation. $\endgroup$ Dec 12, 2020 at 13:32
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    $\begingroup$ @BrunoKrams: Profound would be rather unidiomatic in the mathematical context; deep would be a far better choice. $\endgroup$ Dec 12, 2020 at 20:58

I would foster the use of "deep" as in "Deep result", subsequent to the comments by lulu, and by David C.U.

Exemplary usage by Math pros:


Withstanding the given Merriam-Webster-ian answer let me note that beside the English "profound" there is the French "profond" being the Latin-based etymological precursor of all, which also made it into German as "profund". And replacing the latter by "tiefliegend" would not be a completely synonymous substitution there.


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