Exegesis:

kai edikaiōthē hē sophia apo pantōn tōn teknōn autēs ‘and the wisdom is proved right by all its children.’ The meaning of this saying in its present context is far from clear, and the interpretations vary considerably (see commentaries). There is no point in enumerating them. It will suffice to deal with a few questions which may influence the translation. (1) The clause sounds very much like a proverb which is applied by Jesus to the present situation in which both John the Baptist and he are rejected by their contemporaries. Since edikaiōthē hē sophia does not appear to refer to this rejection but rather to suggest some form of acceptance, it seems justified to interpret kai as a weak ‘and yet,’ or ‘but,’ though the (probable) proverbial nature of the saying does not commend an emphatic rendering of kai. (2) On the same grounds sophia seems to have some reference to Jesus himself, whether it is personified by him or refers to the ‘will of God’ (v. 30), which is realized both in John and in Jesus. (3) teknon ‘children’ of wisdom are those who accept wisdom as their true guide in life. They vindicate wisdom, i.e. they prove that wisdom is right, by their life, and/or by their acceptance of the message of John and of Jesus.

Translation:

Wisdom. To avoid that the word be taken as a reference to human wisdom one may better add a qualification, e.g. ‘God’s wisdom,’ ‘God’s wise ways,’ ‘that God is wise.’ For the noun see on 2.40.

Is justified by all her children, or in active construction, ‘all children of wisdom justify her, or, acknowledge/prove her to be right.’ For the figurative use of ‘children of’ cf. such renderings as, ‘people that spring from’ (Balinese), ‘those who belong to/accept,’ and cf. “all who are really wise” (An American Translation).

Adjustments and shifts like those just mentioned may result in such renderings as, ‘the knowledge of God receives right from all people that spring from it’ (cf. Sranan Tongo), ‘God’s Wisdom is known to be right by the doing of it’ (Kele), ‘God’s wise ways are acknowledged as right by all those who follow them,’ ‘all whom God has made wise acknowledge/prove him to be wise (or, the really wise One).’ Cf. also Good News Translation.

Quoted with permission from Reiling, J. and Swellengrebel, J.L. A Handbook on the Gospel of Luke. (UBS Handbook Series). New York: UBS, 1971. For this and other handbooks for translators see here . Make sure to also consult the Handbook on the Gospel of Mark for parallel or similar verses.