“by me.” The Hebrew text literally means “in me” and this is the use of the word “in” to indicate a close relationship, being “in relation with me,” or “in union with me.” The Greek has the same use of the word “in,” which some scholars refer to as the “static” use of “in.” We could have, and some people might argue we should have, translated this verse, “In union with me, kings reign,” etc.
The fact is, that as clear as it seems in English, the translation “by me” is somewhat shallow. It is not just “by” Wisdom that kings reign, but it is when kings and those in authority are truly “in union with Wisdom,” when they have a deep and internalized relation with her, that they can rule in a godly way like Jesus would rule. That is why it is vital for rulers and those in authority over others to take the time to really understand the Word of God. God’s word really is “Torah,” the instruction and guidance we need to live wisely and rule or guide others. God so badly wanted kings to understand His heart so they could rule over others in a godly manner, that each king was to write his own copy of the Torah (Deut. 17:18). [For more on the static use of “in” see commentary on John 10:38].
“rulers.” The Hebrew is actually a verb here, “the ones ruling,” but “rulers” read more easily and did not change the sense of the verse.