Solomon's administrative wisdom shows up in details easy to skim past but worth noticing — twelve district officers reorganizing the kingdom's supply system, a peace so stable that "Judah and Israel dwelt safely, every man under his vine and under his fig tree" (1 Kings 4:25), a reputation for wisdom that draws visitors from surrounding nations. The Queen of Sheba's visit is the clearest single picture of how far that reputation traveled — she comes "to prove him with hard questions," sees the wealth and order of his court firsthand, and is left, in her own words, saying "the half was not told me" (1 Kings 10:1–7). Notice what actually impresses her: not just Solomon's answers, but the visible, functioning order of an entire kingdom run well. Wisdom, in Solomon's own writing, was never meant to be abstract cleverness — Proverbs defines it from its opening chapter as skill in actual living, "the fear of the LORD is the beginning of knowledge" (Proverbs 1:7), and the Queen of Sheba is seeing that skill applied at national scale.
Solomon's own writing — traditionally credited with Proverbs, Ecclesiastes, and Song of Solomon — gives you the interior of a mind that had both the wisdom Gibeon promised and, by his own later admission in Ecclesiastes, the wealth and pleasure to test every possible answer to what life is actually for. "I said in mine heart, Go to now, I will prove thee with mirth... I gathered me also silver and gold... and, behold, all was vanity and vexation of spirit, and there was no profit under the sun" (Ecclesiastes 2:1, 8, 11). Read alongside what actually happens to him later in 1 Kings, Ecclesiastes reads less like philosophy and more like a confession — a man who had everything Gibeon offered and then some, testing whether any of it could function as a substitute for the God he'd started drifting from, and telling you plainly, from the inside, that it couldn't.