Short answerMostly true
Hexagons tile a surface using the least wall material, and wax is expensive for a colony to make — so the shape is genuinely efficient. But the bees are not calculating it: cells start closer to round and settle into hexagons as worked wax flows at cluster temperature.
A genuinely optimal geometry, a very old admiration for it running back through classical writing, and the natural assumption that an optimal result implies somebody optimising.
Of the shapes that tile a plane without gaps, the hexagon encloses the most area for the least perimeter. For a colony that must convert a substantial quantity of honey into every gram of wax, that saving matters, and the geometry is a real economy rather than a coincidence.
This is worth getting right because the mathematical-genius framing is common and it makes the actual explanation less interesting than it is. An efficient structure arising from material behaviour and simple work rules is a better story than a bee with a protractor.
Widely repeated and not supported by current evidence. Listed so the correction is here rather than only the claim.
Cells begin closer to circular and the hexagonal form emerges as worked wax settles under surface tension and packing at cluster temperature. The efficiency is real; the calculation is not evidenced.
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