Do white wines have tannins?

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Dear Dr. Vinny,
I'm still not convinced about the absence of tannins in white wines. If tannins are present in wood barrels, why are there no tannins in the wines, especially very old white Burgundies? Besides the acidity, how do they manage to age without tannins?
—Ricardo M., Miami Beach, Fla.
Dear Ricardo,
All wines have tannins, but white wines have much lower tannin levels than red wines. Tannins come from grape skins and seeds and barrels; unlike red wines, white wines typically aren't fermented with their skins or seeds, so the extraction of tannins in whites is greatly reduced. Good thing, too, since tannins can impart a bitter element, which would stick out more in a white wine than in a red. In whites, the ability to age derives primarily from acidity, as you mention, but also from alcohol and fruit extract.
—Dr. Vinny