Maxims typically date back many years, but “feed a cold, starve a fever” may beat them all. This saying has been traced to a 1574 dictionary by John Withals, which noted that “fasting is a great remedy of fever.” The belief is that eating food may help the body generate warmth during a “cold” and that avoiding food may help it cool down when overheated.
But modern medical science says the old saw is wrong. It should be “feed a cold, feed a fever.” From Scientific America