In 2000 a physicist was asked to study the health risks of wireless networks. He found [PDF] that there “was likely to be a serious health hazard.” Except he was wrong.
In his research, Dr. Curry looked at studies on how radio waves affect tissues isolated in the lab, and misinterpreted the results as applying to cells deep inside the human body. His analysis failed to recognize the protective effect of human skin. At higher radio frequencies, the skin acts as a barrier, shielding the internal organs, including the brain, from exposure. Human skin blocks the even higher frequencies of sunlight.
Despite all the studies showing a link between smartphones and cancer being debunked, I don’t think this idea will ever go away.