Who Were the Celts?

I come from a family that took defiant pride in being Irish-American. My mother was about two-thirds of Irish descent, and I am, it turns out, about one-third Irish or Celtic. But what does it mean to be Celtic?

Recent DNA studies show that the European Celts (the original Celts) have no DNA connection to the Brits or Scots or Welsh or Irish. It is likely not true that the Celts ever invaded Ireland. What did permeate the British Isles was (probably) a language and culture spreading along the European coast. 

Millions of people in India today speak English, but that does not make them Angle-Saxons.

Red hair, I also learned recently, is a genetic gift from the Neanderthals. Or so they say.