Who is a Jew?

1. Where is it brought down that a Jew is someone who is born to a Jewish Mother? What is the basis for this statement if true? 2. With DNA testing proven to be accurate, is someone born to a Jewish Father but not to a Jewish Mother a Jew? Thank you for any information you may provide regarding this. Tizku LeMitzvot Rabbot

The Rabbis learn it from the verse in Devarim chapter 7 verses 3 and 4. The source in the Talmud is Kidushin 68,b. in the name of R' Yochanan in the name of R' Shimon bar Yochai. The explanation is that the soul of the child is through the mother. Therefore DNA testing has nothing to do with it. Even if we know %1000 that the child is of a Jewish father and the mother is non Jew the child is not considered Jewish. I heard in the name of Rabbi Y. Komietzki z"l from a very reliable source that if the father was a Jew and the mother a non Jew we should try to convert the child for the reason of zera kodesh - holy seed.