There are no races.

There is no biological meaning to the sentence "That person is a member of [XX] race."

This is not merely my opinion. It is the overwhelming consensus of experts in the field. "Race: Man's Most Dangerous Myth" by Montagu is dense but worth reading for its devastating and total refutation of the idea. A much more readable book covering some of the same subject is The MisMeasure of Man by Gould. Online resources that set forth the refutation of the idea of biologically meaningful races include: http://en.wikipedia.org/wiki/Race_%28classification_of_human_beings%29 and http://en.wikipedia.org/wiki/Race_and_genetics.

In the face of the above, you might think it unnecessary to propose yet another refutation of the idea of race. However, since so many people taken the existence of races for granted, since books, newspapers and magazines regularly reinforce the false idea by referring to people in racist terms (for example: saying Obama is black), it is necessary to make the argument mathematically.

Here is my mathematical refutation of "race" as a meaningful biological way to classify humans.

1. Those who defend the concept can not agree on how many races there are, or how they are composed. If humanity were actually divided into real races, then the number of races would not be in dispute. (For those who say that there are actual races but the definitions are "fuzzy" and the border lines are vaque are being sophomoric.)

2. Suppose, for the sake of argument, that there were, at this moment, exactly 4 (biological) races, and that every human could be assigned to one of them. Even if that were true today, it would not be true tomorrow because babies will be born whose parents come from different "races". It will never be possible to assign those babies to one of the existing (biological) races because the combination of genes possessed by those babies will be outside of the combination that defines the race of each of their parents.

In other words, even if there existed a moment in time in which all humans could be exactly assigned to a finite number of biological races, it would not be possible to do so in the very next moment in time.

There are no races.