There is actually a science to this. Most women can see Mauve, and most men can't. This is because the brain interprets color the same way computers do - a combination of Red, Green, and Blue. However, the ability to see red is only in the 'X' chromosome. Therefore, women are twice as good at differentiating between colors that consist of red. Mauve is like purple, but it contains more red. However, since men are lacking an 'X' chromosome compared to women, the colors look the same.
In addition, of course Mauve exists. All colors exist, but our ability to see them is lacking. There is an infinite number of colors, we just give names to the ones we can differentiate between.
As a scientist I am forced to say it exists, but as a man I am forced to say it can not. Oh.. And neither does burgundy! Haha