I've come to be suspicious of anything in finance claiming to be "mathematically optimal". You can only optimise according to some simplified model, and simplified models of complex systems have a tendency to unpredictably break down.
Don't throw out the baby with the bathwater. Just because you have a large industry of sharks doesn't mean the good work being done by reputable investment houses is invalidated.
In general, index funds work. Some are better than others because of fees or their stock selection process. But they do work. The reason is that stocks in a sector have high covariance, and the outliers that might pop up occasionally with low covariance are only a small part of the index anyway. It is trivially easy to optimise on variance with some goal such as a limit on the number of holdings.
