Random and evolution...

I'm somewhat of a math geek.  OK, more like a wannabe, but I try to represent.  And I have a small bone to pick with the use of the term "random" in evolutionary science.  Here's my case..

Swiping some excerpts from Wikipedia... (My emphahsis added)

The modern evolutionary synthesis ascribes the observed diversity of life to natural selection, in which some random genetic mutations are retained in the gene pool due to the non-random improved chance for survival and reproduction that those mutated genes confer on individuals who possess them.

Why do bioligists drop the word random so easily into that definition?  I don't think they can say the genetic mutations driving evolution are random unless they intend to twist the definition of random to include things they haven't figured out yet.  I don't see anything like that in this explanation of random..

randomness implies a lack of predictability. Randomness is a concept of non-order or non-coherence in a sequence of symbols or steps, such that there is no intelligible pattern or combination. 

We do know genes can mutate for a reason ...

In molecular biology and genetics, mutations are changes in a genomic sequence:  the DNA sequence of a cell's genome or the DNA or RNA sequence of a virus. Mutations are caused by radiation, viruses, transposons and mutagenic chemicals, as well as errors that occur during meiosis or DNA replication. They can also be induced by the organism itself, by cellular processes such as hyperpermutation.

So why refer to the the beneficial gene mutations responsible for evolution as random and overlook potential patterns between environmental effects and  gene mutations? Why is that slight distinction even important?  Here's my thinking.. Genes mutating similarly among many individuals within a species due to a common environmental cause are more responsible for evolution than genes that just mutated randomly among individual members of a species.  

It accelerates the speed we might otherwise predict for the evolutionary processes.  If a beneficial genetic mutation happens only randomly it will be less likely to propagate its entire species than if a large number of a species experience the same beneficial genetic mutation after exposure to the same environmental cause.  Granted the same exposure will create unpredictable mutations from one organism to another, but in a large population patterns will result.
There is some recent evidence to support the case against random..  Lizards Evolve Rapidly Once Introduced on Different Island    Its not even plausible that such useful mutations occured randomly so soon. There must have been some environmental cause that resulted in the genetic mutation and the resulting leap forward in the evolutionary processes.  And in my book, if it happens for a reason, its not random.