What do you mean by 'prove'? If you mean whether or not there is evidence to support the theory of descent with modification through natural selection, then that evidence is overwhelming and includes (off the top of my head) nested hierarchies of species, the fossil record, observed speciation, homologous anatomical structures, vestigial and atavistic features, the geographical distribution of species and molecular biology.
Actually, one has to take into account that Darwin's books were written more than 150 years ago, and while the central concept is valid you can find many details that we have a much better understanding of now than we did then. For instance, Darwin had no way of knowing anything about the medium of heredity, commonly reffered to as DNA. The knowledge base of science develops over time to achieve a continously better understanding of the world around us and hence you can easily find faults with concepts that are now hundreds of years old.
This is in no way exclusive for biology, but applies to all disciplines of science. We now know that Newton was, to a certain degree, wrong about some things, as was shown by the Theory of General Relativity, which itself might end up being modified by Quantum Theory and perhaps also String Theory. The point is that science does not deal with absolute truths but rather accumulates evidence, facts and workable theories to enhance our understanding of the universe. And while some might see this as a weakness (for some reason :bigfrown ), it is in fact one of the greatest strenghts of science.
In addition to that I reffer you to lordkalvan's answer, which is correct in every way.
The evidence is there and overwhelming, you just need to take the time and study the material either by yourself or through a reputable educational provider like a University.
However, nothing can be proved, only supported by the evidence. I might add that you could have huge volumes of evidence and that can still be dismissed by closed minded individuals who claim they know all the truths and answers a priori.
yours
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