The limitations of geological periods, imposed by physical science, cannot, of course, disprove the hypothesis of transmutation of species; but it does seem sufficient to disprove the doctrine that transmutation has taken place through 'descent with modification by natural selection'. -- Lord Kelvin (Of Geological Dynamics, 1869).
It might seem odd that I start a post about evolution with a quote claiming natural selection is inadequate to account for the transmutation of species. It is, though, highly relevant to what I'm going to discuss in the post, and strikes at the heart of why it's fundamental for us to understand the theory of evolution by natural selection. See, in 1869, Lord Kelvin's position was fairly reasonable, and, as you'd expect for a man of such high scientific standing, the available evidence in physics did seem to conflict with Darwin's theory. The Sun was one particularly salient point of contention: to get the diversity of species we see on Earth, evolution needs a long time to work (on the order of hundreds of millions, if not billions of years), yet according to 19th-century physics the Sun could only have been burning for 40-million years.