In what stage does the cell grow and copy it's DNA?

Up until 1938, paleontologists accepted the idea that coelacanths (an ancient fish) went extinct at the time that they last appear in the fossil record, about 80 million years ago. but in 1938, a live coelacanth was discovered off the coast of south africa that was compared to the fossil record and found to be the same species what goal of science does this discovery represent