2. Mathematics and Classical Genetics (The Early Days)
From ancient times breeders of animals and plants were aware that progeny resemble their parents. Why did it take so long to pin down the ideas of inheritance we know of today? The answer seems to be that animal breeders did not have the paradigm of the scientific method to obtain insight. The leap forward that Mendel appears to have made was the mathematical analysis (statistical analysis) of his experimental data, obtaining connections between the phenotype (physical appearance) of the peas he bred experimentally with a conceptual model of how these phenotypes were related to an explanation of a genetic mechanism that explained what experimenters were observing.
Mendel performed a dramatic series of experiments that shed light on the fact that the traits that were inherited from parents were not blended versions of those of the parents but rather determined by unchanging factors. Today we think of these factors as the genes that reside on the chromosomes. Interestingly, Mendel had studied mathematics in Vienna, including a course with Christian Johann Doppler (1803-1853), who, though he is best known as a physicist, actually held a university appointment at one time in mathematics. Doppler emphasized Newtonian thinking as an approach to doing science, an approach that is related to today's use of mathematical modeling. Although Mendel's work was presented publicly in 1865 and published in 1866, surprisingly little notice was taken of it. Only with the rediscovery of his ideas about 1900 (by Hugo de Vries (Dutch), Carl Correns (German) and Erich von Tschermak (Austrian)) were steps towards a beginning theory of genetics organized. Ironically, there has been considerable recent work to try to understand exactly how Mendel thought about what the results of his experiments meant, and whether or not some of the data he produced was too good to be true! Furthermore, as time has gone on we now know there are exceptions to all of Mendel's laws.