Without knowing precisely what genes were, working mostly alone with humble plants in a monastery garden, Gregor Mendel formulated his laws of inheritance. Essentially, he created the science of genetics. Mendel used thousands pea plants for his experiments, as he tried to discover what caused variations in pea flower color and placement, pea pod shape and color, pea color and smoothness, and size of the plants. It took him two years to even begin his first experiment, because it took him that long to be sure he had bred unmixed strains of plants with each trait. Throughout, he made great use of mathematics, to reason out the implications of his discoveries.
In 1865, Mendel delivered a paper explaining why when he crossed a white-flowered pea plant and a purple-flowered plant, for example, the offspring always had purple flowers. He explained this by describing a "factor" for purple flowers as Dominant. It always prevailed over the white flower "factor". But when he bred these second generation purple flowers to each other, the result was that one quarter of the pea flowers were white. This, he explained, was because the white factor was hidden, what he called Recessive, but it was not gone. Each plant, he concluded, had two factors for color, one received from each parent. If the second generation plant received two purple factors, it would be purple. If it received one purple factor and one white, it would still be purple, because the purple trait would dominate the white. Only if the plant received two white factors could it be white.
Starting with two pea plants with one purple and one white factor each, on average, of four offspring one would have two purple factors, two would have one purple and one white factor, and one would have two white factors. Only the plant with no purple factor could be white, because any purple would dominate, and hide, the white factor.
He also experimented with tall and short peas, and with peas having smooth and wrinkled seeds. Each time, his experiments proved that each plant received two factors, one from each parent. Mendel also experimented with crossbreeding pea plants while studying more than one characteristic. He found that, in his plants, traits were inherited separately. Thus, the tendency of a plant to be tall, for example, had nothing to do with its tendency to have white or purple flowers. The results of hours of patient plant breeding and observation he codified as his two laws.
The Law of Segregation is the first of his laws. According to Mendel, each plant has two alleles (he didn't call them that, but modern geneticists do) governing each trait, which are found throughout the organism. When the plant reproduces, these alleles separate, and one of them is chosen randomly to be included in the seed of the next generation. So in the case of a plant with one purple factor and one white, half the time the offspring would get the factor for purple, and half the time the factor for white. The other parent, assuming it was also a purple and white mixture (a hybrid), would also contribute a white allele half the time, and a purple half the time.
The Law of Independent Assortment is the second law. This law states that each trait is inherited separately. Thus the tendency of a pea plant to have smooth or wrinkled seeds would have nothing to do with its tendency to have flowers of a certain color.
Mendel's findings were uniformly ignored. Only in 1900 were papers written referring to his research. At that time, three separate researchers wrote papers, and his hard work obtained the recognition it deserved. Then, when Thomas Hunt Morgan, who won a Nobel Prize for his work, added his insights about chromosomes to Mendel's foundation, classical genetics became the science we know.
AMENDMENTS TO MENDEL'S LAWS
Mendel somehow chose his subjects, the pea plants, well. Inheritance in peas is full of examples of complete dominance. But not all inheritance works that way. Incomplete dominance is quite common. Hair color is an obvious example. Also, contrary to the Law of Independent Assortment, many genes that are close together on the chromosomes are linked, and are inherited together. None of this of course, takes away from the monumental achievement of Gregor Mendel.