I wrote this essay for entry earlier this year for entry to the Galton Institute’s Mendel Essay Prize 2016, an essay competition open to British and Irish A-Level Students to write on Gregor Mendel and his legacy. I chose to write on what I identified to be Mendel’s principle contribution to biological thinking, a novel fusion of mathematical methods with biological subject matters, which in addition to furthering out understanding of inheritance and opening up the new field of genetics also provided a more rigourous mathematical framework which Biology has followed for much of the 20th century.

Abstract: Gregor Mendel is well known as the Moravian monk who in 1866 presented what became known as his Laws of Inheritance, later incorporated with Darwinian Natural Selection in the Modern Synthesis to form the basis of modern genetics. He is popularly seen as a model Baconian inductive scientist, however I will argue that Mendel’s true innovation was his synthesis of the two disciplines of combination theory and the study of inheritance. This allowed Mendel to describe a biological phenomenon using a mathematical model, a methodology adopted by that vast majority of 20^{th} and 21^{st} century scientists.

Scientific creativity is commonly seen as being either one of two apparently incompatible extremes. The first is that of logical creativity, whereby scientific discoveries are made and problems are solved through the use of logic and deductive and inductive reasoning. By this view, it is very likely that any particular theory would be postulated eventually, as all scientists use the same methods of reason and logic to reveal the same truths about the world. The other extreme is that of the creative genius, whereby the idiosyncratic cognitive patterns of a particular gifted individual allows, as William James writes, “the most abrupt cross-cuts and transitions from one idea to another”.^{1} Therefore, it is very unlikely that two geniuses will ever construct exactly the same theory, as each will have different ways of connecting ideas, whereas the laws of logic are always the same.

Gregor Mendel is popularly seen as the former; as a logical, deductive toiler. This concept of Mendel has it that, by carrying out many experimental crosses between plant strains, Mendel gained a large data set from which he logically coaxed out his Laws of Inheritance; making him a model Baconian inductive scientist.^{2} However, a closer reading of Mendel’s biography reveals that Mendel’s work was, as it is for all scientists, as much a product of his “standing on the shoulders of the giants” allowing him to “see further”, drawing on past scholarship in order to be creative. But crucially, Mendel’s creative innovation came through his ability to place one foot on the ‘shoulder’ of two different ‘giants’ and straddle the disciplines of mathematics and biology, and hence synthesis the two in an entirely novel and creative way.

Before Mendel, the study of inheritance was predominated by the idea of blending inheritance, whereby offspring inherited a combination all their parents’ traits, so would have an appearance midway between those of the parents.* *However, by the mid-19^{th} century, other scientific disciplines had fallen in the path of an all-consuming “‘avalanche of numbers’”^{3}. Therefore, it was arguably inevitable in this mathematically-fashionable context that another scientist would have applied some sort of mathematics principles to the problems of inheritance; indeed, both Hugo de Vries and Carl Correns did so independently, but not in so precise a manner as Mendel over thirty years earlier. The precision of Mendel’s Laws derived from his novel use of combination theory, which was taught to Mendel by its originator Andreas von Ettingshausen. Combination theory is a way of describing mathematically the arrangement of objects in a group in term of underlying laws, which Mendel readily understood and adopted.^{3} Therefore, Mendel’s innovation came in his ability to use his teacher’s tool to construct a mathematical model in the novel context of biological inheritance.

Though the destruction of Mendel’s experimental notes after his death means that the motivations for his experiments can only be guessed at, it is likely that Mendel approached the issue of inheritance with the hypothesis that the inheritance of particular traits was governed by underlying mathematical laws, derived from combination theory. In order to elucidate any laws present, Mendel had to use a deductive Newtonian, not Baconian, method: he first formulated a hypothesis and designed experiments to prove or disprove this hypothesis.^{4} The success of Mendel’s Newtonian methodology is shown by his ability to predict the ratio of pea pod colour in offspring produced by a monohybrid cross. Using modern terminology, Mendel’s experimental data shows that crossing together two heterozygous (Gg) green podded F1 plants produces F2 offspring with the phenotypic ratio of 3 green: 1 yellow, but with the genotypic ratio of 1 GG (green): 2Gg (green): 1gg (yellow), as the G (green) allele is dominant to the recessive g (yellow) allele. This F2 genotypic ratio can be determined using combination theory by simply multiplying out the F1 genotypes of Gg and Gg. Therefore, experimental observations confirm this mathematical model of the biological phenomenon of inheritance, permitting the adoption of this deductive, Newtonian methodology by much of 20^{th} and 21^{st} century natural science, to great success.

The Philosopher of Science Thomas Kuhn argued that scientific understanding consists of paradigms, or broad frameworks of theories. As experiments throw up anomalies in the current paradigm, the paradigm enters a period of crisis, leading a revolution after which a new paradigm is established.^{5} By synthesising the concepts of two different fields together, Mendel was able to creatively provide a revolutionary solution to the anomalies of blending theories of inheritance. Though Mendel lived in a period of interest in the application of mathematics, his ability to, as Robin Marantz Henig writes, “maintain […] two different mental constructs of the world simultaneously and apply […] the principles of one model to problems in the domain of the second”^{3} allowed Mendel to mathematically describe biological phenomena, a truly creative innovation not merely derived from inductive toil.

Mendel’s creativity does not fit neatly into either of the common conceptual extremes of scientific creativity. Mendel both carried out the “abrupt cross-cuts” of the genius in using combination theory to solve biological problems and underwent inductive toil to gather empirical evidence. Therefore, Mendel’s example suggests that scientific creativity cannot be achieved by one of these two extremes; rather only by combining logical problem solving with the “seething cauldron of ideas”^{1} of the mind of a genius can truly innovative and revolution science occur.

*Creativity in Science: Chance, Logic, Genius and Zeitgeist*. Cambridge, UK. Cambridge University Press.

*An Introduction to the Philosophy of Science.*UK. Clarendon Press.

*A Monk and Two Peas: The Story of Gregor Mendel and the Discovery of Genetics.*London, UK. Phoenix.

*Czech J. Genet. Plant Breed*.

**50**pp. 43–51.

*The Structure of Scientific Revolutions.*3rd Edition. London, UK, University of Chicago Press