The success of modern science is the ability to explain the apparent diversity of the physical world in terms of a finite number of constituent elements. Classification of sub-atomic particles, and Mendeleev's `atomic table' provide simple, finite descriptions of complex physical phenomena. The `double-helix' model of DNA gives a straight-forward structural basis for understanding biological diversity. Moreover `chaotic' phenomena, such as turbulence or the weather, appear to be describable--possibly even predictable--in terms of a small number of parameters. Science attempts to explain diversity through a few simple `universal' concepts.
In the science framework this is easily answered. All of us know that scientific theory requires mathematics:
Conversely, mathematicians have often anticipated the requirements of scientific theories. They developed new areas through a process of natural enquiry, motivated by aesthetic or structural reasoning. Mathematics provides the foundation for scientific theory and technological development.
In the current social arena the presence of mathematics is quite evident. Economic predictions based on statistical analysis--trends and underlying trends--appear daily in the papers. Pollsters shower us with their election predictions. Less evident is the enormous beneficial effect on public health of the application of statistical methods to epidemiology. The efficiency of mathematical scheduling procedures, on all forms of transport time-tabling, provides another intangible economic benefit.
My point is not, however, the diverse and pervasive influences of mathematics but its universality and timelessness. These are its most striking features and the root cause of its ``unreasonable effectiveness''.
The realization that two turnips and two politicians share an important common feature, their binary characteristic--in either case there are two of them--is a fundamental part of our intellectual process.
Although different counting procedures have arisen, the recognition of the value of enumeration itself has been universal. More technical concepts of trigonometry and geometry also were developed quite independently in distinct cultures: Asian, Incan, Arabian, etc. These concepts appeared as the natural solution to common problems such as navigation and construction.
Their mathematical expression encapsulates eternal truths.
Whilst linguists value the diversity of language--viewing each as a method of thought in addition to a method of speech--mathematicians value the universality of their discipline. One of my books is translated into Russian. Although I understand nothing of the translated text, the formulæ remain unchanged and completely recognizable. The essential content is invariant under change of language.
This aspect of mathematics--its universal, international, multi-cultural nature--is in stark contrast to the diversity of language. As the broad spectrum of language indicates a wide variety of thought patterns, the universality of mathematics indicates the existence of a unique core to the intellectual process.
Horace Rumpole, in summing up, frequently reflected that one simple precept, the `presumption of innocence', was the golden thread that ran through all of Common Law. I suggest that there is one golden thread that runs through all of human activity.
That golden thread is mathematics.