E.O. Wilson is truly one of the great scientists of our time. In addition to his very extensive portfolio of important and painstaking academic publications, he has won two Pulitzer prizes for general nonfiction. Wilson has fearlessly ventured into arenas such as sociobiology (applications of evolutionary biology to social behavior) and the boundary between religion and science, areas where others often fear to tread.
But Wilson is deeply mistaken when he claims that great scientific discoveries emerge from ideas without needing much training in mathematics.
For many young people who aspire to be scientists, the great bugbear is mathematics. Without advanced math, how can you do serious work in the sciences? Well, I have a professional secret to share: Many of the most successful scientists in the world today are mathematically no more than semiliterate. (E.O. Wilson)
That may possibly have been true 20 or 40 years ago, but it is certainly not true today. Literacy, even expertise in algebra, calculus, statistics and “discrete mathematics” (e.g., matrices) is already and will be essential. There again, perhaps Wilison’s career spent at Harvard led him to a different understanding of the term “semi-literate.”
We quite agree with E.O. Wilson that great scientists need not be great mathematicians, any more than great historians need to be prize-winning novelists, although though they do need to be able to write well and clearly. But this is not how his comments have been interpreted. And in this regard he is doing disservice to the field.
Indeed, one need only review the trajectory of biology for the past few decades to see that biology, like many other scientific disciplines, has gone from being math-and-computer-poor to math-and-computer-rich.
Consider, for a moment, the explosion in DNA sequencing technology. When the Human Genome Project was launched in 1990, many were skeptical that the project could meet its ambitious goal of a complete genome by 2005. The very slow rate of advance in the first few years did not look encouraging. However, behind the scenes DNA sequencing technology was galloping ahead at an exponential rate (even faster than Moore’s Law), and, in fact, the genome project had a near-complete draft by 2000, and a complete draft by 2003.
Since 2003, this technology has continued to fall in price at a breathtaking rate, and a $1000 genome will soon be within reach. Genomes have been sequenced for thousands of human beings, and hundreds of other species as well. In short, the field of biology is now awash in data, and analyzing this data for subtle clues as to disease, genetic disorders, and evolution will occupy the talents of biologists for the next several decades.
As a single example, maximum likelihood estimation methods (a sophisticated set of techniques based on probability theory and statistics) are now used to reconstruct the “tree of life” of evolution, including the most likely common ancestral genome of a set of present-day species. Such analyses require very sophisticated mathematics indeed.
We should add here that sequencing technology not only spurred a mathematics-and-computer revolution in biology, but it was also driven by clever ideas from mathematics and computer science, notably by Michael Waterman and Eric Lander. Their ideas were then generalized and subsequently made even faster by Craig Venter and his team, resulting in a revolution in DNA sequencing.
Similar trends can be seen in other disciplines as well. For many years, the field of cosmology, namely the study of the origin and evolution of the universe, was considered by many to be little more than fanciful theology. Then with the discovery of the cosmic microwave background radiation in the 1960s, followed by the development of the standard model of physics in the 1970s, the Cosmic Background Explorer mission in the 1980s, and Type Ia supernova measurements of the 1990s, the field became very firmly grounded in empirical data.
Today, the field of cosmology is awash in data, and analyzing that data is a premier challenge of the many physicists, astronomers and computational mathematicians who labor in this field. For example, analyzing the latest Planck satellite data is projected to require millions of processor-hours on some of the largest supercomputers, together with some of the cleverest mathematical algorithms that can be devised. And even more challenges lie ahead with future missions in this area.
Perhaps in an earlier era, one could be a great scientist without knowing a great deal of mathematics or statistics. But the sun is rapidly setting on that day. Moreover, it was not true of Einstein, Feynman, Dirac, Born, or Heisenberg, to name a few giants of twentieth century physics, or of great biologists such as Francis Crick, Rosalind Franklin, Hodgkin and Huxley or Sydney Brenner.
Scientists of the future, whether they be physicists, chemists, biologists, sociologists or medical researchers, will rely on deep understanding of computational techniques, machine learning, advanced visualization methodologies and statistical analysis protocols. Mathematics is the foundation for all of this. Yet unanticipated fields of mathematics will be critical—as Riemannian geometry was for Einstein’s relativity, matrix and group theory were for quantum theory, and game theory was for sociobiology.
Those scientists who, for whatever reasons, do not acquire sufficiently advanced mathematical expertise may be able to do some useful, primarily experimental, research work in certain fields. But increasingly they will be outside the mainstream of modern science, if they can gain employment in the field at all. Wilson’s own encyclopedic knowledge of entomology may explain some of his philosophy, and the truly brilliant can break most rules. That said, E.O. Wilson’s advice is most definitely not the advice needed for the average aspiring scientist.
It may be somewhat presumptuous for us to cite Charles Darwin, but in the Autobiography of Charles Darwin one finds
During the three years which I spent at Cambridge my time was wasted, as far as the academical studies were concerned, as completely as at Edinburgh and at school. I attempted mathematics, and even went during the summer of 1828 with a private tutor (a very dull man) to Barmouth, but I got on very slowly. The work was repugnant to me, chiefly from my not being able to see any meaning in the early steps in algebra. This impatience was very foolish, and in after years I have deeply regretted that I did not proceed far enough at least to understand something of the great leading principles of mathematics, for men thus endowed seem to have an extra sense. (Charles Darwin)
Darwin wrote this a century and a half ago. What would he say today?
[This also appeared in the Huffington Post.]
[Added 8 May 2013: Here is a related comment by Frenkel and Wu, which appeared in the Wall Street Journal (although this copy is a preprint).]