That was the assessment of the Society for Industrial and Applied Mathematics (SIAM) back in 1996. “This comment is still apropos,” they wrote in their latest report of 2012. “Although the mathematical sciences are pervasive, they are often invoked without an explicit awareness of their presence.” That was the very first paragraph of the introduction to a study recently released by the US National Academies, entitled, Fueling Innovation and Discovery (FID): The Mathematical Sciences in the 21st Century: A must-read! I have just ordered 20 copies to distribute to my university’s administrators, and to various science policy makers. ”Our first Coursera online course is on Game theory. It will be given by a faculty in computer science,” said the provost to the Board of Governors. I cringed in my seat.
How many around this table, I wondered, do realize that “Game Theory” is nothing but a relatively recent development in mathematics: a theory developed in the second half of the last century by two of my mathematical heroes, John Von Neumann (of Los Alamos fame) and John Nash (The beautiful mind).
Mathematics is everywhere, yet no other discipline suffers from such a curious case of invisibility, both in the business world and in the academic world. A recent Op-ed in Scientific American states: “The deepest mysteries are often the things we take for granted. Most people never think twice about the fact that scientists use mathematics to describe and explain the world. But why should that be the case?”
And most people, including Deans of Business schools, are not aware of how mathematics is driving innovation — in its most financially lucrative form, I must add. From the stochastic models and differential equations controlling the financial markets, to the advanced number theory used to protect credit card transactions, to the Fourier transforms performing instagram enhancements, to the eigenvectors determining Google search results.
People use the results of mathematical research everyday, yet they don’t seem to know it. Do you want a proof? Just go to any social event, announce that you are a research mathematician, and you will invariably get the inevitable question. What mathematics is there left to research?
In the business world, mathematics is invisible because it is often not called “mathematics.” It is called “analytics,” “modeling,” “operations research”, or simply generic “research.” Credit for applied mathematical advances may go to “information technology,” “industrial engineering”, “financial engineering” or just “plain engineering”. Unfortunately, it means that approaches to industrial problems that are based on new and sophisticated mathematical technology, could be difficult to sell to a higher management that is often not scientifically literate enough to appreciate it.
The FID report wonders how many people are aware of the mathematics used to make a single cell phone call –beyond the fact that we enter numbers in the decimal system, which are then converted into sequences of bits (zeros and ones)? Techniques such as “error correcting codes,” “linear and nonlinear filtering,” “hypothesis testing,” “spatial multiplexing,” “statistical waveform or parameter estimation,” are indeed at the core of wireless technology. They are all based on tools of the mathematical sciences, such as matrix analysis, linear algebra, random matrices, graphical models, and so on.” Yet, wireless technology is credited to engineers and “innovators”– whatever the latter means.
The OECD defines mathematical literacy as “an individual’s capacity to identify and understand the role that mathematics plays in the world, to make well-founded judgements and to use and engage with mathematics in ways that meet the needs of that individual’s life as a constructive, concerned and reflective citizen.” The OECD was thinking of 15-year olds, when they wrote this. They may need another definition for CEOs, business leaders, and university administrators.
Twitter had its own take on the situation: ”I just read that last year 4,153,237 people got married. I don’t want to start any trouble, but shouldn’t that be an even number?”
That Mathematics is also invisible in the academic world is a more subtle phenomenon, but much more painful. Painful enough to make me want to agree with physicist, Eugene Wigner: “Mathematics is a wonderful gift which we neither understand nor deserve.”
This will be discussed in a future blog entry, which will be dedicated to my friend, John Hepburn.