Fundamental Science: How Much Does a Theorem Cost? And why is it so cheap?

A professional mathematician can carry out the most varied activities. From internationally competitive research to working in industry or public administration sectors. Two questions then arise: how much does a professional mathematician cost? Is it worth paying for?

This discussion is born out of the most fundamental motivation for those who pursue mathematical questions. In general, math doesn’t care to be useful or applicable. She just is. A theorem, a Pollock painting, a novel by Bessa-Luís or a film by Zanussi: when Nadirashvili and Vladut use non-associative algebras in the study of differential equations, it is like Godard bidding farewell to language in 3D.

The problem is that in a democratic society it is necessary to justify the cost of this intellectual adventure. Mainly because this same society accepts to pay for it.

Let’s simplify things and imagine that a professional mathematician has a Ph.D. in the field. Thus, the cost of producing a professional is associated with the cost of training a doctor. We can identify this cost with a scholarship; currently, and considering the main national development agencies (such as CNPq and CAPES), we are talking about 2,200 reais per month, for four years. Therefore, the total cost of producing a doctor would be 105,600 reais.

Once formed, this professional starts his activities. Unlike many basic and life sciences, mathematics has very cheap inputs: pencil, paper and mobility. Pencil and paper is easy to understand. But what about mobility?

It’s simple: the work of a mathematician involves discussing questions, problems, ideas. It involves listening to what is on the minds of colleagues, assimilating perspectives and, in many cases, understanding why some research directions are more interesting than others. The most efficient way to carry out this exchange is to circulate around. Visit colleagues abroad, bring employees into the country and participate in meetings in the area.

The cost of pencil and paper, let’s ignore it. But the price of mobility is important. In a year, it is reasonable to assume that a mathematician makes two visits abroad and receives two colleagues in Brazil. In addition to participating in two international conferences. In this scenario (which, I admit, is a little schematic), and considering a cost of 15 thousand reais per displacement, we are talking about 90 thousand reais a year.

It goes without saying that a professional produces, on average, one theorem per year (again, simplifying many things). If the price of a theorem is the cost of training a professional added to that of their work, it is easy to conclude: we are counting 200 thousand reais. It’s too little? Is very? To tell you the truth, it’s a bargain.

In 2013, a study by the British Engineering and Physical Sciences Research Council (EPSRC) looked at the impact of mathematics research on the UK economy. The study identified three major instances of impact of mathematics on the productive sphere: data analysis, security, and uncertainty handling. The manifestations of mathematics in industry unfolded in sectors such as manufacturing, retail, telecommunications, health and pharmaceuticals, transport and logistics, and public administration.

But the most curious thing is not the various areas of so-called “real life” in which mathematics appears. What stands out in this study are the numbers. In particular, the number of jobs created and the value added to the economy.

In 2010, research in mathematics in the UK was found to have generated more than 300,000 direct jobs. In public administration, including the defense sector, there were more than 200 thousand direct jobs.

Counter-intuitive, but positively surprising, are the more than 700,000 math-induced jobs in the hotel, food and… pubs sector! In general, and when considering only the year 2010, it turned out that almost 10 million jobs were due to mathematics.

And that’s all without considering the added value, whose numbers are stratospheric. In 2010, research in mathematics accounted for £556 billion of value added to the UK economy — around 40% of the total. Of this amount, 208 billion are directly linked to mathematics and arise in sectors such as banking and financial services, computing, civil construction and public administration and defense.

Whether for the simple elaboration of the spirit, for its impact on the modernization of society or for its effects on economic life, mathematics is an object of national interest. In its defense is the fact that a theorem has one of the best cost-benefit ratios in the world.

*

Edgard Pimentel is a researcher at the Center for Mathematics of the University of Coimbra and a professor at PUC-Rio.

Subscribe to Serrapilheira’s newsletter to follow more news from the institute and from the Ciência Fundamental blog.