Measuring the worth of Mathematics

There is a sense where every self-directed extended human activity has an economic value. If nothing else the opportunity cost when occupied doing one (more or less productive) thing, as opposed to other (less or more productive) things. If the time thus spent is directed to some external project, it figures in the ultimate balance of value that stems from the project however accounted (cost-plus; capital gain; assurance; demand shift; monetarised policy objective; speculative gain…).

Mathematical training equips for a class of problems/ projects that require abstract thinking (or thinking in the abstract), bridging the conceptual gaps in tackling a new domain, or revisiting a well trammelled domain where new parameters or boundaries apply.

Advancing the corpus of mathematical knowledge is (or should be) the standard against which all subsequent application is made. This is how the subject is taught: abstractions beget abstractions. This is also the hardest to claim monetary value. A life time in mathematics does not leave such visible monuments; indeed some of the best mathematicians have led short and ignominious lives, yet their work is as central to the concept of the discipline as any public achievement by a Pasteur in biology; a Fermi in physics; a Davey in chemistry all of whom can claim to have added and continue to add to economic achievements.

It is necessary to show the derivative mathematics that most of us acquire in our school years is qualitatively different to mathematics as practised in and of itself. It might equally be said that conversance and fluency in the theory of statistics has placed the products of statistical reasoning in the hands of other scientists, indeed of most people working with real and unruly data sets and tameable. Then why still invest in the discipline?

There is a large element of speculation in any investment in core disciplines, as distinct from support for the governance mechanisms at the core of enterprises, public or private. Existing knowledge base is for many purposes sufficient; its mastery is implied in standard disciplinary training. Managing uncertainty when expressed at an executive level reduces to a question of  personality: only rarely is it seen as scientific. That scientific authority is contested makes its dismissal easier, and makes the case for investing in the hard disciplines of science tenuous.

Yet it is the creative output of these disciplines – the part most speculative – that yields dividends, that renews the worth of the discipline for the public, and from whence comes its most direct source of authority – external as well as internal.

But is it really such a high stakes game? A state rests not on force of arms but on its cultural strengths – the well being of its people; its history reconciled to its present course; its interpretation of its history and the reconciliation of past and present; its resilience to the uncertainties of nature. And its respect for the process of questioning old and acquiring new knowledge; not as elided into net current productive value but in another economy – what we need to know collectively about the world in which we are immersed if we are to be truly human.

There is a misconception about science that sees it as universal, as trafficable, as imperial; draftable into one or another enterprise of the state or its proxies in the market. This appears to be a truism as only such bodies can afford to build the scientific edifice, can align forces towards some goal (the eradication of malaria, sending a man to the moon); as if science can be engineered.

Of course it can, and there are natural alliances obvious when science is providing the knowledge in knowledge-based industry.  Unfortunately the power of engineering – encapsulated in the idea of high technology, is too easily mistaken as the standard of worth for the disciplines that have fed it. The culture that allows those disciplines to thrive, hinges on a respect for knowledge in the large, as well as those elements of knowledge that contribute to economic progress.

Economies become vulnerable when resting on the marketable only, on what works. Things work, or make a profit, or generate jobs and wealth, only up to the limits of ability to meet the unforeseen. Unforeseen is what is totally external (or seemingly so) like a GFC or a meteor or a war or an eruption; equally what has not yet been fully observed (unforeseen effects of a treatment); or properly internalised (adverse effects of fertilizer treatment); or manipulated to give a profit at the expense of competing values (sand mining; drilling the reef; mining antarctica; cross contour plowing). In other words what has been operationalised on market knowledge, not a forensic analysis of performance or public answerability for the use of privatised  knowledge.

The impacts of economic activity should be as accountable as the productive capacity generated, and it is as much an engineering as a scientific question as to how to design a process that is tuned to its environment.

This leads back to the core disciplines founded as they are on human experience, and aspirations. By bringing together the transformational goal of the activity (‘adding value’) and the transactional implications it may be possible to humanise progress to the extent of reducing cost and distributing benefits . That we think about ourselves in this fashion is a constant; the way we do is as process-tied as progress in the disciplines concerned: advancing by long periods of quiescent mastery, and short bursts of creative change.

How then do we measure the health of a discipline like mathematics?  One way is in the strength of renewal; the quality of teaching; the export of success; the attraction of collaborators; peer recognition (important in a competitive market for talent). Another way is in the breadth and sophistication of application, the passage from discovery to problem application; and its reverse, of public awareness of the role of the discipline, of skill value in innovation teams, in quality assurance for industrial process, in the construction of algorithms, of software, in the spawning of satellite disciplines – analytics, computer programming, genomics, biometry, actuarial science, evaluation, operations research. In each case the core is not questioned but the application builds the apparatus for understanding the foundational knowledge in context of solving a problem or feeding a process.

These two pillars separately define the social and economical worth of the discipline – what the discipline stands for – and prevent it from spiralling into debased obscurity, or pseudo-knowledge. They are the foundation for intervention, and authority; they will draw the next generation of trained scientists and consumers of science (the public, in government, among the entrepreneurial class). Both celebratory and performative they are inextricably linked.

A crude model for economic value (deriving from the state investing in the core disciplines) involves accounting for influence: students – through direct teaching, textbooks, examination, inspiration, extension – colleagues – administrative support, collaboration, superstructure; industrial partners – consultancies; algorithms/ software; the public at large – cultural element, adding to the national coherence, and respect for its institutions, attracting collaborative agreements, diplomacy; government – advice, policy contributions.

Not all can be measured by output through to outcome without the use of models or speculation (or both). Yet all provide indicators of health; can be used to detect deficiencies, and costs (opportunity costs), inefficiencies and flow on effects. This overall health combined with standardised output measures will identify the value of the discipline and the sources and fluctuations of that value over time.


Prepared ahead of a two-day meeting of the academy of sciences in the context of a consultancy on the economic gain from national core science investment.

Useful further reading

Stephan, P E (1966), The economics of science, Journal of Economic Literature, 1966 – JSTOR

Dasgupta, Partha and Davids, Paul A. (1994)Towards a new economics of science Research Policy 23(1994) 487-521

natureOUTLOOK, Assessing science, lessons from Australia and New Zealand, 24 July 2014/ Vol 511/ Issue No 7510