By Volker Mehrmann
It is common wisdom that mathematics drives innovation in most areas of science and engineering, but also economics and social sciences. Mathematical modeling, Simulation and Optimization (MSO) provides the language and the tools for progress that goes beyond classical trial and error. As the reports from several countries, e.g., the UK, the Netherlands and France indicate, mathematics has a huge economic impact on the GNP and on the job market. Although much of this is indirect via work that uses mathematical methodology, there is a clear branch of mathematics, where the impact is direct and immediately recognizable: this is the area of industrial mathematics. This is reflected in the names of many national and international societies, including ICIAM or SIAM. Why is an area of mathematics that is so important, attracting so little attention and acknowledgement? Where are we failing?
So, do we need to talk about it? Yes we should, and we need to spread the word to the public much more than we currently do. Furthermore, there are not many people that are actually doing industrial mathematics. If one looks at ICIAM meetings or at funding by national or international funding agencies, industrial mathematics is rather negligible.
How can we as industrial and applied mathematics societies improve industrial mathematics?
Attitudes towards industrial mathematics Before I give some suggestions how to improve industrial mathematics, let me quote some citations that I have overheard and noted at recent ICIAM/SIAM etc. meetings.

Industrial mathematics is not as beautiful as doing analysis or discrete mathematics

This person has not proved a theorem in years, why is he giving a plenary talk? • Industrial mathematics is weak mathematics.

There is nothing really new, it is just application of wellknown results. We should leave this to the engineers

My numerical method has been proven to converge for the model problem, why should I care to work on a industrial problem.

These industrial mathematics people only go after the money, they prostitute themselves.
We should ask ourselves: Is this the attitude of a minority or does it represent a mainstream opinion?
What makes industrial mathematics difficult?
The number of joint research projects with industry in most countries is very low. Why?
Integrating mathematics and statistics with software to perform analysis of physical systems. Photo credit: Wikimedia Commons
One reason is certainly that industry projects have very short time lines, where delivery of an MSO product or the solution of a problem on time is essential. Furthermore, in the industrial context mathematical software needs to work, i.e., give a solution, all the time, even if the problem is illposed. Data are often secret and the codes become intellectual property rights of companies. Legal problems are often hard to solve.
But, in particular, most of us (including myself) are not trained to do this kind of work or have the staff to do this in a short timeline.
What all of us can do
We definitely should change our attitude towards industrial mathematics. We need to learn to discuss with industrial partners (this means to learn their language) and we have to talk to governments and funding agencies to support the cooperation in topics that are relevant for industrial mathematics. We should also enter funding streams in high technology funding as proposers, and evaluators.
We should try to do work on the mathematics that is needed in practice and not just on the mathematics that we know how to do. We should educate young researchers that can do the whole life cycle of MSO and transfer to industry. We should go out to the public and talk about the great things that mathematics can do for society and then do it.
What mathematical societies can do
Mathematical societies should discuss with governments and funding agencies to set up programs where industry and academia can do joint research, (such as initiatives that exist in France, Germany, Italy, Japan, Spain, etc.)
They should help to create funding programs that cover the whole chain (which I would call the incubator model): from an application driven problem, implementation of fundamental mathematics to obtain needed insight, development of algorithms, solution strategies and software implementation and finally, closing the loop to transfer these developments to industry.
They should convince the mathematical community that mathematical challenges from industry are serious scientific challenges.
They should convince governments that new curricula are needed where young researchers are trained in the mathematical technologies that are needed for industrial mathematics.
They should support the community to change their evaluation strategies of mathematical research, as illustrated in the following graphics
They should help to set up research centers that proceed in this direction, where there is permanent staff of mathematical translators, MSO experts, mathematical engineers.
What governments and funding agencies can do
Interdisciplinary research and collaborations between mathematics and other sciences as well as industry should be supported. For this it is essential that the evaluation procedures need to be adapted.
Mathematical MSO should be included as a key technology in high technology research areas and experts in this area should become evaluators in the calls in these areas.
Governments should help to set up research centers in industrial mathematics.
What can ICIAM do?
The challenges and measures to deal with how to improve industrial mathematics are not new. The procedures have been installed in several countries and not in others. Here ICIAM should give support to communities that are not so well established in industrial mathematics. But that can only be a start. Success stories should be collected and published to show the impact of industrial mathematics on the wellbeing of society. We should discuss this topic more often and also as a Society help to change the attitude towards industrial mathematics. The reward will be multifold, it will be great for the whole mathematical community, it will bring research projects, money and jobs. It will lead to a lot of young people choosing this exciting field for their careers.
This post is being republished from the July issue of Dianoia, the ICIAM newsletter.

Volker Mehrmann received his PhD from the University of Bielefeld (Germany) in 1982. He is a recently appointed ICIAM OfficeratLarge and his research interests are in the areas of numerical mathematics/scientific computing, applied and numerical linear algebra, control theory, and the theory and numerical solution of differential algebraic equations. 