Mathematical skills have become strategic for the business world and the most advanced companies hire high level scientists who tackle the underlying, fundamental, theoretical questions. However, this increasingly vital role of maths specialists often brings with it new demands and unforeseen responsibilities.

**ParisTech Review – We can observe today computer programmes capable of processing increasingly complex sets of data, so maybe we could question the need for mathematicians working for businesses enterprises.**

**Jean-Pierre Bourguignon –** On the contrary, they are all the more necessary! We are at a historic crossroads, but I am not absolutely certain that the enterprise leaders or even the mathematicians themselves are fully aware of the challenges. To frame this in simple terms, the areas in which ‘advanced maths’ are involved have increased sizably in number compared with the situation twenty years ago. They are also more strategic in essence.

Two years ago, at a Medef (France’s Employer’s Confederation] seminar moderated by Philippe Martin, who, at the time, was Director of R&D with the Group Veolia, this very question was addressed. The exchanges revealed clearly that the fraction of professions in which a maths dominant was needed had increased considerably. The ‘math-nerds’ represented some 8-10% of qualified engineers in the labour forces. In the near future this will rise to 20%. This means that we need to draw conclusions in terms of training requirements and that the qualified engineers use their mathematics background more and better – and, of course, those for whom maths is their specialty, will become highly attractive on the job market.

A distinction must be made between ‘classic’ business affairs where off-the-shelf software packages are effectively carrying out an increasing fraction of the work load, via “computer processing funnels” and newer forms of the economy where the mathematical content has a wider spread. What we see today are new jobs and new economic models in which statistics and data processing play an important role. Data retrieval, structuring, transformation and exploitation call for very high level mathematical protocols. In graphs and images, there are now complex algorithms and it is in the formulation of the algorithms that we find the new added value.

**Are we talking here mainly about applied maths?**

Well, not only “applied,” inasmuch as technological progress stimulates research in basic mathematics and lots of topics still need to be explored, in terms of their theoretical contents. In fact, in the new context, basic mathematics cannot be separated from applied mathematics: they must be considered as an ensemble. This is not an anomaly: in the academic world, the French school of mathematics never separated basic from applied mathematics. But, in the business world, the key approach used to be mostly via applied maths. This world is now changing its culture, introducing a growing space for basic mathematics. I’m not just referring to Google® and data flow specialists, but to certain industrialists, notably German companies such as Mercedes or Siemens who are leading the field.

Let us look at an example: so-called ‘smart’ sensors, at the core of the digital urban area and are already imbedded in connected objects. These sensors compress data, making them transposable and useful. The process uses various filters and the intrinsic quality of the filter devices, as you may well guess, is absolutely primordial. Fundamentally, the filters are algorithms and the built-in filter quality depends on the degree of mathematical sophistication of these algorithms.

Thus we see that modern technologies embody more and more very high-level mathematics, at the crossroads of basic ‘sky-blue’ research and development of applications. In this emerging world, mathematical skills are worth their weight in gold.

**If we follow your reasoning, these skills are destined to evolve and consequently to shift to the stage centre?**

Indeed, not only is that correct but the challenge is so crucial that I must insist here. It has become necessary for very high level mathematicians to be able to confer with and understand specialists from other areas or employed in other functions. Classic mathematics training is not concerned a lot by this sort of question: mathematicians do maths, full stop. Under the new paradigm, the communication issue has become a core question – because of the continuity between basic maths and applied maths and with the new positioning of maths at the heart of our economic world.

This indeed explains why the position of corporate mathematicians has become a question with several entry points. It is obvious that companies need them. But, to respond correctly to the demand, these mathematicians also need to evolve and develop new skills, in a word, to change their professional profile or ID. Mathematicians must now be capable of responding to multiple demands, which requires not only a degree of flexibility but also a clear and informed vision of the rest of their activities. Their role, and increasingly so, consists of identifying solutions; this, in turn, carries a prerequisite: to really understand the problems set, *i.e., *to understand the professional problems which *a priori* lie outside their range of mathematical skills.

As I speak to you, this necessary evolution is ongoing and in certain companies, the changes have already been implemented. I mentioned Mercedes and Siemens earlier, but I could also cite Saint-Gobain, a French industrial group that produces high quality glasses for various uses ranging from photovoltaic panels to building cladding not forgetting transportation uses. The former Group Director of R&D, Jean-Claude Lehmann set up a small team of corporate mathematicians about 10 years ago. In the early stages, their skills were not over-stretched! But in just a few years, it was then realized that they had brought with them a high added value and they started receiving orders from very different sectors within the Group. These demands led them to studying veracious scientific fields (material physics, electro-chemistry …) and to become involved in highly varying activities.

Now let me give you another example to exemplify the added value of mathematics *per se* and the special efforts required of mathematicians today. Dassault Systems is a computer processing company, closely associated with the world of defence sector aeronautics. Their first success was with a software package called *Tatra*®, used in aircraft design work. The package was transformed into a multi-sector professional software, for use in a general design context and by extension in various building sectors. Managing such an environment is extremely sensitive, as you can well imagine, and it is decisive in terms of delivery dates and costs. The design and construction phases are carried out by several companies with their activities integrated on a highly complex computer processor platform. The processors are ‘’fed” not only with the base algorithms but also with the knowledge bases for material science physics, fluid mechanics, electronics … Modelling and integration of these various parameters involved combining the work of entire teams of high level mathematicians.

But the adventure does not stop here. Dassault Systems today are seeking to enter a new market-place, *viz., *the smart cities, with the objective to supplying its clients with a computerized tool that integrates all the urban parameters – from transport network management to environmental biology not forgetting energy transmission and distribution …. This is a very ambitious project that should ‘take’ hold in about 10 years times, and it includes a computer ingredient on can call “classic” (data management*, i.e.,* data retrieval, organization and processing) but also an integration of knowledge bases in an extremely sophisticated model. This is another case where we prefer to talk about high level mathematics rather than computer science development. The company is thereby developing itself and reinventing itself on the basis of this new set of skills, hitherto considered as peripheral and which today represent core corporate functions, *viz.,* the company’s capacity today to take mathematical modelling on board.

The economic challenge of mathematics should not be under-estimated. Marwan Lahoud (EADS) is often quoted as saying that an Airbus is better because it incorporates more mathematics than other aircraft. And how right he is! And other examples abound. Recently I had the opportunity to exchange with the Director of R&D for Nissan-Renault at Chennai. In India, it is not complicated to build cars: the mechanical engineering skills are there and labour costs are low. But what is more difficult to handle is driving on the roads, because of the traffic-jams prevalent in India’s cities. So what makes the difference, the market edge added value are the on-board navigation devices … *i.e.,* the on-board mathematics capacity. Added value of mathematics here is measured directly in terms of market sales fractions. Mathematicians in company contexts are moving closer to the core business: their work dovetails directly with economic reality. This alone is a considerable change.

Ten years ago, we had the impression that with the advent of computers, engineers would *unlearn* their maths and *learn* the rest, so to speak. It is the contrary that has happened. I am not sure, personally, that the mathematicians themselves have become totally aware of what the changes entail? But it would be to their benefit to widen the scope of their vision and be more ambitious professionally. It is fundamental that they demonstrate their basic curiosity in moving towards other sectors of knowledge, and that they prove capable of understanding problems – even (and maybe above all) those problems that are badly framed. That, in essence, is what corporate life is all about.

**In this light, should training in mathematics be reviewed, reorganized?**

No doubt at all here, notably by encouraging exchanges and building ‘bridges’ to other specialities beyond the basic maths-intensive course structure.

It is not just a question of stimulating and developing students’ intellectual curiosity, as dictated by an educational ideal, but also to understand the requisites of the period. This is just as important in mathematics as it is in other specialities. Technological sophistication brings in line deeper and more varied scientific skills. In a GPS device, for example, there are general relativity corrections. Twenty year ago, at Stanford, I was surprised to see two young engineers form the aeronautics sector following a course I was giving on this topic. As it turned out, they had simply understood before others that the course would be *useful* to them.

Moreover, Stanford seemed to a good model for the development of a techno-culture with a direct link to basic research. Students there are encouraged early on to spend time in laboratories. They are also encouraged to do an internship that will value add to their application file for admission to a graduate school (Bac+4 and 5). In like manner, returning to our French maths specialists, they would be well advised to move out of their ivory towers.

**But if enjoying close contacts with other specialities seems primordial, this alone is not enough, obviously. Nicole El Karoui, Professor of Mathematics at the University Paris 6 Pierre & Marie Curie, pointed out this difficulty in a paper published recently by ParisTech Review, as applicable to finance. It is not easy over only a few months to train high level statisticians in finance, its dynamics, its professions, its regulatory modes…**

Professor El Karoui was quite right in making her assertions and indeed, they invite other more general remarks about the role maths specialists can occupy in enterprises. Let us, however, try to place things in perspective. Financial affairs offer an excellent observation point, since mathematical sophistication of certain financial products came under accusation after the subprime crisis. Every bank has a Quants Department [quantitative analysts] and they all developed products in their specific market sectors … making sure that the competitors did not benefit from the data retrieval procedures or results. But these models were based on stochastic measurement, *i.e.,* randomized sequences: in order for them to be robust or ‘rugged’, as we say, they need to be “fed” with lots and lots of data. And it was precisely at that time that such data became rare and invaluable. They were ‘privatized’ instead of being shared by all and this led to models that were insufficiently robust. One of the elements that led to the crisis therefore was the coincidence of a theoretical explosion and a shortfall of data. Bankers simply had not understood that they should have share their data resources.

Several lessons can be drawn from that experience: firstly, in the case mentioned, the applications dominated theory; secondly, it is essential to move the available data into the public sphere – in the case, they were clearly common property. Thirdly and finally here, the maths specialists just were not able to make themselves heard and I really want to underscore this fact. In the context we are referring to today for the purpose of this interview seems very important for me that the maths community be listened to, all the more so given that the economic stakes associated with their work are so high and will continue to be so.

Two interpretations are possible here. For the entrepreneurs, thy have a special interest in moving their maths specialists upstage and to the fore, so that such strategic skills as they possess can be implemented at the highest corporate levels. Mathematicians are not ‘in power’. Some leaders, though sheer ignorance, have them do things that turned out to be, in fact, damaging – first and foremost for the company itself and secondly, also for their environment as we saw in the case of the banking sector financial disasters. Some companies have realized how important it is now to valorise such skills, for example, Schlumberger, who treat their mathematicians and their scientists well in terms of their pay-scales (to be more precise, they are treated on a par) and are present now in the highest echelons of the company. In like manner, the high level of recognition that PhDs receive in Germany is certainly an asset and an advantage to Germany industries.

But my message today also concerns the mathematicians themselves. They now form a highly intermeshed, connected community comprising some 100 000 persons round the world, who share a same cultural acquired background, a common language and who are now familiar with networks and networking. They must be given the means to have their voice heard when the stakes are down, or when they work on some major topics – climate change, finance, … you name it … where their mathematical models are involved and used. They themselves must understand the vital need and use of discussions, dialogue and debate and also to listen to others. They are henceforth at the heart of enterprise and global progress as a whole. That carries power but also confers responsibilities.

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