Digital Agenda for Europe
A Europe 2020 Initiative

Mathematics and Digital Science


"I could never have gone far in any science because on the path of every science the lion Mathematics lies in wait for you." Clive Staples LEWIS

Mathematicians work on the important practical issues of our era and their work impacts nearly every area of science, engineering and technology. Today, the abundance of data on social, technical, economic, ecological, and technological systems will need novel mathematical tools so that these data can help us tackle pressing societal challenges.

This online consultation aims to explore how mathematics can help science to better address the Big Data and high performance computing (HPC) challenges.

This consultation will stay open till 30 September 2014 and will gather opinions about:

  • The role of mathematics in big data. Could new mathematical methods (from e.g. topology, stochastic, probability theory etc.) help Europe fully profit from available data and solve main problems in data sciences? What methods can mathematics contribute to the data challenges? How can mathematicians, politicians, businesses and society best work together in making use of data to tackle important societal challenges?
  • The role of mathematics in HPC, in particular exascale computing.  In the light of the changes imposed on computing due to the data deluge: How can mathematicians help Europe advance towards data-centered  HPC?
  • The role of e-infrastructures in maths. Could e-infrastructures help resolve the biggest challenges in maths? How e-infrastructures could help mathematicians manage the existing level of complexity of mathematical problems in ways that are not feasible today and may result in significant scientific breakthroughs? What are the needs in terms of specific e-infrastructure services?
  • The impact of applied and industrial mathematics on innovation. How can we maximise it?
  • The preparation of the FET Proactive (HPC) and/or the e-Infrastructure Work Programmes 2016-17 under the Excellent Science pillar of Horizon 2020.
    Do you have a concrete proposal for a topic linked to this discussion to be included in the next work programmes?
  • Other suggestions for new mathematics related topics to be discussed online or in an upcoming workshop, including new practices in mathematics that could be stimulated by e-infrastructure and online collaborative media. Please suggest!

A workshop based on the outcome from this consultation will take place on 06/11/2014 in the premises of the European Commission in Brussels. The registration will open soon. At the registration page the workshop participants will have the opportunity to submit a request to make a presentation.

Background papers:

To join this discussion:

  • subscribe to the group (create an ECAS login (register) if you do not have one yet) though the consultation web-page,
  • then "log in" (link on top of the page) and enter your contribution in the "Add new comment" box, at the very bottom of the page.

You can also participate by commenting on submitted ideas and/or voting for them.

Please send any questions you may have about the process.



105 users have voted.


Manuel Cruz's picture

Maths can help a lot in industry for two main reasons: first, as lingua franca between engineers, physicians, mathematicians and executives (even with a mathematician as "translator") that is one of the fundamental premisses to have a good model for the scientific representation of real world processes.
Second, in a very competitive world almost all the SME's need to optimize their processes in order to become more competitive. The role of hand-made models (and corresponding software) is crucial, as the comercial products/software in the market usually don't take into account the particularities of their own companies. This fact, together with a precise definition of validity domains for each applied domain is crucial to a good and sustainable development.

48 users have voted.
Steven Bishop's picture

In the UK, we celebrate the work of Alan Turing whose mathematics was critical in advancing computing science. The UK Government have announced that a major Turing Centre will be set up with something like £42m set aside for this. In weather forecasting (surely one of the big users of HPC) mathematics has lead to jumps in improvement of our predictive power (e.g. for hurricane paths) that would not have been achieved by increased computer power alone. Steven Bishop, UCL
PS a new film is due to be released soon with Benedict Cumberbatch which will only increase the interest in this area

36 users have voted.
Steven Bishop's picture

Mathematics can play an important role in digital science distinct from its contribution to the big data revolution. The new applications of graph theory to networks is advancing our understanding of how patterns can be detected, understood and managed (ok controlled if you like) and this may yet provoke mathematicians to devise new mathematical techniques.

Meanwhile, some of the same methods can help sort and organise big data which may require HPC in order to manage distributed sources and analysis.

35 users have voted.
Steven Bishop's picture

Great point about mathematics being the common language and vehicle to carry ideas across international and discipline borders. As for SME's it is important to say that using mathematics even a single person can make advances showing that smaller groups can contribute to the digital revolution - it does not have to be the big data companies (although once you have an idea they will surely make an offer and so it may appear that only the bigger companies are making the innovative advances). Steven Bishop, UCL

25 users have voted.
Jordi Castro's picture

Mathematics, and in particular Operations Research and Mathematical Optimization, may be of great help in all these topics. For instance:

- Big data: structure detection in big social networks and information retrieval from "big data" databases can be formulated as a large mathematical optimization problem. Mathematics are also needed in big-data confidentiality issues: how to guarantee that individual confidential information is not disclosed?

- HPC: mathematical optimization problems are among the most CPU time consuming today algorithms, and they may require HPC infrastructures for its efficient solution. This includes exploitation of parallelism capabilities. At the same time, optimization problems are a source of difficult instances to test new HPC paradigms.

- Applied and industrial mathematics: all industrial problems, in any field, involve the solution of an optimization problem, either to minimize costs or to maximize benefits.

37 users have voted.
Tiziana Ferrari's picture

I would like to comment on the role of e-Infrastructures for Mathematics. European e-Infrastructures can support the computational needs of mathematicians by providing the capacity and capability in terms of storage and computing that may not be available locally to the scientist, as part of the ICT services offered by the home research institute.

The European Grid Infrastructure (EGI, provided to user communities active in the Mathematics domain 30 Million CPU hours of computation since 2004, where the largest amount of computing resources was offered by the Dutch national infrastructure, followed by CERN, France and Greece (

Being EGI a federation of national infrastructures, it can help mathematicians by offering the ICT services that may not be available locally/nationally. So far, EGI has offered services for Authentication, Authorization and Identity Management, computing and data management.

To date, we (EGI) lack a Virtual Research Community active in the Mathematics disciplinary area, so it is difficult to approach Mathematicians at a European level, most of these are being supported by the national e-Infrastructures as part of the long-tail of science.The EC could help EGI in approaching European networks of Mathematicians with dedicated workshops. Such events would help European e-infrastructures to better network with this European research community and to understand the needs both in terms of ICT capacity and capability.

24 users have voted.
Volker Mehrmann's picture

The development of new products or new production processes is at the heart of European industry. With growing complexity and shorter innovation cycles, mathematical modeling, simulation and optimization (MSO) becomes an indespensible prerequisite for the development of European Industry and technologies. The virtual product that accompanies the real product and allows product verification, risk analysis and product optimization is the future. For this we have to strengthen interdisciplinary cooperation and to include mathematical MSO into all major technology funding streams. European research groups have been very active to support this development but there is a strong imbalance within the Euurpean research area that needs to be balanced. The role of mathematical methods in big data and HPC is typically underestimated. Too much emphasis is paid on new hardware developments, here new developments require the incoporation of mathematical MSO.

The progress in performance in the methods is larger than in the hardware and this has to be continued.


Emphasis should be given to new mathematical methods and also to the creation of e-infrastructures that allow the whole European science community to make use of new methods.

To maximize the impact of MSO on innovation can be inparticular successful in the development of infrastructure networks, such as gas, electricity, communication, etc where the developments of the last years have been tremendous and where a major European research initiative may  allow in the near future to take a holistic point of view and to simulate, analyze, and also control and optimize a whole national or supranational network in its planning and in its operation. For this direction a FET initiative, bringing together the experts from the applications and from mathematical MSO, would be the right framework and could have a major impact. On the national level in some countries such initiatives have started, involving industries and academic institutions, but more national researchinitiatives should get involved from different countries.




41 users have voted.
Maria J. Esteban's picture

Mathematical tools are fundamental for the simulation processes that are necessary in the design of new technologies and procedures. Mathematical modelling carries with it robustness, stability and safety, in the sense that mathematicians can deliver solutions with error estimates and the knowledge that the proposed method does what it is supposed to do, which is not necessarily the case of any simulationMathematicians, allied with other scientists, engineers and computer scientists can make a big difference for companies involved in innovation and new technologies. But solving complex problems often needs to involve groups with different expertise, groups that do not necessarily come from the same place or country. In that sense, disposing of databases of expertise, past experiences and success stories in solving real life problems, etc, is of fundamental importance. Also having databases of successfully used algorithms and numerical or simulation methods to tackle particular problems. A European e-infrastructure devoted to the interaction of mathematics with new technologies and innovation would provide a prefect solution to share this kind of information and being able to build the ad-hoc experts' groups at best. Companies would be able to find the right people to help them with their needs.Another possible important aspect of an e-infrastructure in industrial mathematics would be to offer services to companies like a pan-European job market of experts or young people. Engineers and scientists working in companies could also be offered continuous education courses in the latest mathematical technologies in numerical computation, control, optimization, etc. Science advances quickly and it is difficult to keep in touch with the new tools that offer much better solutions. Such an e-infrastructure could offer such information and possibilities to companies which want to upgrade the scientific level of their engineers and scientists.Europe and the European economical competitiveness would certainly take a big advantage of the existence of such an e-infrastructure, providing the best existing services and solutions for companies aiming at building the most innovative solutions for all aspects of our European society.

41 users have voted.
Anni Hellman's picture

From the contributions already received, I am convinced we will have a very interesting workshop, alive with active discussions about mathematics and what it has to offer to tackle modern digital challenges. Many thanks for everything that has been posted already!

I have had today discussions with some mathematicians, both academians and those working with industry, all showing enthousiasm in getting together to discuss and identify mathematics as one of the powers behind the digital revolution. This will be a very interesting workshop, I am convinced!

The potential for mathematicians to contribute, at various levels, to the development of new digital tools and methods, is clear. That development potential and need is not only growing at high speed but at an exponentially growing speed. The more complex our environment becomes - the more data, the more powerful computers, the more linked everything is with everything else - the more demand there is for optimisation algorithms, pattern recognition, modelling, in general finding new, innovative solutions to tackle the new problems encountered due to new magnitudes. It will be good to identify what this means or can mean in practical terms - perhaps we can start that reflection at the workshop!

There has been discussion around a Virtual Research Environment for mathematics. This linked to a specific thematic field of mathematics, bringing together SMEs and researchers as well as research centres, mathematicians and technicians, to tackle and generalise mathematical challenges to serve the European research community, continues to be an excellent idea. Our Workprogramme for Research Infrastructures - one of the background documents - contains a topic inviting these interests to come together: Topic EINFRA-9-2015 – e-Infrastructures for virtual research environments (VRE).

As collaborators for industry, mathematicians have a lot of innovation potential - and can be solution oriented. Several areas are already mentioned in the comments: Mathematical modelling, simulation and optimization amongst others are areas which are key to both HPC development and Big Data, and on the other hand, can produce fantastic results from the vast amounts of data that we are struggling to find ways to tackle in Europe.

I thank you for all contributions so far and encourage new contributions!

Please key to your calendars the preliminary dates: at present we are hoping to organise the Workshop in Brussels 6 or 7 November. To be confirmed...

and ps: thanks for the tip on the Turing movie...! another Beautiful Mind -style I suspect!



28 users have voted.
Jesus Lopez-fidalgo's picture

The science of data needs a lot of Mathematical Statistics research to develop new robust procedures to deal with this (good) monster of big data. The support should be this and can not came from smoking sellers, whcich is a real threat out there with this topic. 

36 users have voted.
Group managers
Anni HELLMAN European Commission DG CONNECT deputy Head of Unit C1, einfrastructure
Sonia SPASOVA European Commission eInfrastructure Unit Project and Communication Officer
Group Participants