The consultation on mathematics for Horizon 2020 has proven a great success and it also brings the message, loud and clear, that mathematics have a lot to offer to science and innovation. The response has exceeded all our expectations both in terms of quantity of responses and in the quality of contributions received.

The report highlights the importance of collaboration between sciences and mathematics, and between mathematics and the industry. It will be presented within the Commission in the context of the drafting process of the Horizon 2020 Work programmes for the period 2018-2020.

There are several fields of mathematics emerging as areas for future development, and some very interesting mathematical tools and methodologies are proposed. Most importantly, many contributions to the consultation highlight the necessity of working across silos: we should build bridges between mathematics and other fields such as biology, chemistry, physics, finance. Moreover, within mathematics a collaboration between different mathematical fields is essential to respond to future needs.

Mathematics does not cease to bring surprises: for example topology was deemed a rather theoretical subject years ago when I studied it. Now it is proving very important for big data analysis. There are some interesting contributions on this.

It is indeed clear that to tackle the big data challenge and to be able to extract that wealth of information that lies within, new ways to employ existing mathematics, and even new fields of mathematics may be required. New methods to sample and extract the necessary data without losing key information are needed. HPC and its development towards exascale, not to mention quantum computing, are fields where mathematics plays a key role.

Modelling, simulation and optimisation (MSO) has also proven to be a field of crucial importance. MSO is hugely important to the industrial processes for manufacturing, from aviation and automobile industry to fashion design and life sciences' industry - and it relates closely to big data and implies serious computing power requirements, hence a link to HPC.

Biomathematics is present very strongly with some excellent contributions. As I have heard a fellow mathematician say, "biology is the new physics". We believe that the role of mathematics will grow strongly in this field.

There are other, equally important fields touched upon in the contributions. We will analyse this all and aim to publish the report by end of June on this platform. Thank you to all contributors!

Finally, we would like to inform you that due to the success of this discussion, we have decided to hold a session on mathematics during the ICT Proposers Day on 26-27 September in Bratislava. The session that will take place on 27 September aims to bring together mathematicians and potential proposers for topics where mathematics are needed, such as those relating to simulation, modelling, requiring creation of algorithms or big data analytics. The full programme is available.