The challenges of teaching mathematics and the future of research: Interview with Jean-Pierre Bourguignon
In this interview, we talk to Jean-Pierre Bourguignon, French mathematician, former President of the European Research Council (ERC) and member of the Board of Directors of the new International Centre for Mathematics in Ukraine (ICMU). He shares his experience and views on the state of mathematics in French institutions, its role in times of crisis and the impact of the pandemic on the careers of young researchers in Europe as well as some comments on his experience as ERC President.
Last year, in our Springer Monographs in Mathematics (SMM) series, you published an English translation of your famous Variational Calculus course. Can you tell us a little more about the importance of teaching in your life?
I've been affiliated with the French National Centre for Scientific Research (CNRS) for my entire career but have been seconded to several institutions. One of these was the École Polytechnique, where I was teaching from 1986 to 2012. As a full-time professor from 1986 to 1993, I developed and taught the course you mentioned to around 400 students every year.
Writing this course was a challenge as I had to provide the basics of an intermediate level course while tackling new and constantly evolving topics in mathematics. I really enjoyed the contact with the students, even if it wasn't easy to manage, as the motivation and commitment of the students varied greatly. Today, more than thirty years later, I'm delighted to see that some of my former students still remember the course, even have the handbook with them.
Over the last ten years, mathematics has lost 8% of its professorships in French universities, even though it is the discipline in which France excels the most1. How do you explain this contradiction?
This situation is very alarming, especially as student numbers have risen by almost 20% over the same period. The number of academic positions in fundamental mathematics has even decreased by 22%! All this is leading to a major deterioration in the working conditions of university professors, with a very strong impact on their ability to carry out high-level research, a reduction in career prospects and a risk of not being able to meet the growing demand for qualified mathematics professionals. A number of factors have contributed to this situation, not least the community's long-standing attitude to make much less use of local recruitment than other disciplines, a choice that often puts mathematics at a disadvantage in the allocation of academic posts. In addition, the majority of mathematician jobs are located in universities, with very few in research organisations (a few years ago, the ratio was 85%-15%).
Appropriate measures need to be taken quickly if we are to avoid a significant decline in mathematical research in France but putting them in place is not easy because of the autonomy of the French universities. The only way to generate the necessary support is to recognise that there is a national cause to be defended.
You have been elected as the first member of the Board of Directors of the new International Center for Mathematics in Ukraine (ICMU), which the Institut des hautes études scientifiques (IHES) is supporting in its first steps. Can you tell us a little more about it? How do you see the role of science and mathematics, in particular, in times of crisis?
The creation of the ICMU was an initiative of a group of Ukrainian mathematicians which received very broad international support, in particular from a number of eminent colleagues. The aim is to provide conditions conducive to the practice of high-level mathematics in Ukraine, even before the end of the war, by promoting international contacts for Ukrainian mathematicians and welcoming researchers from all over the world for research visits. In our modern societies, it is essential to bring basic research closer to practical applications and to train large numbers of young graduates to an advanced level. This is particularly important for mathematics, whose relevance to the economy has grown with modelling, the massive use of data and artificial intelligence.
After the war, Ukraine will need to rebuild and develop activities in cutting-edge, high added-value fields, which will require a high level of training in mathematics.
You have been President of the European Research Council (ERC) for just over 6 years. What was your experience?
Although I have followed the development of the ERC from the outset - I even chaired the first mathematics selection committee in 2007 - becoming President of the ERC in 2014 came as a surprise to me. The ERC is a programme designed by and for scientists, enabling them to support projects that they initiate themselves. It is the ERC's Scientific Council that is solely responsible for defining the programme each year, but it has been and is a constant battle with certain people at the European Commission who are uncomfortable with this governance by scientists. The quality and commitment of the members of the Scientific Council are essential to winning this battle. As President, I have had the privilege of meeting and talking to many high-level scientists at all stages of their careers - 2/3 of ERC grant winners are under 40!
Two things made this period particularly enjoyable: the quality of my relationship with Carlos Moedas, the European Commissioner for Research during my term of office, and the commitment and competence of the staff at the agency that manages the ERC. As President, I have also developed close relations with the world of politics, which has enabled me to better understand the crucial role of the European Parliament and to establish strong links with certain ministers.
In 2021, you called for an assessment of the impact of the pandemic on the careers of young researchers in Europe. What is the situation today, two years later?
The conference on early careers in research was organised in response to the pandemic's impact on young scientists, who faced severe restrictions on direct contact and travel. This situation led to signs of declining interest in pursuing research careers among doctoral students, risking the loss of a generation, particularly in Europe. The age of recruitment to permanent positions has risen considerably over the last few decades, further complicating the issue. The conference, held in Brussels in June 2022, involved partners such as the Portuguese Agency Ciencia Viva, Initiative for Science in Europe, and the CNRS. The French Ministry of Higher Education and Research joined the initiative at the last minute when a new Minister took office.
With the support of young researchers' organisations, the conference produced a manifesto focusing on early career issues. The manifesto's primary demand is a comprehensive European survey to assess the potential loss of a generation, as it remains unexplored on a continental scale. Some countries, like Germany, seem to have managed to mitigate the situation. However, without solid data, deciding on appropriate measures is challenging. Nevertheless, there is a growing awareness of the necessity for significant actions to enhance early career development, although the specific measures are not yet well-defined and there is a need for a long-term action plan.
About the author
Jean-Pierre Bourguignon is a French mathematician. He was President of the European Research Council from 2014 to 2019 and then interim President from July 2020 to August 2021. Specialising in differential geometry and its links with partial differential equations and mathematical physics, he is particularly interested in the Ricci curvature. A former student at the École polytechnique, he joined the CNRS in 1969 and taught at the École polytechnique (1985-2012).
He was Director of the Institut des hautes études scientifiques (1994-2013). He was President of the European Mathematical Society (1995-1998). He is a member of the Academia Europaea, the Spanish Royal Academy of Sciences, the Portuguese Academy of Sciences and the Royal Academy of Sciences of Barcelona.
He has been awarded several Honorary Doctorates: in 2008 by Keio University (Japan), in 2011 by Nankai University (China), in 2018 by the University of Edinburgh (Scotland), in 2021 by the Polytechnic University of Bucharest (Romania) and in 2022 by the University of Warwick (Great Britain) and the University of Primorska (Slovenia). In 2005, he was elected honorary member of the London Mathematical Society, in 2017 of the Deutsche Mathematiker Vereinigung and in 2019 of the Polish Mathematical Society.
