PROMYS Europe participants 2019

PROMYS Europe is a partnership of PROMYS, Wadham College and the Mathematical Institute at the University of Oxford, and the Clay Mathematics Institute. It is a programme designed to encourage mathematically ambitious secondary school students to explore the creative world of mathematics. Competitively selected pre-university students from around Europe gather at Wadham College, Oxford for six weeks of rigorous mathematical activity.

The aim is to provide an environment for talented young people that will arouse their curiosity and encourage a deep personal involvement with the creative and collaborative elements of mathematics and science. The programme encourages habits of thought that will lead to scientific independence and creativity. At the same time, it seeks to foster interaction between the PROMYS Europe community and the larger community of research mathematicians.

Through intensive work on an assortment of challenging problems in Number Theory, students practise the art of mathematical discovery. The problem sets encourage them to design their own numerical experiments and to employ their own powers of analysis to discover mathematical patterns, formulate and test conjectures, and justify their ideas by devising their own mathematical proofs. They are asked to develop new skills and to push the limits of their knowledge.

The PROMYS Europe community of first-year students, returning students, undergraduate counsellors, faculty, research mentors, and visiting mathematicians provides all participants with a highly supportive and collaborative environment within which to learn. Students are advised by resident counsellors: undergraduates who are embarking on their own mathematical careers at some of the finest universities. In addition, the returning students, who live in the same college housing as the first-year students, are an ever-present source of helpful hints and suggestions. Seasoned research mathematicians are a constant resource providing mathematical depth, support, and encouragement to the students.

The emphasis at PROMYS Europe is on asking good and creative questions, on hard work and persistence, on clarity of thought and precision of expression, on respect for people and ideas, and on the sheer joy of acquiring mathematical insight. PROMYS Europe participants are asked to work beyond their centers of competence and to push the limits of their knowledge. The PROMYS Europe community network provides all participants with a highly supportive and collaborative environment within which to learn.

PROMYS Europe is dedicated to the principle that no student should be unable to attend for financial reasons.

PROMYS Europe is closely modelled on the very successful PROMYS programme at Boston University. Professor Glenn Stevens, the founder and Director of PROMYS Europe is also the founder and Director of PROMYS. Since its founding in 1989, PROMYS has been sustained and enriched by two guiding principles: (1) an emphasis on mathematical habits of mind that support independence and creativity in facing unfamiliar mathematical challenges; and (2) a belief that mathematics is a deeply human activity best experienced within a richly interacting and mutually supportive community of learners including secondary school students, undergraduate and graduate students, and experienced mathematical researchers.

Key distinguishing features of both PROMYS and PROMYS Europe are the six-week duration, the immersion in mathematics, the collaborative rather than competitive environment, the focus on depth of understanding rather than contest preparation, and the students developing mathematics for themselves.

The close links between PROMYS Europe at Oxford University and PROMYS at Boston University enriches both mathematical communities.

Mathematics may well be the most widely misunderstood branch of the sciences. Young people contemplating careers in science find it difficult to imagine what a research mathematician really does. One common image features a mathematician programming a computer to do difficult calculations. Another pictures a lone mathematician working in isolation on ideas so abstruse that no normal person could comprehend them. Neither of these images comes close to capturing the spirit of mathematical inquiry. It is certainly true that many modern mathematicians use computers to perform numerical and geometrical experiments. But this experimental phase is only one component of the mathematical experience, and the use of computers in this phase is the exception, not the rule. Nor is it true that mathematicians work in isolation. Indeed, a distinctive feature of mathematics is the open sharing of ideas within a community nurtured by a common language, shared values, and shared goals. All too often, mathematics is presented to students as a highly polished and well organized collection of definitions, algorithms, and theorems. The long struggle of many individuals that culminated in this “finished product” remains a hidden secret. Students rarely learn of the dynamic nature of mathematics, nor do they see the creative side. They do not come to understand that mathematics is a thriving field of research activity which is progressing faster today than at any other time in its distinguished history.

These misunderstandings may stem from the fact that mathematics deals so heavily in ideas. In mathematics, perhaps more than in any other science, research is an activity of the mind. The primary goal of the mathematician is to understand – to discover the essential ingredients of complex systems in order to render them simple, to find order within apparent chaos, to draw analogies between different structures, and to find connections between seemingly disparate branches of mathematics and science. To make interesting new contributions in the field of mathematics requires a healthy mix of creativity, experience, and hard work. We aim to engage young people in the struggle to understand an intricate collection of significant mathematical ideas. Participants come with unbounded energy and are anxious to grapple with challenging ideas. At the beginning of their investigations, they may sometimes feel lost and perplexed. But through carefully designed problem sets, we hope to subtly direct students along productive paths towards understanding - to suggest that they experiment with examples and formulate conjectures, to encourage them to ask good questions, and to help them realize that through careful thought they can penetrate formidable obstacles and invent their own answers to difficult questions. The attitudes acquired through this experience will be even more valuable than the particular topics mastered.

Professor Glenn Stevens

Director of PROMYS Europe