A Churchill College mathematician attended an immersive nine-week research experience in Massachusetts, where he tackled original problems in number theory and probability, and learned that making mistakes is an essential part of discovery.
Ivan Bortnovskyi, a second-year Mathematics student from Ukraine, spent last summer at Williams College as part of the SMALL Undergraduate Research Project, working alongside approximately 30 other undergraduate mathematicians in the rural Massachusetts hills. The opportunity was made possible through a partnership between Churchill College and the Winston Churchill Foundation of the United States.
Unlike traditional summer programmes that provide close supervision and pre-defined problems, SMALL gave Ivan and his peers complete freedom to choose their research directions, working schedules, and methodologies. “At first, this level of freedom was overwhelming and many of us, myself included, struggled to decide what to pursue, knowing that some ideas could turn out to be intractable,” Ivan explained. “But after a few weeks, our ideas began to take shape, and we started making meaningful progress.”
Working in small groups of four to five students, Ivan participated in four separate projects: two involving signal processing and two focused on the Zeckendorf theorem, including the Ordered Zeckendorf Game and vector Zeckendorf decompositions. The teams met almost daily to discuss progress, with supervisors available for guidance but encouraging independent thinking and problem-solving.
One project proved particularly challenging, with Ivan’s group struggling for nearly a month without progress. With support from supervisors and peers, the team eventually managed to improve the uncertainty principle they were studying. “That experience taught me how much patience and persistence scientific work requires,” Ivan reflected. “Overall, SMALL gave me a realistic and inspiring view of how mathematical research is done and, most importantly, on this problem you can do it without fear of making mistakes.”
The programme wasn’t confined to research alone. Students explored the local area through weekend hikes, tried nearly every restaurant in the town, and Ivan also managed to fit in visits to New York and Boston. The research component culminated in conference presentations, with Ivan attending the 2025 Young Mathematicians Conference in Ohio and the Williams College poster session, where he connected with students from other summer programmes and presented his team’s findings.
The experience has significantly influenced Ivan’s career trajectory. Conversations with supervisors and exposure to various mathematical topics at conferences made him more confident about pursuing a PhD, recognising that it could open doors to both industry and academia.
Ivan’s groups are now finalising their research papers for submission, with hopes of presenting their results at future conferences. Some SMALL participants have gone on to publish papers and complete PhDs in Mathematics based on work begun during the programme.
Reflecting on his experience, Ivan is clear about the importance of making such opportunities available to students.
“Students can easily get lost in the different career paths available after graduation. Access to research internships and programmes like SMALL provides a different perspective on your subject and the chance to apply what you’ve learnt, which is vital for understanding which environment might suit you best.”
Ivan’s participation was enabled through the Winston Churchill Foundation of the United States, which generously covered the programme costs, with Churchill College providing additional support as needed.
