What exactly is number theory, and what drives researchers to dedicate their careers to this field? How does this seemingly abstract branch of mathematics connect to the cryptography that secures our digital world?

A couple of weeks ago, Luxembourg hosted the 33rd Journées Arithmétiques, providing us with the perfect opportunity to explore these questions. We sat down with two mathematicians: a visiting researcher and a local expert, offering insights from both international and Luxembourg-based perspectives.

Our first guest is Prof. Jennifer Balakrishnan from Boston University, who led the team that cracked the notorious "cursed curve" problem. We couldn't resist discussing it and learning more from Jennifer about current big questions.

We also explored the mathematical foundations of cryptography with Tim Seuré, a PhD student at the Faculty of Science, Technology and Medicine (FSTM) at the University of Luxembourg, focusing on fully homomorphic encryption.

USEFUL LINKS:

More about Prof. Jennifer Balakrishnan: https://math.bu.edu/people/jbala/

Quanta Magazine article about cracking the "cursed curve": https://www.quantamagazine.org/mathematicians-crack-the-cursed-curve-20171207/

33rd Journées Arithmétiques: https://www.uni.lu/fstm-en/conferences/ja25/

Great Internet Mersenne Prime Search: https://www.mersenne.org/