The music of numbers

Javier Cilleruelo (1961-2016) will be greatly missed by his friends, colleagues and many collaborators. The following notes and pictures represent a humble tribute to his legacy, both mathematical and personal.

Javier had a delicate arithmetic intuition and a special taste for additive problems with a combinatorial flavour. As he used to say, he became attracted to number theory while trying to find magic squares of primes as an undergraduate, a problem suggested by Antonio Córdoba, who some years later became his PhD advisor. He was very keen on sharing his mathematics and newest discoveries.

"I will always remember those moments in the cafeteria in which his eyes would
light up, he would smile and, with his usual enthusiasm, would say: I am about to
tell you an interesting result.", Antonio Córdoba.

He had over 40 collaborators all over the globe. Having written more than 30 papers in the past 5 years, he was in his most creative and fruitful mathematical moment.

Founder of the Colombian research group ALTENUA as well as the Ibero American Number theory Network, Javier organized and participated in many mathematical meetings that have strengthened the connections between number theorists in Spain, Colombia, Mexico, Venezuela, Chile and Argentina.

He was a very passionate teacher and always took great care of his students. In his own words:

"Having PhD students and postdocs is a great responsibility, but it is immensely gratifying,
especially if in addition to having great mathematical potential they are also good people.
I have always been very lucky in that respect.", Gaussianos, 2011.

Javier was extremely generous. With his advice, his problems and his time. He enjoyed mathematical discussions and his enthusiasm was contagious.

Javier became one of the world experts on Sidon sets, made major contributions to problems related to these additive structures and was very proud of those. He found a very beautiful and remarkable construction of an infinite Sidon sequence that took many of us, and probably even himself, by surprise. He wrote a very nice book about Sidon sets in Spanish that contains a beautiful collection of problems.

In addition to his intense research activity, Javier was a great communicator, both for experts and the general public. He often collaborated in media to popularize mathematics, and number theory in particular. He created and directed for 16 years the section El diablo de los números at the RSME gazette and published several popular science books.