SIMEON MICHAEL BALL
Universitat Politècnica de Catalunya, Spain
András and I first met in the mid 1990’s. We discovered we had a mutual interest, not only for the type of mathematics we liked, but also for playing chess and bridge and discussing everything from politics, society and education to science fiction, most notably a shared appreciation of Douglas Adams’ novels.
We had both been working on trying to classify functions over a finite field which determine few directions. The general feeling was that one should be able to classify those functions which determine less than half of the directions and this turned out to be the case. In 2001, András circulated a preprint (which finally appeared in print in 2003) in which he classified all functions that determine up to two-thirds of the directions, in the case that the field is of prime order. This came as a great surprise and I spent most of the summer of 2001 studying the preprint. In it, András introduced an ingenious method of estimating the dimension of subspaces of polynomial functions based on the degrees of the polynomials.
During the 2000’s I made various trips to Budapest. We shared many enjoyable times out and about in Budapest. As a collaborator, András was always a pleasure to work with. He had a great talent for sifting the good ideas from the not so good ideas. If András got enthusiastic about an idea, it was sure to be a good one. This is highlighted by his work with Tim Alderson. Tim was developing a promising model of non-linear extensions of linear codes. Together with András, they proved a wonderful result. Even to the non-expert one can appreciate the beauty of the following theorem just from the simplicity of the statement: every linear code which has an extension has a linear extension.
Universiteit Gent, Belgium
I met Andras for the first time when he was a TEMPUS student at Ghent University. This led to many future occasions where we met. We met in Budapest, in Ghent, and at international conferences.
Andras inspired me in many ways.
His PhD thesis contained results, obtained via the polynomial method. I read his PhD to understand the techniques he used and developed, and to see how I could use his results and techniques to obtain new results.
But a second technique inspired me also. Andras wrote two articles containing spectrum results on substructures in finite projective spaces.
In a spectrum result, the existence of a particular substructure is proven for every size k in a large interval [a,b].
These results inspired me to obtain similar results for other types of substructures. I gave this topic to my PhD student Cornelia Roessing, and this led to three new publications of Cornelia Roessing and I, one of which was also joint work with Valentina Pepe.
In this way, the work of Andras inspired other researchers. It also shows that one of the best things a person can do in mathematics, is to spread ideas.
By spreading ideas, this person helps other researchers to find new results.
In particular, the results that I obtained thanks to the inspiration of the ideas spread by Andras, also keep me remembering him as a nice cheerful person.