I'm finding very hard to choose the words to respond to Nicolas's sad
news. Any formulation of this message seems to me inadequate to
celebrate appropriately Peter's contribution, and the importance that
his work and his friendship have had to me.
I began to ear about Peter's work in proof theory and constructive
mathematics when I was an undergraduate student at the university of
Padova, around 1995. If I remember correctly, he came to spend a
sabbatical year at the Padova mathematics department two years later.
During his stay, he gave an introductory course on constructive
mathematics. I remember how I found unique his ability of giving crystal
clear presentation of fundamental concepts and proofs, at the same time
preserving their complexity and richness in shades.
As Nicola says in his message, this clarity of thinking, the capability
of getting to the root of the discussed matter, has been since something
I found unfailingly in each and every of his scientific contributions.
Peter has been an external referee of my Ph.D. thesis. I had the
privilege of collaborating with him, and of benefiting of a number of
conversations, on the occasion of many conferences, and when he invited
me in Manchester. I will always be grateful to him and his family for
their kind hospitality.
He knew and understood far more than he wrote. I vividly remember his
curiosity and the sparkle in his eyes when he got an idea to pursue,
even after his retirement, an enthusiasm I rarely found in younger
scholars. This curiosity, and desire of investigating new areas, are
perhaps responsible for the fact he did not bring the book draft with
Michael Rathjen on Constructive Set Theory to final version. If that
book had actually seen the light, I think the current landscape of
constructive mathematics would be considerably different.
Despite its clarity and importance, his work on constructive mathematics
has still largely to be understood by the wider constructivists
community.
As Nicola has written, he was a very kind person. However, he also was a
radically rigorous and intellectually honest scholar, he would not have
agreed with you on something for politeness. This characteristic made
his appreciations and criticism of great value for his interlocutor.
He will certainly be deeply missed.
Giovanni Curi