Eight months ago, the Sicilian friend Vincenzo Cutello (Enzo) paid a visit to Jack, carried out with him experiments on homogeneous texture transformations in Photoshop, and persuaded Jack to plan a visit to Catania. In the following days, from a distance, I could follow Jack's travel plan taking shape — at the time, in fact, Jack as Skyping me quite regularly, mainly to report about his daily work on 3D-graphics, namely 3D modeling of African masks and the like. Jack had in mind to come to Italy in February 2009, to see Venice with his granddaughter, and to offer scientific conferences in Catania, Sicily, and in Trieste, in the northeastern part of Italy where I currently live.

Had it materialized, this dream would have added a new chapter to a long stream of interactions between Jack and a crowd associated with what Alberto Policriti at some point named "Computable Set Theory." The first chapter of this story was written thirty years ago, after Jack returned from a sabbatical leave of 1978, which he had devoted, in part, to computational logic for set theory, as witnessed by two of his co-authored by Martin Davis. In a season which Alfredo Ferro often evokes with Jack's words, "Any new results?" Jack began working with Alfredo, with me, with Michael Breban and others; later he would develop at IBM (Yorktown Heights) a prototype system for computational logic names Yulog, and would promote a series of weekly meetings at Courant in which many people took part regularly: Martin, Gregory Chaitin, Malcolm Harrison, Vincent Digricoli, Alfredo Ferro and myself.

When I left New York, at the beginning of 1981, Jack gave a valedictory for me, titled "Surmises on proof verification." I have here a couple of photos of that day, which I thought would be the conclusion of the story — at least for me. I didn't know, at the time, that one of Jack's favorite proverbs was "All that ends is short." Another relevant motto was cited by Diana at Jack's 65th birthday: "In dreams begin responsibilities."

Accordingly, the stream of activities inspired by Jack on computable set theory went on and on, it involved over the years Domenico Cantone (Mimmo), Alberto, Enzo, and many more. The youngest of this crowd, now aged 24, Alexandru Tomescu, only had a chance to interact with Jack via e-mail and phone, but spent many days experimenting with a proof-checker known as AetnaNova/Referee which Jack implemented in SELT, and set to work on a server at his place three years ago. (By the way, I regard this proof-checker as an important late achievement of Jack, and I wish several of us will find the energies to carry this project on.)

At the beginning of last February, as it had become clear that Jack would not be able to travel to Italy, I came to New York. During one week Jack and I exchanged many phone calls (among others, after urging me to go and meet Annie Liu at Stony Brook, he wanted to know everything about my visit there). Jack and I could not meet in person, during that week, but he transmitted several printed documents to me, thus demonstrating that he was as eager as ever to carry on his scientific activity and to foster similar enthusiasm on others. Some of the documents I received from Jack referred to our common project, others were presumably directions for future work (sometimes deeply rooted in research that Jack had undertaken many years ago). Among others, I received from Jack on a USB key a folder named "setl_bigstrings_and_database," which has a particular significance for what it recalls.

As a matter of fact, had Jack's travel through Italy this February taken place, it wouldn't have been the first of its kind. A long time ago—maybe ten years ago—Jack offered a conference on visual illusions in L'Aquila, a town in central Italy where I then lived, and then moved with Mimmo to the Lipari summer school organized by Alfredo in Sicily. In between, he made with Alberto and myself a quick touristic trip to Perugia and Siena, during which I would see him seized by a sort of contemplative mood a couple of times, for example when he realized—all by himself, since history was one of this passions—that we were standing on a field of a cruel battle of Carthaginians against Romans near the lake Trasimeno (3rd Century before Christ). But never, during the touristic trip, Jack forgot completely that we had left behind, alone in my house, my dog: at some point he alluded to her as "Pimpa abbandonata"; another time he said, more explicitly: "I feel that Pimpa is itchy and there's nobody there to scratch here." When we got back, Jack borrowed from Blockbuster the movie "Men of Glory", and set down to watch it with my family, Pimpa lying down at his feet.

That's when I began to separate more easily in my mind the myth of Jack Schwartz from Jack as a person. But in those very same days in which he showed such empathy for Pimpa and for ancient Romans, in my house, Jack began working on the implementation of "setl_bigstrings_and_database," a theme that he would later propose to Salvatore Paxia (Toto) as a topic for study, potentially interesting for his PHD dissertation. At the Lipari summer school, Alfredo placed Jack in the hotel room which had the best panoramic view of the sea; but on the last day of the school, with horror, Alfredo discovered that Jack had been so profoundly focused on implementing "setl_bigstrings_and_database" that he had not even rolled up his window blind, and had kept working on his Mac in darkness.

This has been Jack, for many of us: a person endowed with a rare ability to join deep empathy with others (even with Pimpa) and extreme, protracted concentration on his work. It's so sad that Jack is no longer among us, but there's no doubt that we will carry on the houses we began constructing together. We'll miss his friendship, his encouragement to continue doing serious work, his wisdom and sharpness of judgement, and—dare I say?—his sense of humour.

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