Cristian S. Calude, To Halt or Not to Halt? That is The Question. World Scientific, 2024
Cristian Calude, a former student and follower of Solomon Marcus, exemplifies the latter’s approach to understanding and practicing mathematics in the best possible way: namely, as a unified body of ideas, striving to avoid confinement to a hyper-specialized niche—though this does not exclude specialization and exceptional expertise in one field or another. Moreover, it’s about practicing mathematics in continuous dialogue with the arts and the humanities. I would call it humanism were it not for my hesitation to use such grand terms.
I’ve said „mathematics” even though Cristian Calude is a computer scientist. He has spent his life studying theoretical computer science, and he continues to feel intimately connected to the mathematics from which it emerged. This way of understanding his field, quite different from that of most contemporary practitioners who are more focused on immediate applications, has not hindered him. On the contrary, it has allowed him to become a highly regarded name in his domain. This is clearly evidenced by the list of his publications, collaborations with highly selective names, invited conferences, and the universities he has visited. What a pity that Professor Calude, now at the University of Auckland in New Zealand, left Romania before he had the chance to establish his school here.
This comprehensive and integrative approach to computer science is also evident in his recently published book on the Halting Problem. It is one of the most important and fertile problems in theoretical computer science, but it originates in mathematics and logic, stemming from Hilbert, Gödel, and Turing. Simply put, the question is: can we imagine a procedure (algorithm) that decides, in finite time, whether a computer program (any program, not a specific one) will halt at some point or continue running indefinitely? […]