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📢 New Info Session: Going Abroad! 🌍✈️
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🗓 Wed, 5 May | 1.30 pm
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Join us and start your adventure! 🎓✨
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Two recent non-technical pieces on the philosophy and practice of mathematics:
"Mathematical methods and human thought in the age of AI", by Tanya Klowden and myself: https://arxiv.org/abs/2603.26524 (also discussed in https://terrytao.wordpress.com/2026/03/29/mathematical-methods-and-human-thought-in-the-age-of-ai/ ). This was a solicited piece for a forthcoming compendium in the philosophy of mathematics.
"What does it mean to think like a mathematician?", https://terrytao.wordpress.com/wp-content/uploads/2026/03/talk-ver-3.pdf . These are slides for a talk I gave during a Pi Day (Mar 14) event at the local Curtis Center. The talk will be posted shortly.
Artificial intelligence (AI) is the name popularly given to a broad spectrum of computer tools designed to perform increasingly complex cognitive tasks, including many that used to solely be the province of humans. As these tools become exponentially sophisticated and pervasive, the justifications for their rapid development and integration into society are frequently called into question, particularly as they consume finite resources and pose existential risks to the livelihoods of those skilled individuals they appear to replace. In this paper, we consider the rapidly evolving impact of AI to the traditional questions of philosophy with an emphasis on its application in mathematics and on the broader real-world outcomes of its more general use. We assert that artificial intelligence is a natural evolution of human tools developed throughout history to facilitate the creation, organization, and dissemination of ideas, and argue that it is paramount that the development and application of AI remain fundamentally human-centered. With an eye toward innovating solutions to meet human needs, enhancing the human quality of life and expanding the capacity for human thought and understanding, we propose a pathway to integrating AI into our most challenging and intellectually rigorous fields to the benefit of all humankind.
The Descriptive Complexity of Relation Modification Problems
Florian Chudigiewitsch, Marlene Gr\"undel, Christian Komusiewicz, Nils Morawietz, Till Tantau
https://arxiv.org/abs/2603.22043 https://arxiv.org/pdf/2603.22043 https://arxiv.org/html/2603.22043
arXiv:2603.22043v1 Announce Type: new
Abstract: A relation modification problem gets a logical structure and a natural number k as input and asks whether k modifications of the structure suffice to make it satisfy a predefined property. We provide a complete classification of the classical and parameterized complexity of relation modification problems - the latter w. r. t. the modification budget k - based on the descriptive complexity of the respective target property. We consider different types of logical structures on which modifications are performed: Whereas monadic structures and undirected graphs without self-loops each yield their own complexity landscapes, we find that modifying undirected graphs with self-loops, directed graphs, or arbitrary logical structures is equally hard w. r. t. quantifier patterns.
Moreover, we observe that all classes of problems considered in this paper are subject to a strong dichotomy in the sense that they are either very easy to solve (that is, they lie in paraAC^{0\uparrow} or TC^0) or intractable (that is, they contain W[2]-hard or NP-hard problems).
toXiv_bot_toot
A relation modification problem gets a logical structure and a natural number k as input and asks whether k modifications of the structure suffice to make it satisfy a predefined property. We provide a complete classification of the classical and parameterized complexity of relation modification problems - the latter w. r. t. the modification budget k - based on the descriptive complexity of the respective target property. We consider different types of logical structures on which modifications are performed: Whereas monadic structures and undirected graphs without self-loops each yield their own complexity landscapes, we find that modifying undirected graphs with self-loops, directed graphs, or arbitrary logical structures is equally hard w. r. t. quantifier patterns. Moreover, we observe that all classes of problems considered in this paper are subject to a strong dichotomy in the sense that they are either very easy to solve (that is, they lie in paraAC^{0\uparrow} or TC^0) or intractable (that is, they contain W[2]-hard or NP-hard problems).
Autoritäre Systeme beginnen selten mit Gewalt. Sie beginnen mit Ritualen, Fahnenappellen, Liedern und Lehrplänen. Mit Sätzen, die in Klassenzimmern gesprochen werden, bis sie wie Wahrheit klingen. Der Film von David Borenstein und Pawel Talankin versteht die banale Mechanik der Macht erstaunlich gut. Nicht als spektakuläre Enthüllung, sondern als langsame Verschiebung der Wirklichkeit. Es kommt nicht oft vor, dass Sie einen Oscar prämierten Dokumentarfilm bereits vor der Preisverleihung schon in der Mediathek sehen können. Noch dazu einen, der vom @ZDF und ARTE koproduziert wurde. (ARTE, Neu!)
Zum Blog: https://nexxtpress.de/mediathekperlen/david-borenstein-pawel-talankin-ein-nobody-gegen-putin-2025/
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