Mathematical aspects of computation, including algorithms, computational complexity, automata theory, formal methods, quantum computing theory, and the foundations of computer science
4 papersFrench geometer Michel Chasles intertwined historical research and mathematical practice, using "epistemic techniques" like archival research, deconstructive historiography, and periodization to shape his theories. His work demonstrates how analyzing past geometrical methods and notational technologies helped him develop novel approaches and modernize geometry.
This paper argues that Wittgenstein, not Lakatos, was the true forerunner of the philosophy of mathematical practice. It highlights Wittgenstein's concepts of "rule bending" and "mathematics as rules of description" as key contributions that challenge traditional views of mathematical foundations and emphasize the importance of studying actual mathematical practices.
The integration of history of mathematics into mathematics education is a growing field, focused on utilizing historical elements not just as motivational anecdotes but as tools to enhance understanding of mathematical concepts and the nature of mathematics itself. Key research areas include theoretical frameworks for integration, the impact of historical resources on student learning and teacher knowledge, and the role of history in interdisciplinary approaches like STEM.
This paper explores leading singularities of traintrack integrals, a class of multi-loop Feynman integrals relevant to quantum field theory calculations. The authors identify "half traintracks" as the most general degenerations with conventional leading singularities and prove that full traintracks possess a rigidity of L-1, computing their leading singularities as integrals over (L-1)-dimensional Calabi-Yau manifolds.