Related papers: Murray Gell-Mann, A Short Appreciation
Some Goedel centenary reflections on whether incompleteness is really serious, and whether mathematics should be done somewhat differently, based on using algorithmic complexity measured in bits of information. [Enriques lecture given…
This is an expanded version of the author's lecture at the XX Congresso U.M.I., held in Siena in September 2015. After a brief review of L-functions, we turn to the classical converse theorems of H.Hamburger, E.Hecke and A.Weil, and to some…
We present the "Annotation and Benchmarking on Understanding and Transparency of Machine Learning Lifecycles" (ABOUT ML) project as an initiative to operationalize ML transparency and work towards a standard ML documentation practice. We…
Among Zellig Harris's numerous contributions to linguistics his theory of the sublanguages of science probably ranks among the most underrated. However, not only has this theory led to some exhaustive and meaningful applications in the…
Recent developments in machine translation and multilingual text generation have led researchers to adopt trained metrics such as COMET or BLEURT, which treat evaluation as a regression problem and use representations from multilingual…
These are some basic notes concerning Holder and Lipschitz classes on metric spaces.
The present notes provide an extended version of a small lecture course given at the Humboldt Universit\"at zu Berlin in the Winter Term 2022/23 (of 36 hours). The material starting in Section 5.4 was added afterwards. The aim of these…
The celebration of the Centennial of the International Commission on Mathematical Instruction offered the occasion to look back at the history of ICMI and outline the evolution of mathematics education until it achieved its present status…
This writeup follows the presentation at the Symposium, with emphasis on topics and ideas discussed there. It is purposefully informal, not a review of the field, and neither does it include a complete list of references. However, I hope…
We reassess the claims of human parity and super-human performance made at the news shared task of WMT 2019 for three translation directions: English-to-German, English-to-Russian and German-to-English. First we identify three potential…
Talk given at the XLVIII Rencontres de Moriond, Electroweak Interactions and Unified Theories, La Thuile, Italy, 2-9 March 2013, to appear in the Proceedings.
Learned metrics such as BLEURT have in recent years become widely employed to evaluate the quality of machine translation systems. Training such metrics requires data which can be expensive and difficult to acquire, particularly for…
Thomas C. Schelling, awarded the 2005 Nobel Memorial Prize in Economic Sciences, pointed out that ``individuals decisions (micromotives), while often personal and localized, can lead to societal outcomes (macrobehavior) that are far more…
Long-term memory is a critical capability for multimodal large language model (MLLM) agents, particularly in conversational settings where information accumulates and evolves over time. However, existing benchmarks either evaluate…
A focused modernization of Sophus Lie's brilliant writings about the foundations of geometry that every contemporary geometer should have at least once a look at. Translated, updated, commented.
This paper explores the use of large language models (LLMs) to score and explain short-answer assessments in K-12 science. While existing methods can score more structured math and computer science assessments, they often do not provide…
These are expanded notes from a four lecture mini-course given by the author at the Spring School on Non-archimedean geometry and Eigenvarieties, held at the University of Heidelberg in March 2023. The course discusses coherent sheaves,…
We describe the development of the mathematics of Helmut R. Salzmann (3. 11. 1930 -- 8. 3. 2022) and the main difficulties he was facing, documenting his lifelong productivity and his far reaching influence. We include a comprehensive…
Witten- Helffer-Sj\"ostrand theory is a considerable addition to the De Rham- Hodge theory for Riemannian manifolds and can serve as a general tool to prove results about comparison of numerical invariants associated to compact manifolds…
The famous scientist Hermann von Helmholtz was born 200 years ago. Many complex physical wave phenomena in engineering can effectively be described using one or a set of equations named after him: the Helmholtz equation. Although this has…