Related papers: The Future of Set Theory
10 years ago or so Bill Helton introduced me to some mathematical problems arising from semidefinite programming. This paper is a partial account of what was and what is happening with one of these problems, including many open questions…
The past two decades have witnessed tremendous progress in the microscopic description of atomic nuclei. The Topical Review `The Future of Nuclear Structure' aims at summarizing the current state-of-the-art microscopic calculations in…
In this work we suggest the use of a set-theoretical interpretation of semantic tableaux for teaching propositional logic. If the student has previous notions of basic set theory, this approach to semantical tableaux can clarify her the way…
Using ideas from synthetic topology, a new approach to descriptive set theory is suggested. Synthetic descriptive set theory promises elegant explanations for various phenomena in both classic and effective descriptive set theory.…
This contribution to the concluding session at IAU Symposium 205 offered comments on some current controversies, including the scientific status of the ''multiverse'' concept and on the prospects for cosmology in the coming decade.
The theory of one-relator groups is now almost a century old. The authors therefore feel that a comprehensive survey of this fascinating subject is in order, and this document is an attempt at precisely such a survey. This article is…
We look at reasoning on GSM8k, a dataset of short texts presenting primary school, math problems. We find, with Mirzadeh et al. (2024), that current LLM progress on the data set may not be explained by better reasoning but by exposure to a…
It is the purpose of the present article to collect arguments for, that there should exist in fact -- although not necessarily yet found -- some law, which imply an adjustment to special features to occur in the future. In our own "complex…
Most people participate in meetings almost every day, multiple times a day. The study of meetings is important, but also challenging, as it requires an understanding of social signals and complex interpersonal dynamics. Our aim this work is…
These five lectures on undecidability were given to students with a good level in mathematics but with no special knowledge on logic. The first conference presents the formalization of mathematics with a short historical survey, the…
The idea of predicting the future from the knowledge of the past is quite natural when dealing with systems whose equations of motion are not known. Such a long-standing issue is revisited in the light of modern ergodic theory of dynamical…
On Tuesday 26th November 2024, four discussants participated in a moderated virtual panel titled Future of Quantum Computing as one session of the 8th International Conference on Quantum Techniques in Machine Learning hosted by the…
We provide a simple proof for the union-closed sets conjecture, a long-standing open problem in set theory with immediate applications to graph theory, number theory, and order-theory.
In an article written five years ago [arXiv:0809.0522], we described a method for predicting which scientific papers will be highly cited in the future, even if they are currently not highly cited. Applying the method to real citation data…
This is the written version of a short talk given at the University of Leipzig in December 1998. It reviews some general aspects of string theory from the viewpoint of the search for an unifying theory. Here, special emphasis lies on the…
Some attempts to predict the very distant future of Radio Astronomy are given. It is not easy to predict a list of the first priority problems which may appear, but the facilities potential is more predictable. It is suggested, that in…
The first two lectures are devoted to describing the basic concepts of scattering theory in a very compressed way. A detailed presentation of the abstract part can be found in \cite{I} and numerous applications in \cite{RS} and \cite{Y2}.…
HCI is future-oriented by nature: it explores new human--technology interactions and applies the findings to promote and shape vital visions of society. Still, the visions of futures in HCI publications seem largely implicit,…
Plausible findings about futures are inherently difficult to obtain as they require critical, well-informed speculations backed with data. HCI scholars tackle this challenge via user studies wherein futuristic prototypes and other props…
Existing approaches to automatic summarization assume that a length limit for the summary is given, and view content selection as an optimization problem to maximize informativeness and minimize redundancy within this budget. This framework…