Related papers: On different reliability standards in current math…
Linearisability is a central notion for verifying concurrent libraries: a given library is proven safe if its operational history can be rearranged into a new sequential one which, in addition, satisfies a given specification.…
This is an essay that considering the knowledge structure and language of a different nature, attempts to build on an explanation of the object of study and characteristics of the mathematical science. We end up with a learning cycle of…
Since its beginnings in the 1940s, automated reasoning by computers has become a tool of ever growing importance in scientific research. So far, the rules underlying automated reasoning have mainly been formulated by humans, in the form of…
Proving the efficacy of certification standards
We present a research mathematician's perspective on current developments around in K-12 mathematics. We share activities, and highlight the different ways in which students' reasoning can progress, such as amount of abstraction,…
The advent of computers has allowed mathematicians to do increasingly more difficult computations that used to be practically impossible. Peer reviewers will seldom look at any code attached to a math paper, however. In this article, we…
High-quality research software is a cornerstone of modern scientific progress, enabling researchers to analyze complex data, simulate phenomena, and share reproducible results. However, creating such software requires adherence to best…
A close look at students' written work on examinations offers a wealth of information about their performance, their knowledge of the subject, their strengths, weaknesses and misconceptions, and their overall level of mathematical skills…
A common assumption in belief revision is that the reliability of the information sources is either given, derived from temporal information, or the same for all. This article does not describe a new semantics for integration but the…
The paper discusses how to evaluate the reliability of units produced by different production lines. The procedure is based on selecting independent random samples of units produced by different production lines and then evaluating…
This vision paper presents initial research on assessing the robustness and reliability of AI-enabled systems, and key factors in ensuring their safety and effectiveness in practical applications, including a focus on accountability. By…
Assessment of replicability is critical to ensure the quality and rigor of scientific research. In this paper, we discuss inference and modeling principles for replicability assessment. Targeting distinct application scenarios, we propose…
The status of precision tests of the Standard Model is reviewed.
Currently, there are thousands of large pretrained language models (LLMs) available to social scientists. How do we select among them? Using validity, reliability, reproducibility, and replicability as guides, we explore the significance…
The last few years have seen the proliferation of measures that quantify the scientific output of researches. Yet, these measures focus on productivity, thus fostering the "publish or perish" paradigm. This article proposes a measure that…
Investigation of the critical levels and catastrophes in the complex systems of different nature is useful and perspective. Mathematical modeling and analysis is presented for revealing and investigation of the phenomena and critical levels…
A proof is one of the most important concepts of mathematics. However, there is a striking difference between how a proof is defined in theory and how it is used in practice. This puts the unique status of mathematics as exact science into…
Mathematical proofs are often said to justify their conclusions by indicating the existence of a corresponding formal derivation. We argue that this widespread view relies on an under-examined notion of correspondence, or what it means for…
Literature reviews have long played a fundamental role in synthesizing the current state of a research field. However, in recent years, certain fields have evolved at such a rapid rate that literature reviews quickly lose their relevance as…
Reproducibility, the ability to recompute results, and replicability, the chances other experimenters will achieve a consistent result, are two foundational characteristics of successful scientific research. Consistent findings from…