Related papers: On Duplication in Mathematical Repositories
There is a problem with the foundations of classical mathematics, and potentially even with the foundations of computer science, that mathematicians have by-and-large ignored. This essay is a call for practicing mathematicians who have been…
We describe a formal correctness proof of RANKING, an online algorithm for online bipartite matching. An outcome of our formalisation is that it shows that there is a gap in all combinatorial proofs of the algorithm. Filling that gap…
Verifying mathematical proofs is difficult, but can be automated with the assistance of a computer. Autoformalization is the task of automatically translating natural language mathematics into a formal language that can be verified by a…
Developing a 21st Century Global Library for Mathematics Research discusses how information about what the mathematical literature contains can be formalized and made easier to express, encode, and explore. Many of the tools necessary to…
A hypothesis testing algorithm is replicable if, when run on two different samples from the same distribution, it produces the same output with high probability. This notion, defined by by Impagliazzo, Lei, Pitassi, and Sorell [STOC'22],…
While extensive guidance exists for ensuring the reproducibility of one's own study, there is little discussion regarding the reproduction and replication of external studies within one's own research. To initiate this discussion, drawing…
The received Hilbert-style axiomatic foundations of mathematics has been designed by Hilbert and his followers as a tool for meta-theoretical research. Foundations of mathematics of this type fail to satisfactory perform more basic and more…
Scientific knowledge discovery increasingly relies on large language models, yet many existing scholarly assistants depend on proprietary systems with tens or hundreds of billions of parameters. Such reliance limits reproducibility and…
As the amount of information online continues to grow, a correspondingly important opportunity is for individuals to reuse knowledge which has been summarized by others rather than starting from scratch. However, appropriate reuse requires…
A biform theory is a combination of an axiomatic theory and an algorithmic theory that supports the integration of reasoning and computation. These are ideal for formalizing algorithms that manipulate mathematical expressions. A theory…
Meta-analysis is routinely performed in many scientific disciplines. This analysis is attractive since discoveries are possible even when all the individual studies are underpowered. However, the meta-analytic discoveries may be entirely…
Formal logic has often been seen as uniquely placed to analyze mathematical argumentation. While formal logic is certainly necessary for a complete understanding of mathematical practice, it is not sufficient. Important aspects of…
A reproducibility crisis has been reported in science, but the extent to which it affects AI research is not yet fully understood. Therefore, we performed a systematic replication study including 30 highly cited AI studies relying on…
The modeling of probability distributions, specifically generative modeling and density estimation, has become an immensely popular subject in recent years by virtue of its outstanding performance on sophisticated data such as images and…
Structural proof theory is praised for being a symbolic approach to reasoning and proofs, in which one can define schemas for reasoning steps and manipulate proofs as a mathematical structure. For this to be possible, proof systems must be…
Understanding and creating mathematics using natural mathematical language - the mixture of symbolic and natural language used by humans - is a challenging and important problem for driving progress in machine learning. As a step in this…
Replicability is essential in science as it allows us to validate and verify research findings. Impagliazzo, Lei, Pitassi and Sorrell (`22) recently initiated the study of replicability in machine learning. A learning algorithm is…
Reproducibility is a cornerstone of science, as the replication of findings is the process through which they become knowledge. It is widely considered that many fields of science are undergoing a reproducibility crisis. This has led to the…
Recent reproducibility case studies have raised concerns showing that much of the deposited research has not been reproducible. One of their conclusions was that the way data repositories store research data and code cannot fully facilitate…
Education in the practical applications of logic and proving such as the formal specification and verification of computer programs is substantially hampered by the fact that most time and effort that is invested in proving is actually…