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On proof and progress in mathematics

William P.HG Thurston • Bulletin of the American Mathematical Society (1994)

This essay on the nature of proof and progress in mathematics was stimulated by the article of Jaffe and Quinn, "Theoretical Mathematics: Toward a cultural synthesis of mathematics and theoretical physics".Their article raises interesting i...

OPENALEX Open Access DOI: https://doi.org/10.1090/s0273-0979-1994-00502-6

System 2 Thinking in OpenAI’s o1-Preview Model: Near-Perfect Performance on a Mathematics Exam

Joost C. F. de Winter, Dimitra Dodou, Yke Bauke Eisma • Computers (2024)

The processes underlying human cognition are often divided into System 1, which involves fast, intuitive thinking, and System 2, which involves slow, deliberate reasoning. Previously, large language models were criticized for lacking the de...

DOAJ Open Access (DOAJ) DOI: 10.3390/computers13110278

Mathematical Capabilities of ChatGPT

Simon Frieder, Luca Pinchetti, Chevalier Chevalier, Ryan-Rhys Griffiths et al. • neural information processing systems (2023)

We investigate the mathematical capabilities of two iterations of ChatGPT (released 9-January-2023 and 30-January-2023) and of GPT-4 by testing them on publicly available datasets, as well as hand-crafted ones, using a novel methodology. In...

OPENALEX Open Access DOI: https://doi.org/10.52202/075280-1205

The Nature of Mathematical Knowledge

Philip Kitcher (1985)

Abstract The Nature of Mathematical Knowledge develops and defends an empiricist approach to mathematical knowledge. After offering an account of a priori knowledge, it argues that none of the available accounts of a priori mathematical kno...

OPENALEX DOI: https://doi.org/10.1093/0195035410.001.0001

The Handbook of Mathematical Cognition

Jamie I. D. Campbell • Psychology Press eBooks (2005)

Part 1: Cognitive Representations for Number and Mathematics. M. Fayol, X. Seron, About Numerical Representations: Insights from Neuropsychological, Experimental and Developmental Studies. M. Brysbaert, Number Recognition in Different Forma...

OPENALEX DOI: https://doi.org/10.4324/9780203998045

A Mathematical Theory of Evidence

Glenn R. Shafer • Princeton University Press eBooks (2020)

Both in science and in practical affairs we reason by combining facts only inconclusively supported by evidence. Building on an abstract understanding of this process of combination, this book constructs a new theory of epistemic probabilit...

OPENALEX DOI: https://doi.org/10.2307/j.ctv10vm1qb

The Mathematical Brain

Brian L. Butterworth • UCL Discovery (University College London) (1999)

The concept of numbers and the ability to recognize and process them is innate, part of everyone's intellectual apparatus whether they've had formal education or not. This instinct is not dependent on basic intelligence or general knowledge...

OPENALEX

Equations of Mathematical Physics

Alexander N. Tikhonov, A. A. Samarskiĭ, Peter B. Kahn • American Journal of Physics (1965)

Mathematical physics plays an important role in the study of many physical processes - hydrodynamics, elasticity, and electrodynamics, to name just a few. Because of the enormous range and variety of problems dealt with by mathematical phys...

OPENALEX DOI: https://doi.org/10.1119/1.1971985

The Mathematics of Marriage

John Mordechai Gottman, J. D. Murray, Catherine Swanson, Rebecca C. Tyson et al. • The MIT Press eBooks (2002)

Divorce rates are at an all-time high. But without a theoretical understanding of the processes related to marital stability and dissolution, it is difficult to design and evaluate new marriage interventions. The Mathematics of Marriage pro...

OPENALEX DOI: https://doi.org/10.7551/mitpress/4499.001.0001

Design Recommendations for Immersive Virtual Reality Application for English Learning: A Systematic Review

Jessica Rodrigues Esteves, Jorge C. S. Cardoso, Berenice Santos Gonçalves • Computers (2023)

The growing popularity of immersive virtual reality (iVR) technologies has opened up new possibilities for learning English. In the literature, it is possible to find several studies focused on the design, development, and evaluation of imm...

DOAJ Open Access (DOAJ) DOI: 10.3390/computers12110236

Lattice-based ring signcryption for consortium blockchain

Huifang Yu, Zhirui Lv • Journal of King Saud University: Computer and Information Sciences (2023)

Ring signcryption with no group administrator satisfies the decentralization and blockchain anonymity. In this article, we construct new lattice-based ring signcryption scheme suitable for consortium blockchain (CB-LRSCS), in which the smar...

DOAJ Open Access (DOAJ) DOI: 10.1016/j.jksuci.2023.101602

An Agent Cascade for Explainable Relevance Assessment of Procurement Procedures in the Tenders Electronic Daily Environment

Ivan Tikshaev, Anatoly Sidorov • Mathematics (2026)

This paper considers the task of assessing the relevance of a procurement procedure for a supplier under conditions of growing volumes of open procurement data and increasing complexity of electronic publication services. It is shown that, ...

DOAJ Open Access (DOAJ) DOI: 10.3390/math14173125

A game-theoretic sequential three-way decision using probabilistic rough sets and multiple levels of granularity

T. V. Soumya, M. K. Sabu • Discover Computing (2025)

Abstract The sequential three-way decision accepts additional information at each level and makes more accurate definite decisions with less uncertainty. This process can also be extended to two-way classification with the finer-grained inf...

DOAJ Open Access (DOAJ) DOI: 10.1007/s10791-025-09729-5

Mass variation observing system by high low inter-satellite links (MOBILE) – a new concept for sustained observation of mass transport from space

Pail R., Bamber J., Biancale R., Bingham R. et al. • Journal of Geodetic Science (2019)

As changes in gravity are directly related to mass variability, satellite missions observing the Earth’s time varying gravity field are a unique tool for observing mass transport processes in the Earth system, such as the water cycle, rapid...

DOAJ Open Access (DOAJ) DOI: 10.1515/jogs-2019-0006