Abstract The convergence of technology and education has enabled the creation of instructional programs utilizing digital resources, garnering significant interest from educators in developing mathematical culture curricula. This study investigates these factors by incorporating the perceived importance of policy (PIP) variables into the unified theory of acceptance and use of technology (UTAUT) model. Quantitative analysis was employed to collect online questionnaire data from 873 teachers in Henan Province, which was subsequently analyzed using partial least squares structural equation modeling (PLS-SEM). The findings revealed that (1) performance expectation did not significantly impact teachers’ intentions and behaviors regarding the use of digital resources for developing mathematics culture lessons; (2) effort expectations negatively influenced such use; and (3) social influence, facilitating conditions, and perceived policy importance emerged as key drivers, with social influence exerting the most substantial impact. These insights enhance our understanding of the factors influencing teachers’ integration of digital resources in mathematics culture curriculum development. They can inform strategies to improve teachers’ knowledge of teaching with mathematics technology (KTMT) and to promote technology-enhanced mathematics teaching and learning.

Abstract We introduce an algorithm which allows us to prove that there exists an infinite number of matrix strong Diophantine -tuples. We show that Diophantine quadruples generate matrix elliptic (or hyperelliptic) curves which have each  matrix points.

Abstract If general relativity is correct, then the origin of the universe is a simple mathematical problem. The Friedmann equation in cosmology is a well-structured ordinary differential equation, and the global properties of its solutions can be qualitatively analyzed by the phase-trajectory method. In this paper we show that the total energy density of matter in the universe is positive, and the total pressure near the Big Bang is negative. By analyzing the global properties of the solutions to the Friedmann equation according to these two conditions of state functions, we find that the Big Bang is impossible, and the space must be a closed 3-dimensional sphere, the cosmological constant is likely to be zero, and the evolution of the universe should be cyclic. The analysis and the proof are simple and straight forward, therefore these conclusions should be reliable.