Learn how to solve boundary value problems in Python using the finite difference method! 🐍📐 This tutorial walks you step-by-step through setting up the problem, discretizing the domain, and ...

GPT-5.2 Pro delivers a Lean-verified proof of Erdős Problem 397, marking a shift from pattern-matching AI to autonomous mathematical reasoning.

Amid sky-high inflation, water and energy cuts and prospects for a deal with the U. S. dimming, President Masoud Pezeshkian has apparently thrown up his hands. By Farnaz Fassihi and Leily Nikounazar ...

A common argument against the use of AI in critical decision-making is that it has no feelings or emotions. Yet AI is unmatched in scale, prediction and silent adaptation. It can process vast amounts ...

The Madelung Equations are a set of equations proposed by Erwin Madelung in 1926 to describe a more physical interpretation of the Schrödinger Equation. Notably, Madelung's analysis resulted in a set ...

Abstract: A nonlinear equation system often has multiple roots, while finding all roots simultaneously in one run remains a challenging work in numerical optimization. Although many methods have been ...

Abstract: During industrial smart manufacturing, many problems can be described as a time-dependent nonlinear equation system (TNES) that needs to be solved cooperatively due to large-scale ...

As Americans struggle with the high cost of living, an old idea is getting a fresh look. In dozens of pilot programs around the country, policymakers and researchers are exploring what happens when ...

Today’s post continues a series in which educators share what they view as the biggest challenges facing teachers—and how to overcome them. Jason D. DeHart earned his Ph.D. in education from the ...

In this paper, the equation for the gravity wave spectra in mean atmosphere is analytically solved without linearization by the Adomian decomposition method. As a consequence, the nonlinear nature of ...

While 630 young math prodigies were sitting in a conference room on Australia’s sunshine coast, readying their pencils for the International Math Olympiad, a potential rival was still en route from ...