A mathematician working at Anthropic says he used the AI model Claude Fable 5 to uncover a remarkably simple counterexample ...
When designing microscopes, optical engineers have long faced a trade-off between speed, field of view and resolution. But ...
Alpöge’s discovery is the latest in a string of high-profile mathematical breakthroughs made by large language models. Recent examples include OpenAI’s disproof of the unit distance conjecture, and ...
A mathematician announced that he used one of Anthropic's A.I. models to find a counterexample to a problem called the Jacobian conjecture. While experts consider it a milestone, the work raises quest ...
Formulas are powerful tools for performing calculations and analyzing data in Excel. In this beginner’s guide, you’ll learn how to use formulas (with or without help from the Copilot AI assistant) and ...
Penn Engineers have developed a new way to use AI to solve inverse partial differential equations (PDEs), a particularly challenging class of mathematical problems with broad implications for ...
Typically, we use Lyapunov_python_3_9 locally (with conda 4.12.0 and pip 24.3.1) and Lyapunov_python_3_10 on our clusters for compatibility issues. The only differences are in the version of python, ...
Learn how to find the inverse, the converse, and the contrapositive of a statement. The contrapositive of a statement is the switching of the hypothesis and the conclusion of a conditional statement ...
Tim Smith has 20+ years of experience in the financial services industry, both as a writer and as a trader. Somer G. Anderson is CPA, doctor of accounting, and an accounting and finance professor who ...
Five years ago, mathematicians Dawei Chen and Quentin Gendron were trying to untangle a difficult area of algebraic geometry involving differentials, elements of calculus used to measure distance ...
For the past several years, America has been using its young people as lab rats in a sweeping, if not exactly thought-out, education experiment. Schools across the country have been lowering standards ...
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