Abstract: The nature of vagueness, imprecision, and uncertainly is fuzzy rather than crisp and/or random, especially for a multiple objectives decision-making problem. A key component of fuzzy ...

From basic math to pre-calculus, Microsoft Mathematics includes features that makes it easy to create graphs in 2D and 3D, calculate numerical results, solve equations or inequalities, and simplify ...

Since the start of the 20th century, the heart of mathematics has been the proof — a rigorous, logical argument for whether a given statement is true or false. Mathematicians’ careers are measured by ...

This film discusses the concept of functions in mathematics, emphasizing their importance and modern formulations. It explains how to create ordered pairs from a set of numbers and illustrates how ...

Functions are fundamental in mathematics, describing relationships between inputs and outputs. For instance, linear functions are used to describe proportional relationships such as calculating cost ...

In a mesmerising blend of art and mathematics, a research student from University College London (UCL) has recently gained widespread attention for creating intricate images solely through ...

The original version of this story appeared in Quanta Magazine. David Bessis was drawn to mathematics for the same reason that many people are driven away: He didn’t understand how it worked. Unlike ...

ABSTRACT: In the author’s recent publications, a parametric system biorthogonal to the corresponding segment of the exponential Fourier system was unusually effective. On its basis, it was discovered ...

On Thursday, Google DeepMind announced that AI systems called AlphaProof and AlphaGeometry 2 reportedly solved four out of six problems from this year’s International Mathematical Olympiad (IMO), ...

AlphaProof and AlphaGeometry 2 are steps toward building systems that can reason, which could unlock exciting new capabilities. AI models can easily generate essays and other types of text. However, ...