Most people wouldn't think that it would take rigorous mathematical proof to show how many folds it takes to make a donut shape out of paper. Yet, no one could quite figure it out until recently.

How ambitious should you be? Folk wisdom offers conflicting advice: "Shoot for the moon," but also, "Don't let the perfect be the enemy of the good." A new study by researchers at the University of Wyoming, Stanford University and the University of Colorado-Boulder used a mathematical model to show that ambition lies in the middle—above average but finite.

Mathematicians from University College London and the University of California, Davis, have published a mathematical proof that the Universe’s accelerating expansion can be explained without dark energy, dealing a serious blow to the Lambda-cold dark matter model.

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Let’s start with what’s probably the most tired, overused joke in math: A topologist is someone who can’t tell a coffee cup from a doughnut. Both, you see, have a hole in them. Topology is usually described as a sort of “rubber sheet” geometry in which two shapes are considered the same if one can be stretched or compressed into the other without tearing it. But this summary leaves out something…

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Mathematical functions are built from operations, which are used to perform the calculations that make science and technology run. But what if we could do away with multiplication, addition, subtraction, and division? That’s what one mathematician has done in a new paper – he claims that everything in mathematics can be done with just one operation, which he’s calling “eml”. Let’s take a look.

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The Concept A vector space is an additively written abelian group together with a field that operates on it. Intuitive picture vs abstract definition Vector spaces are often described as a set of arrows, i.e. a line segment with a direction that can be added, stretched, or compressed. That’s where the term linear to describe...

Abstract Why do we need yet another article about complex numbers? This is a valid question and I have asked it myself. I could mention that I wanted to gather the many different views that can be found elsewhere – Euler’s and Gauß’s perspectives, i.e. various historical views in the light of the traditionally parallel...

Physicists found that the music of Johann Sebastian Bach contains mathematical patterns that help convey information

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Preamble The classical mathematician practically by instinct views the continuous process as the “real” process, and the discrete process as an approximation to it. The mathematics of finance and certain topics in the modern theory of stochastic processes suggest that, in some cases at least, the opposite is true. Continuous processes are, generally speaking, the...

A division by zero is primarily an algebraic question. The reasoning therefore follows the indirect pattern of most algebraic proofs: What if it was allowed? Then we would get a contradiction, and a contradiction is the greatest enemy of mathematical rigor. Many students tried to find a way to divide by zero once in their...