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'Shoot for the moon?' Aim a bit lower, researchers say

29 May 2026 at 14:00
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.

Two Researchers Are Rebuilding Mathematics From the Ground Up

20 May 2026 at 15:52

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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Mathematician Collapses All Functions to One Weird Formula

20 April 2026 at 16:00
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.

Vector Spaces: Concepts, History, and Applications Guide

13 March 2025 at 12:45
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...

Views On Complex Numbers

7 June 2024 at 12:10
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...

The Lambert W Function in Finance

9 February 2024 at 14:25
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...

Why Division by Zero Is Impossible: 10 Mathematical Reasons

11 January 2024 at 16:41
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...
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