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New mathematical method reveals structure in neural activity in the brain "We have adopted approaches from the field of algebraic topology that previously had been used primarily in the domain of pure mathematics and have applied them to experimental data on the activity of place...

Jupiter's great red spot heats planet's upper atmosphere Researchers have discovered that Jupiter's Great Red Spot may provide the mysterious source of energy required to heat the planet's upper atmosphere to the unusually high values observed. I'm just glad Earth doesn't have "perpetual...

Astronomers confirm faintest early-universe galaxy ever seen Scientists have detected and confirmed the faintest early-universe galaxy ever, using the W. M. Keck Observatory on the summit on Mauna Kea in Hawaii. The team detected the galaxy as it was 13 billion years ago.

Hello iBot and CH, iBot requested that I show how a problem I posed to it is solved: iBot's Request The problem can be found here, and I am posting the solution here so I can use $\LaTeX$. The problem is as follows: In order to solve this problem, we may rely on the following formulas...

Weird quantum effects stretch across hundreds of miles Scientists have discovered strange quantum effects hold, even over hundreds of miles. In longest test of quantum mechanics, researchers find neutrinos, traveling over 450 miles at close to speed of light, have no single identity. The...

Longest maths proof would take 10 billion years to read I thought Andrew Wiles' ~300 page proof of Fermat's Last Theorem was impressive, but this is staggering! :o Speaking of Wiles and Fermat: Remembering when Wiles proved Fermat's Last Theorem Yes, I do remember exactly where I was and...

Astronomers find evidence for ‘direct collapse’ black hole Astronomers have discovered evidence for an unusual kind of black hole born extremely early in the universe. They showed that a recently discovered unusual source of intense radiation is likely powered by a "direct-collapse black hole,"...

If life can make it here, it can make it anywhere Scientists explore the likelihood of complex life existing elsewhere in the universe If the origin of life is common on other worlds, the universe should be a cosmic zoo full of complex multicellular organisms. Scientists use the evolution of...

Black hole born without stellar parent, evidence suggests Scientists have known for some time now that certain stars can give rise to black holes upon their "death." Our sun is far too small to ultimately result in a black hole, and its fate is said to be that of a white dwarf. However...

Scientists model universe using Einstein’s full theory Cosmologists have begun modelling the universe for the first time using Einstein's full general theory of relativity, which will lead to the most accurate possible models of the universe and provide new insights into gravity and its...

Accelerating Research Into Dark Energy One of the puzzling questions facing cosmologists is the accelerating rate of expansion of our universe. This new method for generating virtual universes may help us get to a deeper understanding of this phenomenon. :)

Are you still reeling from Pluto's demotion from the family of planets in our solar system? Then take heart, as planetary scientists are hot on the trail of a possible replacement for Pluto: New clues in search for Planet Nine The primary clue is orbital resonance among several bodies in the...

I found this article to be an interesting read: Will computers replace humans in mathematics? While I am not a mathematician by any means, but more of a math enthusiast, I don't find this frightening or intimidating in the least. However we can gain more understanding of mathematics, will...

For all real $0<a_i$, where $1\le i\le n$, prove: $\displaystyle \sum_{k=1}^n\left(a_k^{-2}\right)\ge\sum_{k=1}^n\left(a_k^{2}\right)$ given that: $\displaystyle \sum_{k=1}^n\left(a_k\right)=n$

Prove that for $n\in\mathbb{N}$, the following is true: $$\displaystyle \sum_{k=1}^n\left(\frac{1}{k^2}\right)\le\frac{5}{3}-\frac{2}{2n+1}$$

$\begin{array}{rcl}a & = & b \\ a+a & = & a+b \\ 2a & = & a+b \\ 2a-2b & = & a+b-2b \\ 2(a-b) & = & a-b \\ 2 & = & 1 \end{array}$ Where did I go wrong?

LaTeX Powered By MathJax Enabled Here In Our "Science & Technology" Forum Hello CH Community, We have enabled the use of $\LaTeX$ powered by MathJax here in this forum. $\LaTeX$ is a markup language used to display pretty mathematical expressions. For example, the code...

This is certainly not "breaking" news, but I saw this article a few years ago and happened upon it again, and wanted to share it here: THE MANDELBROT MONK It seems that what is perhaps the most iconic image of fractal geometry was known centuries before its "discovery" by Benoit Mandelbrot. I...