Here is a problem with truly huge numbers, thought to be unsolvable. 

Imagine that you have 128 tennis balls, and can arrange them in any way you like. How many arrangements are possible? According to a new paper, the answer is about 10^250, also known as ten unquadragintilliard: that's a number so big that it exceeds the total number of particles in the universe.

Such “configurational entropy” - a term used to describe how structurally disordered the particles in a physical system are - could lead to a model for the sort of maths that would be needed to solve bigger problems still, ranging from predicting avalanches, or artificial intelligence systems.

Mariners have long spoken of 'walls of water' appearing from nowhere in the open seas, that is why freak waves are called freak waves.

Oceanographers have disregarded such stories and instead suggested that rogue waves - enormous surface waves that have attained a near-mythical status over the centuries - build up gradually and have relatively narrow crests, but new research says rogue (or freak) waves can emerge suddenly, being preceded by much smaller waves. At least in mathematical models published in Proceedings of the Royal Society A.

Falling oxygen levels caused by global warming could be a greater threat to the survival of life on planet Earth than flooding, according to an estimate led by Sergei Petrovskii, Professor in Applied Mathematics from the University of Leicester's Department of Mathematics.

Their mathematical model estimates that an increase in the water temperature of the world's oceans of around six degrees Celsius, which the most aggressive claims (two degrees is the scientific consensus) say could occur as soon as 2100, could stop oxygen production by phytoplankton by disrupting the process of photosynthesis. 

In 2012, the enthusiasm for poll averaging reached a fever pitch. Very few people were critical of it and instead talked about how science had taken over predictive politics. (1)

I was critical of the accuracy and swam against the tide of those in media gushing about the new frontier opened up by New York Times statistical pundit Nate Silver and others, which posited that we could now predict outcomes with unprecedented accuracy. 'They don't do any polls,' I noted, 'So we are supposed to believe there is some miracle of weighting they do in polls done by someone else.' It's the same flaw we find in epidemiology when a scholar does an unweighted random effects meta-analysis to conclude organic strawberries taste better or whatever.

While most people associate the mathematical constant π (pi) with arcs and circles, mathematicians are accustomed to seeing it in a variety of fields. Two University of Rochester scientists have found it lurking in a quantum mechanics formula for the energy states of the hydrogen atom.

"We found the classic 17th century Wallis formula for pi, making us the first to derive it from physics, in general, and quantum mechanics, in particular," said Tamar Friedmann, a visiting assistant professor of mathematics and a research associate of high energy physics, and co-author of a paper published this week in the Journal of Mathematical Physics.

Major League Baseball can help understand why maps used to predict shaking in future earthquakes often do poorly. 

Earthquake hazard maps use assumptions about where, when, and how big future earthquakes will be to predict the level of shaking. The results are used in designing earthquake-resistant buildings. However, as the study's lead author, earth science and statistics graduate student Edward Brooks, explains "sometimes the maps do well, and sometimes they do poorly. In particular, the shaking and thus damage in some recent large earthquakes was much larger than expected."

Try to remember a phone number, and you're using what's called your sequential memory. This kind of memory, in which your mind processes a sequence of numbers, events, or ideas, underlies how people think, perceive, and interact as social beings. 

"In our life, all of our behaviors and our process of thinking is sequential in time," said Mikhail Rabinovich, a physicist and neurocognitive scientist at the University of California, San Diego.

You might call it a two-tone football.  If you're a real mathematician you may be able to explain to me what the real name of the thing is.  I'm not a real mathematician but I occasionally wrangle with math problems as visualized surfaces in my head.  It's like speaking in metaphor without knowing where the metaphors came from or what they mean.  I have a thin grasp of what an Euler Spiral is and I sort of understand that the surface of an American-style football is a Prolate Spheroid.  Put those two concepts together and you come up with the Yin and Yang of the Yellow Brick Road, which leads to discovery and greater knowledge.
By Michael Greshko, Inside Science – Mathematics that can describe coffeepots, forest fires and flu outbreaks may also underpin the brain’s response to anesthesia, a new study suggests.

The mathematical model of the brain, published in Physical Review Letters, marks the latest attempt to simulate the surprisingly complicated effects of general anesthetics across the brain.

Following one of the largest-scale scientific reproducibility investigations to date, a group of psychology researchers has reported results from an effort to replicate 100 recently published psychology studies; though they were able to successfully repeat the original experiments in most all cases, they were able to reproduce the original results in less than half, they report.