# Mathematics

Weyl points, the 3D analogues of the structures that make graphene exceptional, were theoretically predicted in 1929. Today, an international team of Physicists from MIT and Zhejiang University, found them in photonic crystals, opening a new dimension in photonics.

The solvability of polynomials was a question that intrigued
mathematicians for centuries after a formula was found for both cubic and
quartic polynomials in the early 16^{th} century. It seemed only a matter of time, will, and
cleverness to find a formula for quintic polynomials. The answer Galois provided us three centuries
later was: no - there are no general formulas for 5^{th} and higher
order polynomials.

It’s not just spaghetti alla carbonara, it’s the whole business of inventing dishes and preparing them. It’s an analogy with many parts, and it has consequences.

To introduce myself: I’m a professional mathematician, an amateur cook and an enthusiastic eater. The ideas in this essay are distilled from years of formal reasoning, mad culinary experiments and adventurous meals. In short, I’ve found that:

I do mathematics for much the same reasons that I cook.

The researchers created a range of computer simulations to explore if social hierarchies are beneficial to navigation, and how collision risk is affected by environmental conditions and the birds’ desire to maintain an efficient direct flight path.

I call myself a blues singer, but you ain’t never heard me call myself a blues guitar man. Well, that’s because there’s been so many can do it better'n I can, play the blues better'n me.

And his musical vocabulary was limited. King once told Bono: “I’m no good with chords, so what we do is, uh, get somebody else to play chords… I’m horrible with chords”. He even claimed that he couldn’t play and sing at the same time.

It's unknown how flocks of birds, shoals of fish, lines of ants and other complex natural systems organize themselves so well when moving collectively so researchers from Spain and the U.S. analyzed the movements of Argentine ants (

*Linepithema humile*, an invasive species in many parts of the world) while they forage or explore an empty space (a petri dish) and then they proposed a model explaining how they form their routes.

It took human culture millennia to arrive at a mathematical formulation of non-Euclidean spaces - but that was not because of a limitation of our brains.

Instead, it's likely that even the brains of rodents get there very naturally every day.

There is not the slightest doubt that the the universe is real. It is three-dimensional.

But one popular alternative notion has been the "holographic principle", which asserts that a mathematical description of the universe only requires two dimensions. What we perceive as three dimensional may just be the image of two dimensional processes on a huge cosmic horizon.

Up until now, this speculation has only been mathematically analyzed in exotic spaces with negative curvature. Math, like any language, can talk about lots of things that are not possible and such spaces are quite different from the space in our own universe.

A new paper suggests that the holographic principle even holds in a flat spacetime.

At the Institute of Nuclear Physics of the Polish Academy of Sciences in Kraków, Poland, researchers have been conducting multifractal analysis into the changes in the numbers of sunspots and found that the graphs were asymmetrical in shape, suggesting that sunspots may be involved in unknown physical processes.