Mathematics

Dan Spielman, a Yale computer scientist, wanted to model complex online communities like Facebook, hoping to gain insight into how they form and interact. That's one of the precepts of Science 2.0, understanding how people can participate and scientists can collaborate without being drowned in a lot of 'noise' before being put on the right path to either.

A colleague in Jerusalem observed that aspects of Spielman’s research brought to mind a math problem that had been stumping people since Dwight Eisenhower was in office — the Kadison-Singer math problem. The 1950s? A puzzle that wasn't even from a paper, but from the “Related Questions” section of a paper on extensions of pure states? 

Platonic solids are regular bodies in three dimensions, such as the cube and icosahedron, and have been known for millennia. They feature prominently in the natural world wherever geometry and symmetry are important, for instance in lattices and quasi-crystals, as well as fullerenes and viruses  

Platonic solids have counterparts in four dimensions. Swiss mathematician Ludwig Schlaefli and Alicia Boole Stott showed that there are six of them, five of which have very strange symmetries. Stott, the third daughter of mathematician George Boole, is best known for establishing the term "polytope" for a convex solid in four dimensions, had a unique intuition into the geometry of four dimensions, which she visualised via three-dimensional cross-sections.


They're data mining our children, notes Politico writer Stephanie Simon. She is talking about education technology startup Knewton and their use of data analytics to find out how kids think. They want to be able to predict who will struggle with fractions next week.

Exciting, right? Obviously this can be misused and the fact that its potential problems (if they can forecast it, they can manipulate it) are so obvious is why policymakers will address that. The brilliance will be what this sort of capability can do for science. 
Reading Robert Walker's article on what extraterrestrial mathematics might look like has the wheels in my head a'turning.  We live in a digital civilization, one that specifically evolved toward a binary representation of a decimal-based mathematics.  Our computers count by 1s and 0s, whereas we tend to count by 1s, 2s, 3s, 4s, 5s, 6s, 7s, 8s, 9s, and 0s.  And that is just our conscious countatiousness.  Our bodies count in ways we have yet to enumerate.  I think it's quite likely that any complex biological organism like a jelly fish uses some sort of internal mathematics to regulate itself.

The Jacobi iterative method, a 169-year-old math strategy, may soon get a new lease on life.


When I was five years old I used to be sort of an attraction to relatives. One of my mother's brothers is an engineer, and he was amazed by my ability to do complex calculations by heart. But to me it was only amusing to observe their amazement for what I considered a triviality.

On one occasion - I remember it as it was yesterday - my uncle picked me up and while he kept me with his arms he asked me "Ok, let's see this. Tommaso, what is the square root of 5968?". Mind you, I do not remember the exact number; I only recall it was between 5000 and 7000. I watched up into the void for two seconds, and I replied "77.3". Uncle Ciccio put me down and ran for the pocket calculator - he did have one, although they were a real novelty those years.

Cell migration, which is involved in wound healing, cancer and tumor growth, and embryonic growth and development, has been a topic of interest to mathematicians and biologists for decades. 


Modern maths has a "Heath Robinson" type approach - at least philosophically -  with its many sizes of infinity and logical paradoxes. Would this be the same for ETs? Also, what if they experience time and space differently from us? Perhaps they can only reason using flashes of insight? 

Or, perhaps topology is easy, but counting, for them, is an advanced concept few understand? Or perhaps they use quantum logic or some other logic we haven't thought of yet? Or, might they see everything as fractals?

What do you get when you mix theorists in computer science with evolutionary biologists? You get an algorithm to explain sex.

A fascinating mystery of evolution is how sexual recombination and natural selection produced the teeming diversity of life that exists today. The answer could lie in the game that genes play during sexual recombination, so computer scientists at the University of California, Berkeley, created an algorithm to describe the strategy used by these genes in this game.  


What did USC biomedical engineering assistant professor Megan McCain think when she first saw a real human heart, with all of those thin valves that have to open and close every second of our lives?

“Wow, there’s a lot of plaques of fat. I need to stop eating French fries.”

Nine years later, the “cardiac tissue engineer,” is trying to re-create the human heart on a chip.