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Why the Brain’s Connections to the Body Are Crisscrossed
In all bilaterally symmetrical animals, from humans down to simple worms, nerves cross from one side of the body to the opposite side of the brain. Geometry may explain why.
A New Symmetry Shakes Up Physics
So-called “higher symmetries” are illuminating everything from particle decays to the behavior of complex quantum systems.
Hobbyist Finds Math’s Elusive ‘Einstein’ Tile
The surprisingly simple tile is the first single, connected tile that can fill the entire plane in a pattern that never repeats — and can’t be made to fill it in a repeating way.
New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’
Using “refreshingly old” tools, mathematicians resolved a 50-year-old conjecture about how to categorize important functions called modular forms, with consequences for number theory and theoretical physics.
‘Nasty’ Geometry Breaks Decades-Old Tiling Conjecture
Mathematicians predicted that if they imposed enough restrictions on how a shape might tile space, they could force a periodic pattern to emerge. But they were wrong.
Asymmetry Detected in the Distribution of Galaxies
Two new studies suggest that certain tetrahedral arrangements of galaxies outnumber their mirror images, potentially reflecting details of the universe’s birth. But confirmation is needed.
Mathematicians Prove 30-Year-Old André-Oort Conjecture
A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.
Symmetries Reveal Clues About the Holographic Universe
Physicists have been busy exploring how our universe might emerge like a hologram out of a two-dimensional sheet. New clues have come from the symmetries found on an infinitely distant “celestial sphere.”
Gravitational Waves Should Permanently Distort Space-Time
The “gravitational memory effect” predicts that a passing gravitational wave should forever alter the structure of space-time. Physicists have linked the phenomenon to fundamental cosmic symmetries and a potential solution to the black hole information paradox.