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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.
A New Theory for Systems That Defy Newton’s Third Law
In nonreciprocal systems, where Newton’s third law falls apart, “exceptional points” are helping researchers understand phase transitions and possibly other phenomena.
How Tadayuki Watanabe Disproved a Major Conjecture About Spheres
Watanabe invented a new way of distinguishing shapes on his way to solving the last open case of the Smale conjecture, a central question in topology about symmetries of the sphere.
Mathematician Answers Chess Problem About Attacking Queens
The n-queens problem is about finding how many different ways queens can be placed on a chessboard so that none attack each other. A mathematician has now all but solved it.