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Mathematicians Find Long-Sought Building Blocks for Special Polynomials
Hilbert’s 12th problem asked for novel analogues of the roots of unity, the building blocks for certain number systems. Now, over 100 years later, two mathematicians have produced them.
Mathematician Disproves 80-Year-Old Algebra Conjecture
Inside the symmetries of a crystal shape, a postdoctoral researcher has unearthed a counterexample to a basic conjecture about multiplicative inverses.
Mathematicians Set Numbers in Motion to Unlock Their Secrets
A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.
Undergraduates Hunt for Special Tetrahedra That Fit Together
A group of MIT undergraduates is searching for tetrahedra that tile space, the latest effort in a millennia-long inquiry. They’ve already made a new discovery.
Tetrahedron Solutions Finally Proved Decades After Computer Search
Four mathematicians have cataloged all the tetrahedra with rational angles, resolving a question about basic geometric shapes using techniques from number theory.