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A team of mathematicians has solved an important question about how solutions to polynomial equations relate to sophisticated geometric objects called Shimura varieties.
Using high school algebra and geometry, and knowing just one rational point on a circle or elliptic curve, we can locate infinitely many others.
A new proof demonstrates the power of arithmetic dynamics, an emerging discipline that combines insights from number theory and dynamical systems.
Mathematicians have figured out how to expand the reach of a mysterious bridge connecting two distant continents in the mathematical world.
A new statistical model appears to undermine long-held assumptions in number theory. How much should it be trusted when all that really matters is proof?
The 30-year-old math sensation Peter Scholze is now one of the youngest Fields medalists for “the revolution that he launched in arithmetic geometry.”
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