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Smaller Is Better: Why Finite Number Systems Pack More Punch
Recent progress on the “sum product” problem recalls a celebrated mathematical result that revealed the power of miniature number systems.
How a Strange Grid Reveals Hidden Connections Between Simple Numbers
A graduate student has helped illuminate a long-suspected connection between addition and multiplication.
Mathematicians Seal Back Door to Breaking RSA Encryption
Digital security depends on the difficulty of factoring large numbers. A new proof shows why one method for breaking digital encryption won’t work.
In the Universe of Equations, Virtually All Are Prime
Equations, like numbers, cannot always be split into simpler elements.
New Proof Shows Infinite Curves Come in Two Types
Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.
Without a Proof, Mathematicians Wonder How Much Evidence Is Enough
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?
Titans of Mathematics Clash Over Epic Proof of ABC Conjecture
Two mathematicians have found what they say is a hole at the heart of a proof that has convulsed the mathematics community for nearly six years.
A Number Theorist Who Bridges Math and Time
Akshay Venkatesh, a former prodigy who struggled with the genius stereotype, has won a Fields Medal for his “profound contributions to an exceptionally broad range of subjects in mathematics.”
A Master of Numbers and Shapes Who Is Rewriting Arithmetic
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.”