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Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math
Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?
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.
In Times of Scarcity, War and Peace, a Ukrainian Finds the Magic in Math
With her homeland mired in war, the sphere-packing number theorist Maryna Viazovska has become the second woman to win a Fields Medal in the award’s 86-year history.
John Conway Solved Mathematical Problems With His Bare Hands
The legendary mathematician, who died on April 11, was curious, colorful and one of the greatest problem-solvers of his generation.
Out of a Magic Math Function, One Solution to Rule Them All
Mathematicians used “magic functions” to prove that two highly symmetric lattices solve a myriad of problems in eight- and 24-dimensional space.
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.”
Mathematicians Find Moonshine Link for Pariah Symmetries
A type of symmetry so unusual that it was called a “pariah” turns out to have deep connections to number theory.
The Oracle of Arithmetic
At 28, Peter Scholze is uncovering deep connections between number theory and geometry.
Sphere Packing Solved in Higher Dimensions
The Ukrainian mathematician Maryna Viazovska has solved the centuries-old sphere-packing problem in dimensions eight and 24.