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number theory

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number theory

Behold Modular Forms, the ‘Fifth Fundamental Operation’ of Math

By Jordana Cepelewicz
September 21, 2023
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Modular forms are one of the most beautiful and mysterious objects in mathematics. What are they?

geometry

A Tower of Conjectures That Rests Upon a Needle

By Jordana Cepelewicz
September 12, 2023
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On its surface, the Kakeya conjecture is a simple statement about rotating needles. But it underlies a wealth of mathematics.

Q&A

Why Mathematical Proof Is a Social Compact

By Jordana Cepelewicz
August 31, 2023
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Number theorist Andrew Granville on what mathematics really is — and why objectivity is never quite within reach.

A colorful picture of nested circles.
number theory

Two Students Unravel a Widely Believed Math Conjecture

By Max G. Levy
August 10, 2023
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Mathematicians thought they were on the cusp of proving a conjecture about the ancient structures known as Apollonian circles. But a summer project would lead to its downfall.

number theory

Elliptic Curves Yield Their Secrets in a New Number System

By Kevin Hartnett
July 6, 2023
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Ana Caraiani and James Newton have extended an important result in number theory to the imaginary realm.

A complex machine produces prime numbers onto a conveyor belt that winds backwards into infinity.
number theory

Why Mathematicians Re-Prove What They Already Know

By Anna Kramer
April 26, 2023
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It’s been known for thousands of years that the primes go on forever, but new proofs give fresh insights into how theorems depend on one another.

A modular form is shown as a distorted, rainbow-hued dome atop concentric circles.
number theory

New Proof Distinguishes Mysterious and Powerful ‘Modular Forms’

By Jordana Cepelewicz
March 9, 2023
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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.

number theory

Probability and Number Theory Collide — in a Moment

By Leila Sloman
January 12, 2023
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Mathematicians are taking ideas developed to study random numbers and applying them to a broad range of categories.

2022 in Review

The Year in Math

By Konstantin Kakaes
December 22, 2022
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Four Fields Medals were awarded for major breakthroughs in geometry, combinatorics, statistical physics and number theory, even as mathematicians continued to wrestle with how computers are changing the discipline.


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