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# number theory

## Latest Articles

### 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.

### Mathematicians Find a New Class of Digitally Delicate Primes

Despite finding no specific examples, researchers have proved the existence of a pervasive kind of prime number so delicate that changing any of its infinite digits renders it composite.

### The Mysterious Math of Perfection

Enter the world of perfect numbers and explore the mystery mathematicians have spent thousands of years trying to solve.

### 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.

### How I Learned to Love and Fear the Riemann Hypothesis

A number theorist recalls his first encounter with the Riemann hypothesis and breaks down the math in a new Quanta video.

### The Year in Math and Computer Science

Even as mathematicians and computer scientists proved big results in computational complexity, number theory and geometry, computers proved themselves increasingly indispensable in mathematics.

### An Infinite Universe of Number Systems

The p-adics form an infinite collection of number systems based on prime numbers. They’re at the heart of modern number theory.