# Kevin Hartnett

## Quantum Supremacy Is Coming: Here’s What You Should Know

Researchers are getting close to building a quantum computer that can perform tasks a classical computer can’t. Here’s what the milestone will mean.

## A New Law to Describe Quantum Computing’s Rise?

Neven’s law states that quantum computers are improving at a “doubly exponential” rate. If it holds, quantum supremacy is around the corner.

## How Randomness Can Make Math Easier

Randomness would seem to make a mathematical statement harder to prove. In fact, it often does the opposite.

## A New Approach to Multiplication Opens the Door to Better Quantum Computers

In practice, quantum computers can’t run many programs that classical computers can, because they’re not allowed to selectively forget information. A new algorithm for multiplication shows a way around that problem.

## In Quantum Games, There’s No Way to Play the Odds

These games combine quantum entanglement, infinity and impossible-to-calculate winning probabilities. But if researchers can crack them, they’ll reveal deep mathematical secrets.

## 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.

## 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.

## New Proof Shows Infinite Curves Come in Two Types

Alexander Smith’s work on the Goldfeld conjecture reveals fundamental characteristics of elliptic curves.

## Why Mathematicians Can’t Find the Hay in a Haystack

In math, sometimes the most common things are the hardest to find.

## A Short Guide to Hard Problems

What’s easy for a computer to do, and what’s almost impossible? Those questions form the core of computational complexity. We present a map of the landscape.