What's up in

# explainers

## Latest Articles

### How Do Machines ‘Grok’ Data?

By apparently overtraining them, researchers have seen neural networks discover novel solutions to problems.

### The Hidden Connection That Changed Number Theory

Quadratic reciprocity lurks around many corners in mathematics. By proving it, number theorists reimagined their whole field.

### The Deep Link Equating Math Proofs and Computer Programs

Mathematical logic and the code of computer programs are, in an exact way, mirror images of each other.

### How Many Microbes Does It Take to Make You Sick?

Exposure to a virus isn’t an all-or-nothing proposition. The concept of “infectious dose” suggests ways to keep ourselves safer from harm.

### How Scientists Are Tackling the Tricky Task of Solar Cycle Prediction

Scientists have struggled to accurately forecast the strength of the sun’s 11-year cycle — even after centuries of solar observations.

### Alan Turing and the Power of Negative Thinking

Mathematical proofs based on a technique called diagonalization can be relentlessly contrarian, but they help reveal the limits of algorithms.

### How Genetic Surprises Complicate the Old Doctrine of DNA

For over a century, biologists have had to contend with a complicated picture of genetics, which they’ve only recently begun to understand.

### How Math Achieved Transcendence

Transcendental numbers include famous examples like e and π, but it took mathematicians centuries to understand them.

### How the Brain Protects Itself From Blood-Borne Threats

To buffer the brain against menaces in the blood, a dynamic, multi-tiered system of protection is built into the brain’s blood vessels.