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# Abstractions blog

## Latest Articles

### Celebrated Cryptography Algorithm Gets an Upgrade

Two researchers have improved a well-known technique for lattice basis reduction, opening up new avenues for practical experiments in cryptography and mathematics.

### A Triplet Tree Forms One of the Most Beautiful Structures in Math

The Markov numbers reveal the secrets of irrational numbers and the patterns of the Fibonacci sequence. But there’s one question about them that has resisted proof for over a century.

### The (Often) Overlooked Experiment That Revealed the Quantum World

A century ago, the Stern-Gerlach experiment established the truth of quantum mechanics. Now it’s being used to probe the clash of quantum theory and gravity.

### Evolving Bacteria Can Evade Barriers to ‘Peak’ Fitness

Paradoxically, natural selection can sometimes seem to block organisms from evolving useful adaptations. But a new study of “fitness landscapes” and antibiotic resistance in bacteria shows that life still finds a way.

### Researchers Refute a Widespread Belief About Online Algorithms

Three computer scientists have disproved a long-standing conjecture about a fundamental problem involving imperfect information.

### The Astonishing Behavior of Recursive Sequences

Some strange mathematical sequences are always whole numbers — until they’re not. The puzzling patterns have revealed ties to graph theory and prime numbers, awing mathematicians.

### During Pregnancy, a Fake ‘Infection’ Protects the Fetus

Cells in the placenta have an unusual trick for activating gentle immune defenses and keeping them turned on when no infection is present. It involves crafting and deploying a fake virus.

### Cryptographers Solve Decades-Old Privacy Problem

Three researchers have found a long-sought way to pull information from large databases secretly, moving us closer to fully private internet searches.

### The Hidden Connection That Changed Number Theory

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