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# Quantized Columns

## Latest Articles

### Can Machines Control Our Brains?

Advances in brain-computer interface technology are impressive, but we’re not close to anything resembling mind control.

### How to Solve Equations That Are Stubborn as a Goat

Math teachers have stymied students for hundreds of years by sticking goats in strangely shaped fields. Learn why one grazing goat problem has stumped mathematicians for more than a century.

### How Radio Astronomy Reveals the Universe

Radio waves, longer and less energetic than visible light, give astronomers access to some of the most obscure physics in the cosmos.

### The Mysterious Math of Perfection

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

### Isadore Singer Transcended Mathematical Boundaries

A former graduate student reflects on how Isadore Singer, who died on February 11, brought together mathematicians, physicists and anyone else interested in the deeper connections between diverse fields.

### How to Understand COVID-19 Variants and Their Effects on Vaccines

Researchers are tracking the different strains of SARS-CoV-2 and studying how they spread through our population and our bodies.

### Topology 101: The Hole Truth

The relationships among the properties of flexible shapes have fascinated mathematicians for centuries.

### The Crooked Geometry of Round Trips

Imagine if we lived on a cube-shaped Earth. How would you find the shortest path around the world?

### How Claude Shannon Invented the Future

Today’s information age is only possible thanks to the groundbreaking work of a lone genius.