One can imagine propping a cube up on its corner and boring a large-enough square hole vertically through it to fit a cube of the same size as the original. Later, mathematicians found more and more three-dimensional shapes that eventually came to be called Rupert: they are able to fall through a straight hole in an identical shape. In 2017 researchers formally conjectured that all 3D shapes with flat sides and no indents, known as convex polyhedrons, are Rupert.
Then, just over two decades ago, the Human Genome Project - the international scientific effort to decode the three billion letters of human DNA - changed everything. Critics at the time called it too expensive, too ambitious, too abstract. And they weren't wrong. It was the largest biology project ever proposed, and scientists hadn't even managed to sequence the smallest bacterial genome yet. But the organizers knew that big plans - moonshots - inspire people and attract funding.
There is an iron law in nature: the larger a species, the longer its members live. That's why whales outlive elephants, and elephants outlive lions. Very few animals defy this rule. Humans have circumvented it thanks to culture. But there is a small animal that laughs in its face. Given its size, the naked mole-rat (Heterocephalus glaber) shouldn't live more than two years, yet they often approach 40. What's more, they age healthily, without typical age-related diseases such as cancer, neurodegenerative disorders, or arthritis.
For more than a decade, innovation in high-throughput DNA sequencing (that is, transforming information stored in DNA into human- and machine-readable sequences) has propelled research in the biomedical domain and led to an exponential growth in worldwide sequencing capacity14,15. A large proportion of these data is deposited in publicly funded repositories, such as the European Nucleotide Archive (ENA) maintained by the European Molecular Biology Laboratory's European Bioinformatics Institute (EMBL-EBI)16,
Back in 2019, the gravitational wave observatories LIGO and Virgo detected major ripples in spacetime. While astronomers generally agree that the event, dubbed GW190521, was the result of two black holes colliding, a team of researchers at the Chinese Academy of Sciences has proposed a far more eyebrow-raising explanation. As detailed in a yet-to-be-peer-reviewed paper, first spotted by ScienceAlert, the researchers suggest that LIGO and Virgo instead picked up the signals of a black hole collision in a different universe than ours.
Imagine that someone gives you a list of five numbers: 1, 6, 21, 107 and-wait for it-47,176,870. Can you guess what comes next? If you're stumped, you're not alone. These are the first five busy beaver numbers. They form a sequence that's intimately tied to one of the most notoriously difficult questions in theoretical computer science. Determining the values of busy beaver numbers is a daunting challenge that has attracted a cult following among both professional and amateur mathematicians for over 60 years.
