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Solid-state batteries have spent decades in a strange limbo: always portrayed as the breakthrough that will make electric vehicles lighter, safer and longer-ranged, yet almost never available outside a laboratory or pilot line. The gap has made veterans of the industry wary of spectacular announcements. When the Finnish start-up Donut Lab recently claimed a solid-state cell with roughly twice the energy density of ordinary lithium-ion batteries, no rare-earth minerals and no fire risk, it released little supporting data. Independent analysis later indicated that the cell was actually a high-performance lithium-ion design containing liquid.

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Solar power’s rise is often told as a climate story. Stephanie Pappas’s feature makes a broader argument: solar has become a force in the world economy because it is now extraordinarily cheap, fast to deploy and difficult to embargo once installed. The technology still depends on concentrated manufacturing and supportive policy, but its fuel arrives everywhere for free.

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A collapse story that collapses under scrutiny

Rapa Nui, often called Easter Island, has long been presented as a warning for the whole planet. In the familiar version, its Polynesian settlers multiplied beyond the island’s limits, felled the last trees, exhausted the soil and squandered labor on hundreds of enormous stone statues. Hunger and warfare followed. By the time Europeans arrived, the society had supposedly destroyed itself.

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Why every hairy sphere needs a cowlick

A coconut poses a surprisingly serious mathematical problem. Imagine that every fiber on its surface is combed flat and that neighboring fibers change direction smoothly. No matter how carefully the job is done, at least one place must remain bald, stick straight up or otherwise break the pattern. This is the playful image behind the hairy ball theorem, a result from topology with consequences for weather, radio antennas and nuclear fusion.

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The cube trick that became a conjecture

A cube can perform a geometric trick that seems impossible at first: it can pass through a straight hole cut into an identical cube. The opening does not simply copy one of the cube’s square faces. By tilting the moving cube and choosing the hole’s orientation carefully, the passage can be made just large enough. The question dates to Prince Rupert of the Rhine in the 17th century, and shapes able to pass through an identical copy eventually became known as “Rupert.”

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Lottery tickets are famously poor investments, but the mathematics is subtler than that slogan suggests. Under rare circumstances, a jackpot can grow large enough to give a ticket a positive expected value. Even then, however, the bet may remain irrational for an individual. The distinction reveals both the power of expected value and the limits of reducing a life-changing gamble to a single average.

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A moving-day question becomes geometry

A couch stuck at a hallway corner is an ordinary frustration. Strip away the furniture, gravity and extra dimensions, however, and it becomes a problem that resisted mathematicians for almost six decades: what is the largest rigid two-dimensional shape that can pass around a right-angle bend in a corridor one unit wide?

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A forecast built from one number

Most predictions of human extinction begin with a threat: nuclear war, an asteroid, ecological collapse or some other physical mechanism. The “doomsday argument” begins somewhere stranger. It uses probability and a single estimate—that about 117 billion humans have been born—to suggest that humanity may be much nearer the end of its history than the beginning.

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The search for nature’s deepest laws usually sounds remote from ordinary politics. In this interview, Nobel Prize-winning physicist David J. Gross argues that the two cannot be separated: a final theory may take centuries to discover and confirm, while nuclear war could end the civilization capable of finding it in an afternoon. Protecting humanity’s scientific future, in his view, therefore belongs alongside the scientific work itself.

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Attention Has Stamina

Concentration is often treated as a fixed trait: some people can grind through a demanding exam, while others inevitably fade. Heather Schofield and Supreet Kaur argue for a more useful model. The ability to sustain mental effort over time, which they call cognitive endurance, behaves less like an immutable talent and more like physical stamina. Performance usually deteriorates during a long task, but practice can slow that decline.