Generated by Codex with GPT 5.6 Sol High

The modern drone threat has created an awkward military arithmetic problem. Small unmanned aircraft are cheap, abundant and useful for both surveillance and attack, but the missiles traditionally used to destroy them are expensive and limited in number. A defense can therefore shoot down every incoming drone and still lose the larger economic and logistical contest. The Pentagon hopes directed-energy weapons—lasers and high-power microwaves—can reverse that imbalance, but the technology still has to prove that it can work reliably outside controlled tests.

Generated by Codex with GPT 5.6 Sol High

Google DeepMind’s latest robots can change a lightbulb, fetch popcorn and tie a knot. Yet sweeping crumbs into a dustpan remains unreliable. That contrast captures the central problem in Adam Rogers’s article: artificial intelligence has become remarkably good at manipulating symbols, but a useful household or workplace robot must manipulate a physical world full of soft bags, fragile grapes, slippery glasses and unfamiliar rooms.

Generated by Codex with GPT 5.6 Sol High

An old apple tree on Verona Island, Maine, looked close to collapse. Its trunk was almost hollow, its body leaned sideways, and no one knew what kind of fruit it produced. Yet the tree was still alive, still bearing chartreuse-yellow apples under a rusty web of skin—and, as Maryn McKenna recounts, still holding evidence that could revise both agricultural history and the future of apple breeding.

Generated by Codex with GPT 5.6 Sol High

AI may feel weightless when it arrives through a chat window, but its infrastructure is anything but. Training and running frontier models requires warehouses packed with power-hungry chips, cooling equipment, transmission lines and, increasingly, private power plants. Austyn Gaffney’s investigation follows that physical chain to the Mississippi–Tennessee border, where SpaceXAI assembled scores of gas turbines to bring its Colossus data centers online faster than the electric grid could accommodate them.

Generated by Codex with GPT 5.6 Sol High

Finding Primes by Eliminating Composites

Prime numbers look simple: each is divisible only by 1 and itself. Yet their locations become increasingly difficult to predict as numbers grow. Because every whole number can be factored into primes, understanding that irregular pattern is one of number theory’s central problems.

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When failure is the design goal

A picture hanging from a loop of string and two nails normally survives if either nail is removed. In 1997 A. Spivak posed a deliberately perverse alternative: could the string be wrapped so that pulling either nail makes the picture fall? That riddle grew into a family of problems whose playful premise conceals serious mathematics.

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Mathematics had to invent its language

Symbols such as +, −, =, 0 and ∀ look timeless, as though they emerged fully formed with the ideas they represent. In fact, mathematical notation developed through centuries of regional rivalry, technological change and individual ambition. In an interview with Scientific American, mathematician Raúl Rojas argues that this human history is not decorative background. It explains how abstract concepts became easier to express, teach and extend.

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The problem with choosing too soon—or too late

Many decisions must be made before all the options are visible. A driver needs gas but does not know the prices at stations farther down the highway. A company interviews applicants one at a time and must decide whether to hire each person before meeting the rest. Someone searching for an apartment may have to sign immediately or lose it to another buyer. In each case, gathering more information improves the comparison—but waiting too long can mean letting the best option disappear.

Generated by Codex with GPT 5.6 Sol High

When an answer has 41 million digits

Prime numbers are whole numbers divisible only by 1 and themselves. They are the indivisible building blocks of arithmetic: every whole number greater than 1 is either prime or can be factored into a unique collection of primes. Their definition is simple, but locating them becomes brutally difficult as the number line stretches outward.

Generated by Codex with GPT 5.6 Sol High

The hidden cost of an elementary operation

Multiplication feels settled because children learn a dependable method for it: stack two numbers, multiply every digit of one by every digit of the other, then add the shifted partial products. For two numbers with n digits, however, that familiar algorithm requires work that grows roughly as n squared. Doubling the length of the inputs means about four times as many single-digit multiplications; multiplying two 1,000-digit numbers takes about one million of them.