But while the timing makes sense for cities, it’s not so great for abatement workers, whose occupational risks make them especially vulnerable to serious complications of Covid-19.Judging from its physical properties alone, asbestos is useful stuff: The naturally occurring mineral’s long, fibrous crystals absorb sound and resist fire, heat, and electricity.

The problem Greene and Lobb worked on predicts, basically, that every such path contains sets of four points that form the vertices of rectangles of any desired proportion.But again, the problem Greene and Lobb solved involves curves that are smooth, and therefore continuous.

Yet in the middle of the 20th century, mathematicians started uncovering deep relationships between them, and by the early 1970s, Robert Langlands of the Institute for Advanced Study had conjectured that Diophantine equations and automorphic forms match up in a very specific manner.

I was nursing a beer at his winter holiday party as he told me about the solar panels on his Brooklyn brownstone roof.It was a neighbor from around the corner who'd seen my solar array and, like me before him, was intrigued.

The computer scientists Henry Yuen, Thomas Vidick, Zhengfeng Ji, Anand Natarajan and John Wright co-authored a proof about verifying answers to computational problems and ended up solving major problems in math and quantum physics.

Earlier this year one of the top mathematicians in the world dared to confront the problem—and came away with one of the most significant results on the Collatz conjecture in decades.On September 8, Terence Tao posted a proof showing that—at the very least—the Collatz conjecture is “almost” true for “almost” all numbers.

Last Friday, Tesla CEO Elon Musk revealed Version 3.0 of the Solar Glass Roof , a house-topper made of solar panels that looks like slate.

Elon Musk on Friday afternoon revealed details of the latest version of Tesla’s Solar Glass Roof, announcing that installations have begun and should ramp up in the coming weeks.

For example, zero-knowledge proofs can be used to validate cryptocurrency transactions managed on a blockchain and combat fraud without revealing data about which wallet a payment came from, where it was sent, or how much currency changed hands.

About a week after I talk to Tobias and Asprey on the phone, I’m parking my 2007 Jeep Liberty among the hulking Mercedes G-Wagens at the Beverly Hilton for the sixth annual Biohacking Conference, hosted for the first time by Upgrade Labs.

Some of the wood that burned in the cathedral of Notre Dame in Paris on Monday was put in place in the year 1160. But architectural historians around the world were emailing each other frantically: If the lower three-quarters of the building resist, if the stone walls stand, it’ll be possible to imagine restoring Notre Dame.

The Keb is a technical shell, with features like a helmet-compatible hood, plasticized water-resistant zippers, and pockets on the chest so that you can access them while wearing a climbing harness or a hip belt.

Just swap the labels on the tiles from numbers to up or down spins, and the puzzle becomes equivalent to a Nagaoka ferromagnet, with a hole that moves through a lattice of electrons.

And at Tuesday's questioning of Pichai by the House Judiciary Committee, a string of Republicans hit their cues, insisting that the negative results from a Google search of their names or favored legislation must have been personally typed out by vengeful programmers in far-left California.Noam Cohen is an Ideas contributor at WIRED, a writer living in Brooklyn, and the author of The Know-It-Alls: The Rise of Silicon Valley as a Political Powerhouse and Social Wrecking Ball.Pichai patiently explained what an algorithm was and how Google’s algorithm had no reason to offend Republicans.

Bentley’s Tweedy New Convertible Has a Secret Spinning DoorEndless color palettes, prize woods, sacred cow leathers, massage seats, huge engines, active safety technologies—the sun never sets on the list of options that come with Bentley's new Continental GT Convertible.Bentley Motors LtdIn the 99 years since it started making cars, Bentley has offered its well-heeled, well-groomed customers a bounty of choices.

High winds blow embers perhaps miles in advance of a blaze, firebrands that land on clusters of pine needles or leaves on roofs, quickly triggering hundreds if not thousands of house fires, as appears to have happened in Paradise.Part of what makes the destruction of Paradise so shocking is that we tend to assume that cities just don’t burn anymore.