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The sneaky maths trick for solving problems without answering them

How can you have a proof without proving anything? Mathematicians found a way and, in the process, came to blows over it – but 100 years on, this trick is a common part of modern maths, says columnist Jacob Aron

Admin Recifes 15/07/2026 2

The sneaky maths trick for solving problems without answering them

How can you have a proof without proving anything? Mathematicians found a way and, in the process, came to blows over it – but 100 years on, this trick is a common part of modern maths, says columnist Jacob Aron

Admin Recifes 15/07/2026 2

Why praying for rain appears to work – but only in some places

In some parts of the world, the probability of rain rises with every day it doesn’t rain, and communities in these places are more likely to carry out rain-making rituals

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The US-China AI arms race has taken an unexpected turn

Powerful artificial intelligence models built by Chinese companies have gone from inducing widespread panic to being met with a shrug of the shoulders – what changed?

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Do we owe our existence to weird ‘virtual’ particles?

When considering what makes up a human body, a physicist drills down beyond the atomic level. Columnist Chanda Prescod-Weinstein explores the not-exactly-real particles that allow the stuff we’re made of to hang together

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How humans evolved to be twice as big as our ancestors

Artistic representations of ancient humans often show large men with bulging muscles – but our ancestors were actually smaller than us, in both height and body mass. Columnist Michael Marshall reveals surprising details about the short kings of prehistory

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Sugar molecules found in interstellar space for the first time

Researchers have long suspected early life may have been helped by sugars brought to Earth by asteroids – now a sugar found in raspberries has been spotted in a cosmic cloud nearly 27 light years away

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Alzheimer’s, stroke, depression: The preventative power of sauna

Sustained heat stress is bad for our health and can be deadly. But we’re discovering that heat therapies like sauna, when used in the right way, have surprisingly wide-reaching benefits for health

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Shifts in the jet stream are behind Europe’s long heatwaves

Two types of jet stream patterns seem to be causing persistent heat domes over Europe, with big questions for the future

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Hard but lightweight ‘bio-metal’ material discovered in sea worm jaws

Marine bristle worms have jaws made from a mix of proteins and metal ions that may constitute a whole new kind of material, with possible applications in engineering

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The Guide #249: As Glastonbury has a fallow year, here’s why more much-loved culture shoul

In this week’s newsletter: The festival always comes back fresher after allowing Worthy Farm to recover from its yearly musical extravaganza. Star Wars and Charli xcx could learn a thing or twoIn any other year this week’s Guide would be arriving into your inbox from Worthy Farm,

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From Jon Snow: A Last Big Story to Muse: the week in rave reviews

The former Channel 4 News anchor reports on his health before leading another investigation, and the never-knowingly-understated Devon rockers return. Here’s the pick of the week’s culture, taken from the Guardian’s best-rated reviews Continue reading...

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