Riemann’s conjecture about prime numbers has made every list of the most important unsolved mysteries in mathematics ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏ ͏
June 3, 2026—Bernhard Riemann’s conjecture about prime numbers has made every list of the most important unsolved mysteries in mathematics. Plus, how to maintain muscle, even on GLP-1s, and NASA has officially lost its MAVEN Mars orbiter.
—Andrea Gawrylewski
Chief Newsletter Editor
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South Tyrol Museum of Archaeology/Eurac Research/Marion Lafogler.
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More than 5,300 years after the death of Ötzi, the murdered Iceman, researchers found genetic material from his gut microbiome and identified yeasts that continue to exist despite the mummy being kept below freezing. | 3 min read
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Who's Afraid of the Riemann Conjecture?
Ever since it was first published in 1859, Bernhard Riemann’s conjecture about prime numbers has made every list of the most important unsolved mysteries in mathematics. But more than a century later, and with a million-dollar reward at stake, why has no one come close to solving it?
What is the Riemann hypothesis?
Prime numbers are everywhere on the number line, but exactly where they show up appears random. The Riemann hypothesis is a mathematical function that, if it equals zero, describes where prime numbers are on the number line.
It started in the early 1800s with the mathematician Carl Friedrich Gauss, who created a function that roughly showed the trend line of how many primes fall on any interval of the number line, up to three million.
About 50 years later, Riemann created a function (the Riemann zeta function) which plugs in complex numbers (an imaginary coefficient multiplied by the square root of –1, called i) into a gnarly equation and plots them on both the real and complex plane. He found that for every value of zeta that makes that function come out to zero, the exact line on the plot that shows where prime numbers fall comes more into focus, adding definition to Gauss’s sketch.
In 1859, Riemann made a guess: The real parts of every value of zeta which made the function come out to zero were all the same: 1/2. They differed only in what the imaginary parts were.
Mathematicians and computers have tested this by trying billions of versions of zeta where the real part is 1/2, and they found that, so far, the Riemann hypothesis holds up. But no one, not even a machine, can test an infinite amount of numbers. So, the hypothesis waits to be mathematically proven correct. Only then will it graduate into a theory.
What the experts say: The Riemann hypothesis, and prime numbers for that matter, represent primordial, fundamental concepts in mathematics. The quandary can apply to other fields beyond pure math—one physicist realized patterns in the statistics of the Riemann zeta function matched the theory he’d worked out for the energy levels of atomic nuclei. “Asking me why number theorists care so much about prime numbers is kind of like asking why physicists care so much about forces,” says Brian Conrad, a mathematician at Stanford University. —Emma Gometz, newsletter editor
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Muscle Maintenance
Why this matters: Muscles are not just for moving our bodies. They enable us to breathe, pump blood and keep our bones strong. Plus they power the metabolism and help regulate blood sugar and body temperature. Extensive muscle loss puts many of these processes at risk. One study awaiting peer review suggests there is a link between GLP-1 drugs and increased risk of osteoporosis.
What can be done: Doctors recommend eating enough protein and devoting about a third of your weekly exercise time to strength training. New treatments are in development to help retain muscle for those on weight loss drugs. A muscle-retention drug called bimagrumab blocks myostatin, a key protein that helps to suppress muscle growth. So far, trial results have been mixed. Another group of drugs called SARMs, or selective androgen-receptor modulators, are synthetic compounds that activate the body’s androgen receptors in a manner similar to testosterone, a hormone that can trigger muscle growth.
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TRAVEL WITH SCIENTIFIC AMERICAN
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Space Now Open for Icelandic Eclipse Adventure
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New availability! Grab your spot while they last and experience the 2026 solar eclipse in the Land ofIce and Fire on this trip of a lifetime led by Senior News Editor Andrea Thomspon.
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The Hubble Space Telescope snapped a picture of galaxy Messier 88 (M88), also known as NGC 4501. The bright glow is created by its central black hole—which is estimated to be around 100 million times more massive than our sun—as it sucks up gas and dust. The numerous bright red dots strewn around M88’s spiral arms are old stars, while the pink and blue represent star clusters and dust clouds.
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At first glance, the Riemann Hypothesis seems esoteric. In truth, it's a mathematical idea that sits at the intersection of pure theory and practical application. A proof would immediately settle a vast number of results in number theory, algebra, mathematical physics and dynamical systems. That may still sound far removed from everyday life. But history suggests otherwise: some of our most important discoveries rest on mathematical foundations that remained abstract—and unsettled—for generations.
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—Andrea Gawrylewski, Chief Newsletter Editor
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