Documentary: Fermat's Last Theorem

Fermat's Last Theorem is one of the most famous math problems in history, as it remained unsolved for well over 300 years -- and Fermat himself, before his suicide, had written a margin note claiming he had a solution. Fellow _floss blogger Casey Johnston described FLT like so last year:

In 1637, Pierre de Fermat scribbled a note in the margin of his copy of the book Arithmetica. He wrote (conjectured, in math terms) that for an integer n greater that two, the equation an + bn = cn had no whole number solutions. He wrote a proof for the special case n = 4, and claimed to have a simple, “marvellous” proof that would make this statement true for all integers. However, Fermat was fairly secretive about his mathematic endeavors, and no one discovered his conjecture until his death in 1665. No trace was found of the proof Fermat claimed to have for all numbers, and so the race to prove his conjecture was on. For the next 330 years, many great mathematicians, such as Euler, Legendre, and Hilbert, stood and fell at the foot of what came to be known as Fermat’s Last Theorem. Some mathematicians were able to prove the theorem for more special cases, such as n = 3, 5, 10, and 14. Proving special cases gave a false sense of satisfaction; the theorem had to be proved for all numbers. Mathematicians began to doubt that there were sufficient techniques in existence to prove theorem. Eventually, in 1984, a mathematician named Gerhard Frey noted the similarity between the theorem and a geometrical identity, called an elliptical curve. Taking into account this new relationship, another mathematician, Andrew Wiles, set to work on the proof in secrecy in 1986. Nine years later, in 1995, with help from a former student Richard Taylor, Wiles successfully published a paper proving Fermat’s Last Theorem, using a recent concept called the Taniyama-Shimura conjecture. 358 years later, Fermat’s Last Theorem had finally been laid to rest.

In 1996, Simon Singh and John Lynch made a 45-minute documentary about Wiles and his FLT solution. It's a surprisingly engaging story, with twists and turns and math and problem-solving (also liberal use of Penguin Cafe Orchestra in the soundtrack). Wiles comes across as a genuine mathematician -- he was obsessed with FLT since boyhood, and his joy at its solution is clearly visible in this film. It's all available on Google Video, embedded below. Have a look if you're even vaguely interested in math! (Note: the math discussed in the film is aimed at a mainstream audience; you don't have to be a math whiz to get the human drama of the story.)


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Courtesy Murdoch University
Australian Scientists Discover First New Species of Sunfish in 125 Years
Original image
Courtesy Murdoch University

Scientists have pinpointed a whole new species of the largest bony fish in the world, the massive sunfish, as we learned from Smithsonian magazine. It's the first new species of sunfish proposed in more than 125 years.

As the researchers report in the Zoological Journal of the Linnean Society, the genetic differences between the newly named hoodwinker sunfish (Mola tecta) and its other sunfish brethren was confirmed by data on 27 different samples of the species collected over the course of three years. Since sunfish are so massive—the biggest can weigh as much as 5000 pounds—they pose a challenge to preserve and store, even for museums with large research collections. Lead author Marianne Nyegaard of Murdoch University in Australia traveled thousands of miles to find and collected genetic data on sunfish stranded on beaches. At one point, she was asked if she would be bringing her own crane to collect one.

Nyegaard also went back through scientific literature dating back to the 1500s, sorting through descriptions of sea monsters and mermen to see if any of the documentation sounded like observations of the hoodwinker. "We retraced the steps of early naturalists and taxonomists to understand how such a large fish could have evaded discovery all this time," she said in a press statement. "Overall, we felt science had been repeatedly tricked by this cheeky species, which is why we named it the 'hoodwinker.'"

Japanese researchers first detected genetic differences between previously known sunfish and a new, unknown species 10 years ago, and this confirms the existence of a whole different type from species like the Mola mola or Mola ramsayi.

Mola tecta looks a little different from other sunfish, with a more slender body. As it grows, it doesn't develop the protruding snout or bumps that other sunfish exhibit. Similarly to the others, though, it can reach a length of 8 feet or more. 

Based on the stomach contents of some of the specimens studied, the hoodwinker likely feeds on salps, a jellyfish-like creature that it probably chomps on (yes, sunfish have teeth) during deep dives. The species has been found near New Zealand, Australia, South Africa, and southern Chile.

[h/t Smithsonian]

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Gregory H. Revera, Wikimedia Commons // CC BY-SA 3.0
Study Suggests There's Water Beneath the Moon's Surface
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Gregory H. Revera, Wikimedia Commons // CC BY-SA 3.0

Astronauts may not need to go far to find water outside Earth. As CNN reports, Brown University scientists Ralph E. Milliken and Shuai Li suspect there are significant amounts of water churning within the Moon’s interior.

Their findings, published in the journal Nature Geoscience, lean on the discovery of glass beads encased in the Moon’s volcanic rock deposits. As recently as 100 million years ago, the Earth’s moon was a hotbed of volcanic activity. Evidence of that volatile time can still be found in the ancient ash and volcanic rock that’s scattered across the surface.

Using satellite imagery, the researchers identified tiny water droplets preserved inside glass beads that formed in the volcanic deposits. While water makes up a small fraction of each bead, its presence suggests there’s significantly more of it making up the Moon’s mantle.

Milliken and Li aren't the first scientists to notice water in lunar rocks. In 2008, volcanic materials collected from the Moon during the Apollo missions of 1971 and 1972 were revealed to contain the same water-flecked glass beads that the Brown scientists made the basis of their recent study. They took their research further by analyzing images captured across the face of the Moon and quickly saw the Apollo rocks represented a larger trend. "The distribution of these water-rich deposits is the key thing," Milliken said in a press statement. "They're spread across the surface, which tells us that the water found in the Apollo samples isn't a one-off. Lunar pyroclastics seem to be universally water-rich, which suggests the same may be true of the mantle."

The study challenges what we know about the Moon's formation, which scientists think occurred when a planet-sized object slammed into the Earth 4.5 billion years ago. "The growing evidence for water inside the Moon suggests that water did somehow survive, or that it was brought in shortly after the impact by asteroids or comets before the Moon had completely solidified," Li said. "The exact origin of water in the lunar interior is still a big question."

The findings also hold exciting possibilities for the future of space travel. NASA scientists have already considered turning the Moon into a water station for astronauts on their way to Mars. If water on the celestial body is really as abundant as the evidence may suggest, figuring out how to access that resource will definitely be on NASA's agenda.

[h/t CNN]


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