Math Files

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In 1940, some of Britain's leading physicists became convinced that a mysterious wartime telegram contained a secret message about Germany's nuclear research. The message ended with five strange words: "AND TELL MAUD RAY KENT" Nazi Germany had just occupied Denmark, and British scientists were deeply concerned about developments in nuclear physics. The telegram carried news about Danish physicist Niels Bohr and his family. But what did "MAUD RAY KENT" mean? Otto Frisch and Rudolf Peierls were among the researchers who tried to decipher it. Perhaps it was an anagram. They rearranged the letters and considered possibilities such as "RADIUM TAKEN," with a small spelling change. Could this mean that Germany had seized radioactive materials? Other interpretations involved uranium and deuterium, both relevant to nuclear research. The scientists were unable to establish a convincing meaning. Meanwhile, Britain had established a secret committee to investigate the feasibility of atomic weapons. It needed an inconspicuous name. The mysterious telegram supplied one. The committee became known as MAUD. Its investigations eventually produced influential reports in July 1941 that helped advance the Allied atomic bomb programme. But the supposed code had an unexpectedly ordinary explanation. Maud Ray was an actual person. She had worked as a governess for Niels Bohr's children and was living in Kent, England. The telegram was simply asking that she be told the Bohr family was safe. There was no secret nuclear warning hidden in those words. Otto Frisch later recalled the misunderstanding in his autobiography What Little I Remember (1979). Walter Gratzer reproduced the anecdote in Eurekas and Euphorias.

AI-assisted research claims a solution to Hermite's 178-year-old problem In 1848, Charles Hermite asked whether periodic continued fractions could characterize cubic irrationals. A new AI-assisted preprint claims an algorithm whose digits eventually repeat exactly when [ℚ(α) : ℚ] = 3. A potentially major result, but independent mathematical verification is still pending. Original research: hexagonmath.org/pdf/2611.003…

Famous Mathematicians ❤️

In 1904, an American physicist secretly removed a key component from a French laboratory experiment. The scientist conducting the experiment continued reporting exactly the same results. In 1903, French physicist René Blondlot announced that he had discovered a new kind of radiation. He called it N-rays, after his home city of Nancy. Researchers claimed these mysterious rays could pass through certain materials and make faintly luminous objects appear brighter. Scientific papers multiplied. Several French researchers reported observing the phenomenon. But scientists elsewhere struggled to reproduce the results. In September 1904, American physicist Robert W. Wood visited Blondlot's laboratory to investigate. Blondlot demonstrated an apparatus containing an aluminium prism. The prism supposedly separated the invisible N-rays into a spectrum, which could be detected through subtle changes in brightness. Wood saw no such changes. Then, while the room was dark, he quietly removed the prism. Blondlot did not notice. The experiment continued. And remarkably, spectral lines were still reported at the same positions! Wood replaced the prism before the lights returned. If the supposed rays required the prism to produce the observed spectrum, how could the same results appear when the prism was missing? Wood published his findings in Nature on 29 September 1904. The N-rays controversy soon collapsed. The alleged radiation was not accepted as a real physical phenomenon. A powerful lesson in experimental science: observations must be tested under conditions that can reveal when an expected effect is absent.

The Shape That Holds a Finite Amount of Paint but Has Infinite Surface Area

A geometry problem from the 1995 TIMSS international assessment that stumped 90% of students

Want 10 consecutive integers without a prime? Try 39,916,802 through 39,916,811. Each equals 11!+k for some k from 2 to 11, so each is divisible by k. The trick works for any length. There are infinitely many primes, yet arbitrarily long prime-free stretches.

100 prisoners, 100 boxes, and only 50 attempts each. An apparently impossible challenge has a 31.18% chance of success using one mathematical strategy.

The black hole discovery overshadowed by WW-II On 1 September 1939, the day Germany invaded Poland, a research paper appeared in the American journal Physical Review. Its authors were J. Robert Oppenheimer and his former student Hartland Snyder. Entitled “On Continued Gravitational Contraction,” the paper examined the ultimate fate of a sufficiently massive, collapsing star. Using Einstein’s theory of general relativity, they demonstrated how gravitational collapse could produce a region from which light could no longer reach distant observers. Their work became an important foundation of modern black-hole physics. Yet the historical moment was extraordinarily ill-timed. Europe had entered a devastating war, and Oppenheimer would soon turn his attention to nuclear weapons research. The physicist who helped describe the gravitational collapse of stars would become known to history principally for his role in developing the atomic bomb.

Start with 27. If the number is odd, compute 3n + 1; if even, halve it. The sequence climbs to 9,232 at step 77, then finally reaches 1 after 111 steps. Every positive integer tested so far behaves similarly, yet no proof covers them all. That is the Collatz conjecture.

In 1982, three American high-school students discovered a mistake that had escaped the SAT examiners. A small circle of radius r was supposed to roll around a larger circle of radius 3r. The examiners expected 3 rotations. But the correct answer was 4, and it wasn't among the five choices. The College Board subsequently rescored approximately 300,000 examinations.

12 November 1936: Alan Turing's landmark paper, “On Computable Numbers, with an Application to the Entscheidungsproblem,” was formally read before the London Mathematical Society. Turing introduced an abstract machine consisting of an unbounded tape, a read-write head and a finite set of instructions. He also described a universal machine capable of simulating other computing machines and proved that no algorithm can solve every mathematical decision problem. This established fundamental limits of computation decades before modern computers became widespread.

How to Solve a Rubik's Cube in 7 Steps

Clay still lists the $1 million Navier–Stokes problem as Active. For nearly a century, mathematicians struggled with a question hidden inside the equations governing water, air and turbulence. Can a smooth three-dimensional fluid flow develop a singularity in finite time? In September 2026, OpenAI announced that an AI system had constructed such a breakdown under smooth external forcing, with the proof also formalized in Lean. On 11 September, the Clay Mathematics Institute acknowledged the apparent breakthrough. But mathematical acceptance requires scrutiny. As of November 2026, Clay still lists the $1 million Navier–Stokes problem as Active.

Is it a mathematical prank?

Every planar map can be coloured with just four colours so that neighbouring regions differ. The theorem was proved in 1976 only after a computer checked 1,482 configurations. Decades later, the proof itself was formally verified in Coq. Four colours. Thousands of cases.