As a teenager, Bernhard Riemann reportedly borrowed Legendre’s 859-page Theory of Numbers from his school director.
He returned it one week later, saying it had taken him the whole week to master.
Two years afterward, he chose the same book for his graduation examination and answered every question correctly, despite not having looked at it in the meantime.
Source: Stephen Hawking (ed.), God Created the Integers.
Charles Berthoud is one of the most technically gifted bassists alive, Berklee-trained, famous for using every technique a bass has.
So when he found a bass made out of a recycled oil can, he had to slap it. Turns out an oil can can take it.
Tu Youyou became the first mainland Chinese scientist to be awarded a #NobelPrize in a scientific field - for discovering artemisinin, a malaria cure that’s saved millions. Today we reveal the 2026 medicine laureate. Stay tuned.
One of the strangest constants in number theory is
ζ(3) = 1 + 1/2³ + 1/3³ + 1/4³ + ⋯ ≈ 1.202056903159594…
Euler found elegant formulas for ζ(2), ζ(4), ζ(6), … in terms of powers of π. But the odd values proved far more mysterious.
Then in 1978, Roger Apéry unexpectedly proved that ζ(3) is irrational. His argument was initially surprising because it relied on sequences that looked unlikely to have the required integer properties, yet the proof held.
Even today, ζ(3) stands as a reminder that the odd zeta values behave very differently from the even ones.
NEW: @JudicialWatch lawsuit forces the release of another batch of Butler shooting documents: including drone photos taken of the Pittsburgh area by Crooks, cell phone evidence that shows that Crooks received fundraising appeals for Sen. Raphael Warnock (D-GA), and an unusual chat thread between Crooks and an unidentified person.
In 2015, at the ECHO Klassik Awards, pianist Menahem Pressler, then 92 years old, was honoured with a Lifetime Achievement Award. After accepting the award, he asked if he could sit down at the piano and play a short piece.
He chose Chopin’s Nocturne in C-sharp minor. There was no orchestra, just a piano and a man who had devoted his entire life to music. The piece is not long, but under Pressler’s fingers, each note seemed to unfold slowly, delicately, and intimately, like a story being told through sound.
Kepler's mother Katharina was arrested for witchcraft in Leonberg in 1615. The local Vogt who initiated the trial accused fifteen women and burned eight.
Kepler suspended his career to conduct her legal defence himself, with help from Tübingen lawyers and theologians. The trial ran six years, she spent part of it chained in prison in her elderly age, and she was released. Witchcraft was regarded as hereditary, so a conviction would have ended Kepler's career too. It is one of the best documented German witch trials.
Rachel Chen, 18, of Los Angeles (Marlborough School; from Canada), is a young math researcher.
In the 2026 Regeneron Science Talent Search she placed fourth and won $100,000 for the dual canonical basis of the spin representation via Temperley-Lieb algebra.
Extending a 1997 result, she used Temperley-Lieb diagrams to picture quantum particle systems in a magnetic field and gave what she calls the first explicit non-inductive formula for that basis, plus a new axiomatic view linked to the Hecke algebra. She qualified for USAJMO, CMO, and APMO, founded a math club, and directs contests for Athemath.