Hilbert's fully-booked hotel always finds room for one more
David Hilbert's 1924 thought experiment of a hotel with infinite rooms shows how infinity breaks the ordinary rules of counting.
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Deutsche Welle: Germany's broadcaster for audiences abroad
Deutsche Welle broadcasts Germany to the world, not to Germans. That job has led it to hire a British transmitter firm and cost it its Moscow bureau.
How a botched press briefing opened the Berlin Wall in 1989
The Berlin Wall fell on 9 November 1989. The BBC and National Geographic trace how a botched press briefing turned months of protest into an open border.
Six countries pooled coal and steel, and built the EU's machinery
The European Coal and Steel Community put French and German heavy industry under one authority in 1952. Its commission, court and assembly became the EU's.
Germany's allotments began as play space for poor children
Germany has about a million Kleingarten allotments, 70,000 of them in Berlin. They started as fresh air for factory children. Now builders want the land.
Every household in Germany pays for ARD and ZDF, TV or not
Germany's Rundfunkbeitrag charges each household a flat monthly fee, whatever devices it owns, and that money pays for most of ARD and ZDF.
Germany's Basic Law lets judges ban a party outright
Germany's constitution lets its Federal Constitutional Court ban a political party outright, though it has done so only twice since 1945.
Lebensborn's children are tracing the families the Nazis hid
Adults born under the Nazi Lebensborn programme are opening old files and childhood homes to find the parents its secrecy hid from them.
A grandmaster's chess memory relies on patterns, not pieces
Grandmasters recall real chess positions at a glance because they store patterns, not pieces. Scramble the board and the advantage all but vanishes.
The geometry lecture that waited 61 years for Einstein
Bernhard Riemann's 1854 lecture on curved space sat mostly ignored for decades before Albert Einstein built general relativity on its ideas in 1915.
A 1927 IBM gadget solved Nuremberg's language problem
A system used at a 1927 labour conference ended up carrying Nuremberg's war-crimes trial live, in four languages at once.
Germany's small firms lead niche markets worldwide
Almost 99% of Germany's companies are Mittelstand firms, often family-run and exporting early, and many lead their whole niche worldwide.