August 4

Writing from Berlin to Christian Goldbach, Leonhard Euler said he had proved the case of cubes, but that the proof was quite unlike the one for fourth powers, and a general proof seemed far off.

Every whole number above 2 is a multiple of 4 or of an odd prime, so it is enough to prove the theorem for n = 4 and for every odd prime. For nearly a century mathematicians did it prime by prime, each proof harder than the last.

Aloysia’s younger sister, twenty. Leopold’s consent arrived the day after the wedding. Of their six children only two sons, Karl Thomas and Franz Xaver Wolfgang, lived past infancy.

In one session running past two in the morning, nobles and clergy competed to give up their privileges: seigneurial dues, the tithe, the sale of offices. The Assembly declared that it had abolished the feudal system entirely, though many dues had to be bought out.

In the fog the captain sees “It—Him!” and decides to tie his hands to the wheel when his strength fails, “and along with them I shall tie that which He—It!—dare not touch; and then, come good wind or foul, I shall save my soul, and my honour as a captain”. He puts the log in a bottle in case the…

The Schlieffen Plan sent the German right wing through neutral Belgium, whose neutrality Prussia had guaranteed in 1839. Bethmann Hollweg told the British ambassador that Britain was going to war for “a scrap of paper”.

After the war of movement ended in the autumn of 1914, some 700 kilometres of trenches ran from the North Sea to Switzerland and barely moved for three and a half years. Beside the French, British and Belgians fought Indians, Canadians, Australians, New Zealanders, South Africans, West Africans,…

Britain’s blockade slowly starved Germany of food and raw materials; Germany answered with U-boats that sank merchant ships without warning. The two battle fleets met in full only once, at Jutland.

Britain’s ultimatum over Belgium ran out at 11 p.m. London time, midnight in Berlin. With Britain came its empire: India, Canada, Australia, New Zealand and South Africa were at war without being asked. Grey had said his line about the lamps the evening before.

Five weeks from the assassination to general war. Clark’s title for the statesmen who made it is The Sleepwalkers: each took steps that made sense alone and none of them wanted the war they got.

After a stroke, at seventy-two. She had spent the Nobel money, and the houses it bought, on Eduard’s care; Einstein went on paying for it from Princeton.

On a stormy night the Maddox and Turner Joy reported a second torpedo attack and fired for hours at radar contacts. Johnson ordered reprisal air strikes that night. An NSA history declassified in 2005 concluded that no attack took place and that intercepts had been misread.

The centennial Games, with all 197 national committees taking part for the first time. Muhammad Ali, his hands shaking with Parkinson’s, lit the cauldron.