FYI April 25, 2017

It’s Official! Happy National Crotilla Day.


On this day:

1916 – Easter Rising: The United Kingdom declares martial law in Ireland.
The Easter Rising (Irish: Éirí Amach na Cásca),[2] also known as the Easter Rebellion, was an armed insurrection in Ireland during Easter Week, April 1916. The Rising was launched by Irish republicans to end British rule in Ireland and establish an independent Irish Republic while the United Kingdom was heavily engaged in the First World War. It was the most significant uprising in Ireland since the rebellion of 1798, and the first armed action of the Irish revolutionary period.

Organised by a seven-man Military Council of the Irish Republican Brotherhood,[3] the Rising began on Easter Monday, 24 April 1916, and lasted for six days. Members of the Irish Volunteers—led by schoolmaster and Irish language activist Patrick Pearse, joined by the smaller Irish Citizen Army of James Connolly and 200 women of Cumann na mBan—seized key locations in Dublin and proclaimed an Irish Republic. The British Army brought in thousands of reinforcements as well as artillery and a gunboat. There was fierce street fighting on the routes into the city centre, where the rebels put up stiff resistance, slowing the British advance and inflicting heavy casualties. Elsewhere in Dublin, the fighting mainly consisted of sniping and long-range gun battles. The main rebel positions were gradually surrounded and bombarded with artillery. There were isolated actions in other parts of Ireland, with attacks on the Royal Irish Constabulary barracks at Ashbourne, County Meath, County Cork and in County Galway, and the seizure of the town of Enniscorthy, County Wexford. Germany had sent a shipment of arms to the rebels, but the British had intercepted it just before the Rising began. Volunteer leader Eoin MacNeill had then issued a countermand in a bid to halt the Rising, which greatly reduced the number of rebels who mobilised.

With much greater numbers and heavier weapons, the British Army suppressed the Rising. Pearse agreed to an unconditional surrender on Saturday 29 April, although sporadic fighting continued until Sunday, when word reached the other rebel positions. After the surrender the country remained under martial law. About 3,500 people were taken prisoner by the British, many of whom had played no part in the Rising, and 1,800 of them were sent to internment camps or prisons in Britain. Most of the leaders of the Rising were executed following courts-martial. The Rising brought physical force republicanism back to the forefront of Irish politics, which for nearly 50 years had been dominated by constitutional nationalism. It, and the British reaction to it, led to increased popular support for Irish independence. In December 1918, republicans, represented by the reconstituted Sinn Féin party, won a landslide victory in the general election to the British Parliament. They did not take their seats, but instead convened the First Dáil and declared the independence of the Irish Republic, which led to the War of Independence.

485 people were killed in the Easter Rising. About 54% were civilians, 30% were British military and police, and 16% were Irish rebels. More than 2,600 were wounded. Many of the civilians were killed as a result of the British using artillery and heavy machine guns, or mistaking civilians for rebels. Others were caught in the crossfire in a crowded city. The shelling and the fires it caused left parts of inner city Dublin in ruins.

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Born on this day:

1849 – Felix Klein, German mathematician and academic (d. 1925)
Christian Felix Klein (German: [klaɪn]; 25 April 1849 – 22 June 1925) was a German mathematician and mathematics educator, known for his work in group theory, complex analysis, non-Euclidean geometry, and on the connections between geometry and group theory. His 1872 Erlangen Program, classifying geometries by their underlying symmetry groups, was a highly influential synthesis of much of the mathematics of the day.

Felix Klein was born on 25 April 1849 in Düsseldorf,[1] to Prussian parents; his father, Caspar Klein (1809–1889), was a Prussian government official’s secretary stationed in the Rhine Province. Klein’s mother was Sophie Elise Klein (1819–1890, née Kayser).[2] He attended the Gymnasium in Düsseldorf, then studied mathematics and physics at the University of Bonn,[3] 1865–1866, intending to become a physicist. At that time, Julius Plücker held Bonn’s chair of mathematics and experimental physics, but by the time Klein became his assistant, in 1866, Plücker’s interest was geometry. Klein received his doctorate, supervised by Plücker, from the University of Bonn in 1868.

Plücker died in 1868, leaving his book on the foundations of line geometry incomplete. Klein was the obvious person to complete the second part of Plücker’s Neue Geometrie des Raumes, and thus became acquainted with Alfred Clebsch, who had moved to Göttingen in 1868. Klein visited Clebsch the following year, along with visits to Berlin and Paris. In July 1870, at the outbreak of the Franco-Prussian War, he was in Paris and had to leave the country. For a short time, he served as a medical orderly in the Prussian army before being appointed lecturer at Göttingen in early 1871.

Erlangen appointed Klein professor in 1872, when he was only 23.[4] In this, he was strongly supported by Clebsch, who regarded him as likely to become the leading mathematician of his day. Klein did not build a school at Erlangen where there were few students, and so he was pleased to be offered a chair at Munich’s Technische Hochschule in 1875. There he and Alexander von Brill taught advanced courses to many excellent students, including, Adolf Hurwitz, Walther von Dyck, Karl Rohn, Carl Runge, Max Planck, Luigi Bianchi, and Gregorio Ricci-Curbastro.

In 1875 Klein married Anne Hegel, the granddaughter of the philosopher Georg Wilhelm Friedrich Hegel.[5]

After five years at the Technische Hochschule, Klein was appointed to a chair of geometry at Leipzig. There his colleagues included Walther von Dyck, Rohn, Eduard Study and Friedrich Engel. Klein’s years at Leipzig, 1880 to 1886, fundamentally changed his life. In 1882, his health collapsed; in 1883–1884, he was plagued by depression. Nonetheless his research continued; his seminal work on hyperelliptic sigma functions dates from around this period, being published in 1886 and 1888.

Klein accepted a chair at the University of Göttingen in 1886. From then until his 1913 retirement, he sought to re-establish Göttingen as the world’s leading mathematics research center. Yet he never managed to transfer from Leipzig to Göttingen his own role as the leader of a school of geometry. At Göttingen, he taught a variety of courses, mainly on the interface between mathematics and physics, such as mechanics and potential theory.

The research center Klein established at Göttingen served as a model for the best such centers throughout the world. He introduced weekly discussion meetings, and created a mathematical reading room and library. In 1895, Klein hired David Hilbert away from Königsberg; this appointment proved fateful, because Hilbert continued Göttingen’s glory until his own retirement in 1932.

Under Klein’s editorship, Mathematische Annalen became one of the very best mathematics journals in the world. Founded by Clebsch, only under Klein’s management did it first rival then surpass Crelle’s Journal based out of the University of Berlin. Klein set up a small team of editors who met regularly, making democratic decisions. The journal specialized in complex analysis, algebraic geometry, and invariant theory (at least until Hilbert killed the subject). It also provided an important outlet for real analysis and the new group theory.

In 1893 in Chicago, Klein was a keynote speaker at the International Mathematical Congress held as part of the World’s Columbian Exposition.[6] Thanks in part to Klein’s efforts, Göttingen began admitting women in 1893. He supervised the first Ph.D. thesis in mathematics written at Göttingen by a woman; she was Grace Chisholm Young, an English student of Arthur Cayley’s, whom Klein admired. In 1897 Klein became foreign member of the Royal Netherlands Academy of Arts and Sciences.[7]

Around 1900, Klein began to take an interest in mathematical instruction in schools. In 1905, he played a decisive role in formulating a plan recommending that analytic geometry, the rudiments of differential and integral calculus, and the function concept be taught in secondary schools.[8][9] This recommendation was gradually implemented in many countries around the world. In 1908, Klein was elected president of the International Commission on Mathematical Instruction at the Rome International Congress of Mathematicians.[10] Under his guidance, the German branch of the Commission published many volumes on the teaching of mathematics at all levels in Germany.

The London Mathematical Society awarded Klein its De Morgan Medal in 1893. He was elected a member of the Royal Society in 1885, and was awarded its Copley Medal in 1912. He retired the following year due to ill health, but continued to teach mathematics at his home for some years more.

Klein bore the title of Geheimrat.

He died in Göttingen in 1925.


Klein’s dissertation, on line geometry and its applications to mechanics, classified second degree line complexes using Weierstrass’s theory of elementary divisors.

Klein’s first important mathematical discoveries were made in 1870. In collaboration with Sophus Lie, he discovered the fundamental properties of the asymptotic lines on the Kummer surface. They went on to investigate W-curves, curves invariant under a group of projective transformations. It was Lie who introduced Klein to the concept of group, which was to play a major role in his later work. Klein also learned about groups from Camille Jordan.[11]

Klein devised the bottle named after him, a one-sided closed surface which cannot be embedded in three-dimensional Euclidean space, but it may be immersed as a cylinder looped back through itself to join with its other end from the “inside”. It may be embedded in Euclidean space of dimensions 4 and higher.

In the 1890s, Klein turned to mathematical physics, a subject from which he had never strayed far, writing on the gyroscope with Arnold Sommerfeld.[12] In 1894 he launched the idea of an encyclopedia of mathematics including its applications, which became the Enzyklopädie der mathematischen Wissenschaften. This enterprise, which ran until 1935, provided an important standard reference of enduring value.[13]

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