Alfred Pringsheim

Alfred Pringsheim: Rigour, Majolica, and the Wreck of a Life

In June 1939 an eighty-eight-year-old professor emeritus signed away the largest private collection of Italian majolica in Germany — 440 pieces, assembled over a lifetime — to a Sotheby's auction in London. The German state kept the overwhelming majority of the proceeds. What he received in exchange was permission to leave the country. He had already lost his house, which the Nazi Party demolished to build its headquarters, his title, a third of his pension, and his name, to which the state had appended "Israel." He was Thomas Mann's father-in-law, Richard Wagner's friend, and one of the most exacting analysts in Germany.

Silesia, Money, and a Piano

Alfred Pringsheim was born on 2 September 1850 in Ohlau, Lower Silesia, to a wealthy Jewish family. His father Rudolf had made a fortune in construction and held railways and coal mines; his mother was Paula Deutschmann. He grew up in Breslau and attended the Maria Magdalena Gymnasium there, excelling at music and mathematics in roughly equal measure.

The music was not a hobby. Pringsheim became an accomplished pianist, arranged compositions for piano, and formed a friendship with Richard Wagner, whom he supported financially along with the Bayreuth Festival. For most of his life the two enthusiasms ran in parallel and neither gave way.

He began studying mathematics and physics at Berlin in 1868, then moved to Heidelberg and took his doctorate there in 1872 under Leo Königsberger — himself a student of Weierstrass, and a specialist in elliptic functions. He moved to Munich in 1875 and habilitated at the Ludwig-Maximilians-Universität in 1877 as a privatdozent. He became extraordinary professor in 1886, joined the Bavarian Academy of Sciences in 1898, and was made full professor in 1901, retiring in 1922.

The Mathematics

Pringsheim worked on the theory of functions of real and complex variables, on infinite series, and on continued fractions. The judgement of the historical record is unusually blunt: his mathematics was characterised by meticulous rigour rather than by great ideas.

That is a fair description, and it undersells what rigour was worth in his generation. Nineteenth-century analysis was full of results everyone used and nobody had properly proved, and Pringsheim's instinct was to go back and check.

His best-known result concerns power series. If you have a power series with all positive coefficients whose radius of convergence is 1, then the point 1 itself — sitting on the boundary circle, straight out along the positive real axis — must be a singularity. You cannot smoothly continue the function past it. This is a statement about where a function is guaranteed to break, deduced purely from the signs of its coefficients, and it is useful precisely because it locates trouble without any calculation.

He also produced a simplified proof of Cauchy's integral theorem, one of the central results of complex analysis. In 1893 he proved a theorem connecting infinite differentiability to analyticity — that a function differentiable infinitely often is analytic provided the radius of convergence of its Taylor series stays bounded away from zero — though it later required correction.

His continued fraction work introduced the notion of unconditional convergence and produced, in 1898, a criterion now known as the Śleszyński–Pringsheim theorem, after Ivan Śleszyński arrived at it independently. He also contributed to the Abel–Dini–Pringsheim theorem, a test for the convergence of series.

And in a piece of scholarly housekeeping that is very much in character, he examined Johann Heinrich Lambert's 1761 proof that π is irrational — which the textbooks of his day routinely described as defective — and established that it was in fact flawless. It took someone with Pringsheim's temperament to go back to a hundred-and-thirty-year-old argument and read it properly.

Between 1916 and 1932 he produced his monument: the five-part *Vorlesungen über Zahlen- und Funktionenlehre*, covering the real numbers, infinite series, complex analysis and analytic functions with the thoroughness of a man who did not intend to leave gaps.

The House on Arcisstrasse

Pringsheim married Gertrude Hedwig Anna Dohm, an actress and the daughter of the Berlin journalist Ernst Dohm and the women's rights campaigner Hedwig Dohm. They had five children: Erik, Peter, Heinz, Klaus, who became a conductor and composer, and Katharina — Katia — who studied physics and mathematics before marrying Thomas Mann on 11 February 1905. Mann put his father-in-law into the novel *Royal Highness* as the character Samuel Spoelman.

The Pringsheim palace on Arcisstrasse became, in a colleague's phrase, a centre of Munich's social and cultural life. Pringsheim himself was known for witty lectures and for a celebrated annual *Bierrede* — beer speech — at gatherings of mathematicians. The majolica collection grew to 440 pieces, the largest in private hands in Germany, alongside enamels, stained glass and paintings.

The wealth did not survive the century. He invested patriotically in German war loans during the First World War, and what those losses left was finished off by the hyperinflation of the early 1920s.

Dismantling

After 1933 the state took the rest, piece by piece. The Arcisstrasse palace was confiscated in 1933 and demolished; a Nazi Party headquarters went up on the site. In 1934 Pringsheim refused to swear a loyalty oath to Hitler and lost his emeritus status and a third of his pension. In January 1938, aged eighty-seven, he was compelled to insert "Israel" into his name. Later that year he was expelled from the Bavarian Academy of Sciences he had belonged to for forty years, and during the Kristallnacht pogrom in November the SS seized the majolica.

The 1939 arrangement that got him out was, in form, a sale: the government permitted the collection to be exported to Sotheby's for auction on 7 June 1939, retaining eighty per cent of the first £20,000 and seventy per cent of everything after. Before leaving, Pringsheim gave his friend Constantin Carathéodory a rare volume of Jacob Bernoulli containing the solution to the isoperimetric problem. He and Hedwig reached Zürich on 31 October 1939, helped out by university officials and, improbably, a member of the SS.

Why Alfred Is Called a Genius

This is a case where the honest answer is a qualified one, and pretending otherwise would be a disservice.

Pringsheim was not a great originator. The standard assessment — meticulous rigour rather than great ideas — is accurate, and he does not belong in the company of Hilbert or Weierstrass. There is no field he founded and no problem of the first rank that fell to him.

What he had was a specific and undervalued form of intellectual character: an intolerance for arguments that merely looked convincing. The Lambert episode captures it exactly. A whole generation of textbook writers repeated that Lambert's proof of the irrationality of π was flawed, because that is what the previous generation had said. Pringsheim read it and found nothing wrong with it. Doing that requires no genius in the romantic sense; it requires a refusal to defer, sustained over decades, plus the technical command to back it up. The power series theorem and the continued fraction criterion are results of the same kind — not spectacular, but exactly right, and still in the literature under his name.

There is a second sense in which the word applies, though it is not mathematical. Pringsheim was a serious pianist and a collector of real discernment who assembled the finest private majolica holding in Germany, while holding a chair in analysis and running one of Munich's cultural salons. That breadth, sustained at a high level in three separate domains, is rare.

Legacy

Pringsheim died in Zürich on 25 June 1941, aged ninety. Hedwig burned his personal papers, including his letters from Wagner, and died the following year.

His theorems remain in use, quietly, in complex analysis and the theory of continued fractions, and his five-volume *Vorlesungen* stands as one of the more complete expositions of classical analysis anyone attempted. More than four hundred pieces of his collection are logged in the German Lost Art Foundation's database, still the subject of restitution claims by his heirs — some returned as early as 1953, others settled financially decades later. The mathematics survived the regime intact. Almost nothing else he owned did.

Achievements

• Notable work: Śleszyński–Pringsheim theorem
• Notable work: Pringsheim collection
• Notable work: Vivanti–Pringsheim theorem
• Notable work: Abel–Dini–Pringsheim theorem
• Affiliated with Ludwig-Maximilians-Universität München
• Educated at Frederick William University Berlin, Ludwig-Maximilians-Universität München and Heidelberg University
• Worked as mathematician, university teacher and art collector