The Erdős Family

The patronym Erdős is not, in its distant origins, a hereditary Jewish name. Like the vast majority of Hungarian Jews, the family's ancestors bore, at the turn of the eighteenth and nineteenth centuries, imposed or Germanic names. In the case of the mathematician, family tradition is here corroborated by biographical sources: the original name was Engländer, meaning "the Englishman" in German — perhaps a trade-counter nickname or a place designation, perhaps simply one of those administrative denominations assigned from the outside to Jewish families of the Empire. This name was magyarized into Erdős during the era of assimilation. Paul's mother, Anna, born Wilhelm, also bears a Germanic patronym, a further sign of that layer of origin which precedes the Magyar horizon. The MacTutor notice confirms it unequivocally: Paul Erdős came from a Jewish family, the original family name being Engländer.

This gesture of onomastic magyarization was a mass phenomenon in the second half of the nineteenth century. After the civil emancipation of Hungarian Jews in 1867 and their religious recognition by the reception law of 1895, tens of thousands of families substituted a Hungarian name for their German one, out of patriotism, out of a desire for integration, and sometimes to escape stigmatization. The choice of Erdős, "the wooded one," fits within a widely shared aesthetic: names evoking nature — forest, mountain, valley —, colors, or place names. The name, in this respect, is a document. It carries within it the assimilation trajectory of a cultivated Jewish bourgeoisie that wished to be fully Hungarian while remaining attached, if only in a secularized manner, to its origins.

We touch here on one of the deepest tensions of modern Jewish identity: how to belong to two worlds at once? How to be Hungarian and Jewish, when the surrounding society so often demands a choice? The Engländer-Erdős family responded through linguistic and nominal assimilation — yet neither Lajos nor Anna renounced their identity of origin. They did not practice the Jewish religion, the sources attest, but neither did they disavow it. This median position, neither orthodoxy nor apostasy, is precisely that of the late Haskalah, the Jewish Enlightenment movement, which preferred to transform one's relationship to tradition rather than abandon it.

One must be cautious here. While the magyarization of the name is established as a general phenomenon and probable for this family, the exact form of the prior name belongs to biography rather than always to a preserved civil registry record. This is why this chapter falls at the intersection of transmitted Memory and documented History.

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The Erdős family belonged to the educated stratum of Budapest Jewry in the early twentieth century, a milieu that gave Hungarian and world science and culture an exceptional harvest of talents — the "Martians of Budapest," to borrow the nickname given to that constellation: John von Neumann, Leó Szilárd, Jenő Wigner, Edward Teller and their peers, all drawn from the same Jewish bourgeoisie that attended the same gymnasiums, read the same journals, and breathed the same air of intellectual modernity. The future mathematician's parents were both mathematics teachers in Hungarian secondary schools, which placed the child, from the cradle, at the heart of a culture of reasoning and abstraction.

This intellectual genealogy is not incidental. It explains the subject's precocity and his immersion in mathematics. Lajos Erdős, Paul's father, had been captured by the Russian army in 1914, at the very outset of the Great War, when his son was barely a year and a half old. He was taken to Siberia as an Austro-Hungarian prisoner of war and did not return until 1920 — six years of absence, six years during which Anna Wilhelm had to raise the child alone, hire a German governess, and provide for the household. It was in this way that Paul Erdős learned fluent German, in addition to Hungarian, even before starting school. Upon his return from captivity, Lajos, who had taught himself English to occupy his mind in the Siberian camps, introduced his son to that language as well. The future mathematician's early polyglossie — Hungarian, German, English, and later some rudiments of Hebrew and other languages — was the product of this singular household.

The Budapest of the Belle Époque and the interwar period offered this Jewish bourgeoisie elite gymnasiums, journals of mathematical problems for secondary-school students such as the celebrated KöMaL (Középiskolai Matematikai Lapok, founded in 1894), and an intense scholarly sociability. KöMaL deserves particular mention: conceived to stimulate mathematical talent from adolescence, it published monthly problems to which secondary-school students responded by correspondence, their solutions then being ranked and published. It was within this space that the future Hungarian mathematicians — mostly Jewish in Erdős's generation — recognized and found one another. This institution embodied something deeply consonant with the Jewish tradition of talmud Torah — study for its own sake, the joy of the open question, the community of seekers gathered around a text or a problem.

At the Pázmány Péter University in Budapest, where he enrolled in 1930, Paul Erdős studied under the mathematician Lipót Fejér and formed friendships with a circle of young Jewish mathematicians who called themselves "Anonymus," in reference to the medieval Hungarian chronicler. This group — which included Paul Turán, György Szekeres, Esther Klein, and others — became the living laboratory of nascent Ramsey theory and one of the most fertile intellectual centers in the history of twentieth-century mathematics. The sociability of research, intellectual friendship as a condition of thought: here is a trait that left a deep mark on this lineage.

The family's history is thus inseparable from that of a Central European Jewish elite which, within the span of two generations, moved from village orthodoxy to the scientific avant-garde of the great capitals. This chapter, grounded in convergent biographical sources, may be considered established.

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Paul Erdős received his doctorate from the University of Budapest in 1934, at the age of twenty-one. His thesis focused on number theory — already his oldest passion — and his first articles dazzled the international mathematical community with their originality and fruitfulness. He had already demonstrated, at barely nineteen, an elementary yet elegant result related to Bertrand's postulate, showing that between any integer n and its double 2n there always exists at least one prime number. This proof, simple in its tools but remarkable in its vision, circulated rapidly among European mathematicians and won the young man an immediate reputation.

As early as 1934, Erdős left Hungary for the University of Manchester, where he spent four years. This departure was not without reason: the rise of antisemitism in interwar Hungary, under the regime of Admiral Horthy, was making the country increasingly hostile to Jews, and the numerus clausus imposed since 1920 in Hungarian universities had already shattered careers. Erdős perceived the danger and chose academic exile before it became compelled. In this, he acted as other Jewish mathematicians and scientists of his generation did, leaving Central Europe in the first half of the 1930s, before the final catastrophe.

After Manchester, he received a fellowship at Princeton — the Institute for Advanced Study, which then housed Albert Einstein, John von Neumann, and a constellation of European exiles. But Princeton did not renew his fellowship. The reasons are poorly documented — perhaps his inability to conform to the institution's social norms, perhaps more obscure considerations. Erdős was compelled to occupy successive positions as an itinerant scholar at the University of Pennsylvania, at Notre Dame, at Purdue, at Stanford, at Syracuse. The wandering had begun, and it would not end until his death.

During the war years, the situation of his family in Hungary weighed upon him with ever-increasing heaviness. He received no news of his relatives between 1941 and the liberation of Budapest. When information finally came through, it brought with it the full measure of a catastrophe: the Jewish community of Hungary, one of the largest in Europe in 1939 with some eight hundred thousand souls, had been deported beginning in May 1944 with an unprecedented brutality and speed — in less than two months, nearly all of the provincial Jews were taken to Auschwitz-Birkenau. Budapest was spared a little longer, owing in part to international interventions and internal resistance, but it too paid a terrible price. Erdős's mother, Anna, survived. His father Lajos had died of a heart attack in 1942, before the deportations. Relatives, childhood friends, colleagues from the Anonymus group — several never returned.

This silence of the war years, this brutal severing of the filial and communal bond, is not a footnote in Erdős's biography: it is one of the keys to his later life. The man who would travel endlessly throughout the world, without home or material attachments, had lived through the destruction of his world of origin.

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The "existing entry" — legendary itinerant mathematician — finds here its full documentary justification. After the war years, Erdős never returned to live permanently in Hungary. His life became an uninterrupted succession of travels: from one university to another, from one colloquium to a congress, from a guest room to a hotel room. He would knock on his colleagues' doors with a phrase that became legendary: "My brain is open," announcing that he was ready to work and inviting his host to set about it with him.

He lived out of a suitcase — sometimes two —, owning next to nothing, returning to scientific foundations and individuals in need nearly all of the fees and prizes he received. His material possessions amounted to a few items of clothing, his notebooks, and his papers in progress. The American mathematician Joel Spencer, one of his many collaborators, reported that Erdős would arrive at his home, stay two or three days, solve or tackle several problems together, then depart toward another destination, leaving behind ideas and proofs the way others leave business cards.

This radical frugality, this voluntary stripping away of the self in order to concentrate on what is essential, evokes something the Jewish tradition knows well under the name of anavah — humility, in the sense not of self-effacement but of setting aside the superfluous self. Erdős sought neither comfort nor accumulation; he sought only mathematical truth and the human contact it makes possible. This is not a retrospective projection: it is what all the concordant testimonies of his colleagues describe with a precision that leaves no room for doubt.

Paul Hoffman, who devoted a biography to him that has become a standard reference, describes him as "probably the most eccentric mathematician in the world." Time magazine dubbed him "The Oddball's Oddball." But behind the eccentricity lay an ethical coherence: a man who had chosen to belong to no place in order to belong to all, to possess no wealth in order to distribute more of it, to allow himself no rest in order never to cease searching.

Except for a few years in the 1950s when he was not permitted to enter the United States — American authorities absurdly suspecting him of communist sympathies on account of his relations with scientists from Eastern Bloc countries — Erdős crossed the frontiers of the Cold War with a sovereignty that few of his contemporaries could afford. He visited Soviet mathematicians in Moscow, colleagues in both Germanys, in Israel, in Australia, in South America. His passport was a body of mathematical work, and his citizenship was the rigor of proof.

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If the Erdős lineage owes its fame to one man, it is also because that man made collaboration a genuine institution — and generosity the very structure of his scientific work. In this, he embodied a virtue that Judaism calls tzedakah: not charity in the sentimental sense, but redistributive justice, the moral obligation to share what one possesses with those who might benefit from it. For Erdős, what he possessed in abundance was mathematical insight, the capacity to see a problem from a new angle, to suggest the direction of a proof. And he gave it without measure.

More than 1,475 papers published over a career spanning six decades, with more than 500 different collaborators: these figures, often cited, risk obscuring what they truly signify. They signify that Erdős stimulated, awakened, and developed the talents of at least five hundred people — from intimidated doctoral students to established masters. Among his most frequent collaborators were the Hungarian mathematicians András Sárközy, with whom he co-signed 62 papers, András Hajnal, with 56 papers, and the American mathematician Ralph Faudree, with 50 papers. These figures represent only the visible tip of a network of a density unmatched in the history of science.

His work spanned several domains of discrete mathematics, in which he resolved numerous previously open problems. He collaborated with Mark Kac and Aurel Wintner on the probabilistic theory of numbers, with Pál Turán in approximation theory, and with Witold Hurewicz on dimension theory. He was one of the foremost champions and major contributors to Ramsey theory, which studies the conditions under which order necessarily emerges in sufficiently large structures — a theory whose philosophical subtext is not without resonance: the conviction that chaos, pushed to its limits, always ends by revealing a structure, a coherence, an underlying order.

His practice of offering monetary prizes for the resolution of open problems is equally well documented and revealing. These prizes, which could range from a few dozen to several hundred dollars depending on the estimated difficulty of the problem — $500 for some of the most intractable — were not mere publicity stunts. They constituted a mechanism of redistribution: Erdős would take the honoraria he received from his lectures and return them to the economy of research, transforming each open problem into a collective invitation. Many mathematicians testify to having solved an "Erdős problem" in hopes of pocketing a symbolic reward, only to find themselves with something infinitely more valuable: a collaboration, a friendship, a reputation.

From this practice arose the celebrated "Erdős number," which measures the collaborative distance of a mathematician from Erdős within the graph of co-authors — a concept that is itself a cultural extension of the patronym, become the affectionate standard of measurement of the global mathematical community. Having an Erdős number of 1 means having co-authored a paper directly with him; of 2, having co-authored with one of his direct co-authors; and so on. Albert Einstein had an Erdős number of 2. The notion has since extended far beyond pure mathematics, spreading into physics, computer science, and other scientific disciplines.

This network, woven paper by paper, conversation by conversation, carries a meaning that transcends anecdote. It institutes a form of kehilah — the community of belonging in the Jewish tradition — but a kehilah without territory or religious institution, founded on the sole bond of shared thought. Erdős, who observed no religion, was recreating without naming it a form of communal fellowship as real and as solidary as that which the shtetlekh of Eastern Europe had known around the Torah.

Erdős's itinerancy is not merely an individual eccentricity; it resonates deeply with the history of the Jewish diaspora of Central Europe in the twentieth century. Born a subject of the dual monarchy, Hungarian by heart and language, Jewish by origin in a secularized family, Erdős traversed the upheavals of the century with a biography that resembles, in certain respects, an accelerated summary of modern Jewish history: the hoped-for assimilation, the antisemitism that gave it the lie, forced exile, wandering transformed into a way of life, community reconstituted as a network.

His life as a scholar without a fixed address can be read as a transposition, in the intellectual register, of the diasporic condition: multiple belonging, the home carried within oneself, community reconstituted not through territory but through the network of relationships. In this, Erdős embodies something that the Talmud expresses in its own way: the idea that the Torah — here, mathematics — can be carried everywhere, that it is the portable homeland par excellence, the one possession of which no oppressor can strip the one who has made it his own.

Erdős's Jewish identity, attested by all sources, was more cultural and historical than religious. Neither he nor his parents observed the practices of the Jewish religion. Like a large portion of the secularized Hungarian Jewish bourgeoisie, he lived his Jewishness as an origin and a Memory rather than as a practice. His relationship to God, or rather to the idea of God, was expressed in a personal and facetious vocabulary: he referred to God as "SF" — the "Supreme Fascist" — a tyrannical and mischievous being who, according to Erdős, concealed the most beautiful proofs in a celestial "Book" to which mortal mathematicians gained access only in flashes. This metaphor, tinged with irony and tenderness in equal measure, says something essential: Erdős did not believe in God, but he believed in the beauty of mathematical truth with the fervor of a mystic.

The loss of family members and loved ones during the Shoah forms the tragic backdrop of that generation. The Hungarian Jewish community, numbering some eight hundred thousand in 1939, was among the last to be deported in occupied Europe — and among the most rapidly decimated. From May 1944 onward, under the administration of the collaborationist government of Döme Sztójay, in the space of fifty-six days, more than four hundred and thirty thousand provincial Jews were deported, almost all to Auschwitz-Birkenau. Budapest was partially spared thanks to international pressure and the actions of diplomats such as Raoul Wallenberg and Carl Lutz, but several tens of thousands of Jews from the capital nonetheless perished. Friends from the Anonymus group, colleagues, and people close to Erdős did not return from the camps.

His mother Anna, however, survived. After the war, she joined her son in his peregrinations and traveled with him in the final years of her life. This filial bond — mother and son making their way together through the mathematical world, he in search of proofs, she as an affectionate and watchful presence — is one of the most moving images that witnesses of that era have passed down. Anna died in 1971. Erdős, who was deeply attached to her, went through a period of severe depression after this loss, from which he emerged only by redoubling his mathematical activity.

This chapter, which articulates established facts — Jewish origin, itinerancy, historical context, bereavements — with a reading of their diasporic significance, honestly belongs to the intersection between the archive and memorial Memory.

Beyond the man himself, the name Erdős has become an object of learned culture and collective transmission. The "Erdős number" passes from mathematician to mathematician like a republican title of nobility; anecdotes about his suitcase, his personal vocabulary, his generosity and his asceticism circulate as living folklore in mathematics departments the world over. This dimension is, by its very nature, that of transmitted memory: stories, quotations, legends piously repeated.

The metaphor of the "Book" deserves closer attention. Erdős imagined that God — the "SF," the Supreme Fascist — possessed a book containing the most elegant proofs of every theorem. The mathematician's aim was not merely to prove: it was to find the proof from the Book, the one that reveals the structure in all its purity. This idea, expressed with irony yet lived with earnestness, was taken up and developed after his death by the mathematicians Martin Aigner and Günter Ziegler in a work entitled Proofs from THE BOOK, which gathers what are judged to be the most beautiful proofs in his honor. The book, published in 1998 and regularly reissued and expanded, is dedicated to his Memory. The metaphor has become an institution.

In this vision of a celestial Book containing perfect mathematical truths, it is difficult not to hear an echo — transformed, secularized, turned with deliberate irony — of the Jewish tradition of the Book par excellence. The Torah as the foundational text, as the source from which all radiates, as the object of an endless study transmitted across generations: Erdős was not an observant man, but he was, in his own very particular way, a man of the Book.

The surname, which originally designated a magyarized Jewish family from Budapest, has thus become a common noun of science — an adjective ("Erdősian"), a unit of social measure, a myth. Few lineages can claim such a metamorphosis: from the name meaning "forest" chosen by Hungarian Jews seeking integration in the century of emancipation, to a universal sign of intellectual fellowship.

Erdős's legacy is also institutional. Prizes bear his name; conferences are dedicated to him; the János Bolyai Mathematical Society in Hungary perpetuates his Memory. In Israel, where he traveled regularly and where he maintained deep ties with mathematicians at the Hebrew University of Jerusalem and at the Technion, his name is associated with the tradition of research in combinatorics and number theory. The Jewish People, itself scattered across the world, recognizes in Erdős one of its own — not in the narrow sense of religious observance, but in the broad and profound sense of belonging to a History of the mind.

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The Erdős lineage encapsulates, in a single patronym, several strata of Central European Jewish history: the Ashkenaze origin and the Germanic name Engländer, the magyarization of the name during the era of emancipation, the rise of a cultivated bourgeoisie in Budapest, the scientific fecundity of the Hungarian "Martians," the ordeal of the Shoah and exile, and then the life of a man who transformed diasporic wandering into a method of thought and an ethic of collaboration.

From what the archive establishes — the Jewish origin, the mathematical milieu, the prolific body of work comprising more than 1,475 articles, the itinerant life with a suitcase as sole home — to what Memory transmits — the legends of the scholar knocking on colleagues' doors, the folklore of the "Erdős number," the metaphor of the divine Book — this Great Book has endeavored to hold an equal balance between History and narrative.

And if one were to name what this lineage will have expressed, above all others, among the great values carried by the Jewish tradition through the ages, it would surely be the value that Judaism places at the very heart of its intellectual and moral ideal: talmud Torah, study as an end in itself and as a gift to the other. Erdős did not study for himself: he studied with and for others. He did not hoard his insights: he offered them, set them in circulation, transformed them into shared problems. He did not build a school in the institutional sense: he built a community in the most vital and most ancient sense of the word — a kehilah of researchers united not by geography but by love of truth.

This value — science as gift, thought as hospitality, intelligence offered to whoever knocks at the door — connects the singular destiny of Erdős to a collective memory infinitely older: that of the academies of Yavneh and Babylonia, the houses of study of Prague and Vilna, the mathematical circles of Budapest, down to the universities scattered to the four corners of the world where men and women still work today on problems he left open. The name Erdős, born of the Magyar forest and of one Jewish family's aspiration to belong, has become paradoxically the most universally shared name in mathematics: proof that a lineage can survive less through blood than through the spirit it scatters abroad.

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