Paul Erdos was of my grandmother’s generation, born in the same year, 1913, yet half a world away in Budapest, Austria-Hungary. His genius revealed itself early on. “By the time he was 20, he had found a proof for Chebyshev’s theorem.^{[14]} In 1934, at the age of 21, he was awarded a doctorate in mathematics.”

Erdős published around 1,500 mathematical papers during his lifetime, a figure that remains unsurpassed.

https://en.wikipedia.org/wiki/Paul_Erd%C5%91s^{[6]}He firmly believed mathematics to be a social activity, living an itinerant lifestyle with the sole purpose of writing mathematical papers with other mathematicians. Erdős’s prolific output with co-authors prompted the creation of the Erdős number, the number of steps in the shortest path between a mathematician and Erdős in terms of co-authorships.

Paul Erdos committed his life almost exclusively to the mathematics community. For his own reasons he chose not to have a family of his own. Although allowed to travel at will to his country of birth, he chose not to settle there, (until his death as he buried next to his parents “in grave 17A-6-29 at Kozma Street Cemetery in Budapest.”)

… Paul Erdős, became perhaps the most notorious mathematician of the 20th century. Erdős spent nearly his entire life crashing on other mathematicians’ couches and subsisting on the small sums he received for giving talks at universities around the world. He also had a fondness for devising math problems and offering bounties to anyone who could solve them.

https://www.quantamagazine.org/cash-for-math-the-erdos-prizes-live-on-20170605/

So dedicated to his pursuit of mathematics, he used cash prizes to lure others into joining him in its unraveling. By providing a private incentive he wished to enrich the public he enjoyed so much. His prizes still survive today.

Erdős continued that tradition. Over the course of his lifetime he offered rewards for hundreds of problems that he himself dreamed up. Amounts ranged from $25 into the thousands, depending on how challenging he thought the problem was. Today Graham controls a small fund left by Erdős, who died in 1996, for the purpose of making good on those bounties.

In 1974 Erdős paid off his first major sum: $1,000 to the Hungarian mathematician Endre Szemerédi for a problem Erdős had posed some years earlier. Szemerédi tackled the problem because “he said he could certainly use the money,” said Graham. Decades later Szemerédi would win the Abel Prize, commonly regarded as the Nobel of mathematics, for work that stemmed primarily from his solution to this Erdős problem.

https://www.quantamagazine.org/cash-for-math-the-erdos-prizes-live-on-20170605/

For most people, their primary or first degree community is their immediate family; those housed under the same roof. This mathematician cared not for real estate. His community thrived on the images of abstract notions brought down to earth in formulaic representation, sketched out on paper.