Erdős was described by Scientific American as the most prolific mathematician of all time. Born in Budapest in 1913 to Jewish parents who both taught mathematics, he endured family tragedy from birth: his two sisters, aged three and five, died of scarlet fever on the same day he was born. Fearing he might also fall ill, his mother kept him out of school until he was 10.

With his father held in a Russian prisoner-of-war camp for six years and his mother working long hours, young Erdos spent much of his childhood reading his parents' mathematics books.

"I fell in love with numbers at a young age," Erdos later recalled, as quoted by Britanica. "They were my friends. I could depend on them to always be there and always behave in the same way."

Even as a child, he displayed extraordinary mental abilities. At age three, he entertained his mother's friends by multiplying three-digit numbers in his head, and by four he had discovered the concept of negative numbers. According to the biography "The Boy Who Loved Math" by American writer Deborah Heiligman, four-year-old Erdos once astonished a visitor by calculating exactly how many seconds she had been alive.

His brilliance, however, did not make him an ideal student. He struggled to sit still in class and soon refused to attend school, joking that he wished there could be "negative school days." He remained at home under the care of a caretaker and his mother, who handled many everyday tasks for him, from cutting his food to dressing him. He did not butter his own bread until he was 21, when he went to dinner with colleagues.

Hungarian mathematician Paul Erdos. Photo courtesy of the Mathematisches Forschungsinstitut Oberwolfach

A life without a permanent home

In 1930, at 17, Erdos entered Peter Pazmany University in Budapest. Four years later, he completed his undergraduate studies and earned a Ph.D. in mathematics. While still a freshman, he gained recognition for an elegant proof of Bertrand's postulate, a theorem stating that there is always at least one prime number between any integer greater than one and its double.

In 1934, Erdos left Hungary for a four-year postdoctoral fellowship at the University of Manchester in the U.K. Four years later, he moved to the U.S, accepting a one-year appointment at the Institute for Advanced Study in Princeton, New Jersey, where he cofounded the field of probabilistic number theory.

His time at Princeton was brief as some colleagues there "found him uncouth and unconventional," according to "The Man Who Loved Only Numbers," British writer Paul Hoffman's biography of Erdos.

During the 1940s, he began moving from one American university to another, including Purdue, Stanford, Notre Dame and Johns Hopkins. He repeatedly turned down permanent academic positions, preferring the freedom to work with anyone, anywhere, on any mathematical problem that interested him.

That decision marked the beginning of a nomadic lifestyle that lasted more than half a century. Without a permanent home, a family or a fixed job, he traveled to Israel, China, Australia and more than 20 other countries to collaborate with mathematicians.

Erdos often arrived at a colleague's home without warning, announcing, "My brain is open!" He would stay as long as there were interesting problems to solve, according to Scientific American magazine. His hosts sometimes found the experience exhausting.

In Hoffman's book, mathematician Michael Jacobson of the University of Colorado Denver recalled that Erdos once stayed at his home, where they worked until 1 a.m. While Jacobson slept, Erdos stayed awake and at 4:30 a.m. began banging pots and pans to wake his host. Jacobson recalled that his first words were "not ‘Good morning’ or ‘How’d you sleep?’ but ‘Let n be an integer.’"

A lasting legacy

He often worked up to 20 hours a day and published around 1,500 academic papers, far more than nearly any other mathematician. Just as importantly, he encouraged others to work together, helping transform mathematics from a largely solitary pursuit into a highly collaborative discipline. Those collaborations would later influence fields that underpin modern computing and search engines.

Friends and colleagues affectionately called him Uncle Paul. His enormous network of collaborators gave rise to the concept of the "Erdos number," a measure of how closely a researcher is connected to him through co-authored papers.

Anyone who wrote a paper directly with Erdos has an Erdos number of one, their co-authors have a number of two, and so on. Albert Einstein's Erdos number was two. Other well-known figures with Erdos numbers include Angela Merkel (five), Stephen Hawking (four) and Elon Musk (four).

Beyond his published work, Erdos left behind hundreds of unsolved questions that became known as "Erdos problems," which, according to The Wall Street Journal, have become a benchmark for measuring progress in mathematics.

He divided these problems into two categories: marshmallows, described as "a tasty tidbit supplying a few moments of fleeting enjoyment," and acorns, which require "deep and subtle new insights from which a mighty oak can develop."

Although he possessed relatively little personal wealth, he often offered cash prizes for solutions to his problems. Money earned from speaking engagements, awards and temporary academic appointments was frequently donated to unhoused people, charities and young researchers.

Despite his unconventional lifestyle, Erdos received many honors, including the Wolf Prize and the Euler Medal. He was also elected to several of the world's leading scientific organizations, including the Hungarian Academy of Science in 1956, the U.S. National Academy of Sciences in 1979 and the British Royal Society in 1989.

Erdős was described by Scientific American as the most prolific mathematician of all time.

Erdos dedicated his life to a single pursuit. He never married, had no children and remained celibate throughout his life. He did not drive, had few hobbies and never established a permanent home.

Defying the belief that mathematics was a young person's game, he continued proving theorems and tackling new problems until his death at 83, suffering a heart attack just hours after solving a geometry problem at a conference in Warsaw.