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Six Degrees of Quant: Kevin Bacon and the Erdos Number Mystery

  • An ‘inside joke’ that shows mathematicians have sense of humor
  • Unlike in finance, in Erdos-Land a low number is desirable

It’s inside baseball for finance’s brainiest brainiacs: the Erdos Number.

The Erdos here is Paul Erdos, one of the most prolific mathematicians of the 20th century. Never heard of him? Then you clearly don’t have an Erdos Number.

For those in the know -- which is to say, serious math whizzes -- the Erdos Number measures what’s known as the "collaborative distance” between Erdos and another person, via the authorship of mathematical papers.

“It’s a fun thing, an inside joke that shows mathematicians have a sense of humor," said Peter Carr, the former head of market modeling at Morgan Stanley. “It’s a measure of network connectivity, who you have worked with."

Think “Six Degrees of Kevin Bacon” for the “Beautiful Mind” crowd.

Simply put, the lower your Erdos Number, the closer you are to Erdos, who published roughly 1,500 papers in his lifetime.

The lowest Erdos Number -- zero -- belongs to Erdos himself. The 511 mathematicians who collaborated directly with him have an Erdos Number of 1. Those who collaborated with those collaborators have a 2, while those who collaborated with the people who collaborated with the people who collaborated with Erdos have a 3. And, so on.

Quant Future

At a time when many in finance say the future belongs to math-and-data loving quants, when computer scientists and astrophysicists are in hot demand at hedge funds -- and everywhere else -- understanding the Erdos Number couldn’t hurt.

“It shows that they were mentored by top mathematicians including those who collaborated personally with Erdos,” said David H. Bailey, who’s written more than 100 papers in the field of computational and experimental mathematics.

Bailey, a research associate in the computer science department at the University of California Davis who’s written about the Erdos Number, is a 2. Carr, now chair of the department of finance and risk engineering at New York University’s Tandon School, is a 3. That puts them in some serious mathematical company.

Holders of the Fields Medal, often described as the Nobel Prize of math, have a median number of 3 as well, according to Jerry Grossman, a professor at Oakland University in Rochester, Michigan. He runs the Erdos Number Project, which studies research collaboration among mathematicians.

For those who want to search for any connection to a math genius, the American Mathematical Society has a database called MathSciNet of more than 820,000 authors.

Hedge Funds

So who has the best Erdos Numbers in hedge funds?

James Simons, the billionaire founder of Renaissance Technologies, the most successful quant hedge fund of all time, clocks in at a 3. Simons collaborated with Shiing-Shen Chern on a 1971 paper, “Some Cohomology Classes in Principal Fiber Bundles and Their Application to Riemannian Geometry.” Chern collaborated with Aurel Wintner, who collaborated with Erdos.

David E. Shaw, the computer scientist who started a now $40 billion hedge fund, and John Overdeck, co-founder of $37 billion quant-fund Two Sigma, are 4’s, as is Anthony Ledford, chief scientist at Man Group Plc’s $19 billion AHL unit.

Oliver Hart and Bengt Holmstrom, who won this year’s Nobel Prize in Economics, have Erdos Numbers of 3 and 4, respectively. On average, Nobel laureates in economics come in at 5, Oakland University’s Grossman said.

Born in Budapest in 1913, Erdos (pronounced "air-dosh") could multiply three-digit numbers in his head by the age of three. He learned negative numbers at the age of four, Paul Hoffman wrote in the biography, “The Man Who Loved Only Numbers.” Erdos wrote more than 50 of his papers in his seventies alone -- which is more than most mathematicians pen in a lifetime, Hoffman wrote. When he died, in 1996, Erdos left behind a remarkable legacy of mathematical collaboration.

The Erdos Number isn’t taken seriously enough to be used in recruiting quants in any way, said Jean-Philippe Bouchaud, chairman of $7.2 billion quant fund Capital Fund Management in Paris. It’s more of an interesting point for those among the top mathematical minds.

“It shows the small-world effect,” said Bouchaud, a physicist whose Erdos number is 3.

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