Erdős Number

Paul Erdős (1913–1996)
Photo: American Mathematical Society

Paul Erdős (1913–1996) was one of the most prolific and collaborative mathematicians of the twentieth century, publishing more than 1,500 papers across combinatorics, number theory, graph theory, and probability. He had no fixed home, preferring instead to travel constantly, arriving at colleagues' doors with the greeting "My brain is open" — and leaving a co-authored paper behind.

The Erdős number is a measure of mathematical collaboration distance. Direct co-authors of Erdős have Erdős number 1. Anyone who co-authored with an Erdős-1 mathematician (but not Erdős directly) has Erdős number 2, and so on. The concept has propagated well beyond pure mathematics into the physical sciences and beyond.

My Erdős number is at most Er4. I have identified one four-step path and three independent five-step paths connecting me to Paul Erdős through co-authored publications.

Shortest Connection — Er(4)

Er4

Four-step connection

Erdős → Entringer → Mullhaupt → Ghil → Medeiros

Paul Erdős R.C. Entringer A. Mullhaupt M. Ghil B. Medeiros

Paul Erdős

Entringer, R.C.; Erdős, Paul, 1972: On the number of unique subgraphs of a graph. J. Combinatorial Theory Ser. B, 13, 112–115.

R.C. Entringer

Douthett, Jack; Entringer, Roger; Mullhaupt, Andrew, 1992: Musical scale construction: the continued fraction compromise. Utilitas Math., 42, 97–113.

A. Mullhaupt

Ghil, M.; Mullhaupt, A., 1985: Boolean delay equations. II. Periodic and aperiodic solutions. J. Statist. Phys., 41(1–2), 125–173.

M. Ghil

Zhang, Y.; Stevens, B.; Medeiros, B.; Ghil, M., 2009: Low cloud fraction, lower-tropospheric stability and large-scale divergence. Journal of Climate. DOI: 10.1175/2009JCLI2891.1

B. Medeiros

Five-step Connections — Er(5)

Er5

Berkeley Chain

via Hickerson → Dyson → MacDonald → Muller

Erdős Hickerson Dyson MacDonald Muller Medeiros

Paul Erdős

Erdős, Paul; Hickerson, Dean; Pach, János, 1989: A problem of Leo Moser about repeated distances on the sphere. Amer. Math. Monthly, 96, no. 7, 569–575.

D. Hickerson

Andrews, G.E.; Dyson, F.J.; Hickerson, D., 1988: Partitions and indefinite quadratic forms. Invent. Math., 91, no. 3, 391–407.

F.J. Dyson

Happer, W.; MacDonald, G.J.; Max, C.E.; Dyson, F.J., 1994: Atmospheric-turbulence compensation by resonant optical backscattering from the sodium layer in the upper atmosphere. J. Opt. Soc. Am. A, 11(1), 263–276.

G.J. MacDonald

Muller, R.A.; MacDonald, G.J., 1997: Glacial cycles and astronomical forcing. Science, 277(5323), 215–218.

R.A. Muller

Karner, D.B.; Levine, J.; Medeiros, B.P.; Muller, R.A., 2002: Constructing a stacked benthic δ¹⁸O record. Paleoceanography, 17(3), art. no. 1030.

B. Medeiros

Er5

UCLA Chain

via Entringer → Mullhaupt → Ghil → Stevens

Erdős Entringer Mullhaupt Ghil Stevens Medeiros

Paul Erdős

Entringer, R.C.; Erdős, Paul, 1972: On the number of unique subgraphs of a graph. J. Combinatorial Theory Ser. B, 13, 112–115.

R.C. Entringer

Douthett, Jack; Entringer, Roger; Mullhaupt, Andrew, 1992: Musical scale construction: the continued fraction compromise. Utilitas Math., 42, 97–113.

A. Mullhaupt

Ghil, M.; Mullhaupt, A., 1985: Boolean delay equations. II. Periodic and aperiodic solutions. J. Statist. Phys., 41(1–2), 125–173.

M. Ghil

Zhang, Y.; Stevens, B.; Ghil, M., 2005: On the diurnal cycle and susceptibility to aerosol concentration in a stratocumulus-topped mixed layer. Quart. J. Roy. Meteorol. Soc., 131, 1567–1584.

B. Stevens

Medeiros, B.; Hall, A.; Stevens, B., 2005: What controls the mean depth of the PBL? J. Climate, 18, 2877–2892.

B. Medeiros

Er5

NCAR Chain

via Pomerance → Bailey → Swarztrauber → Williamson

Erdős Pomerance Bailey Swarztrauber Williamson Medeiros

Paul Erdős

Erdős, Paul; Pomerance, Carl, 1978: On the largest prime factors of n and n+1. Aequationes Math., 17, no. 2–3, 311–321.

C. Pomerance

Bailey, D.H.; Borwein, J.M.; Crandall, R.E.; Pomerance, C., 2004: On the binary expansions of algebraic numbers. J. Théor. Nombres Bordeaux, 16, no. 3, 487–518.

D.H. Bailey

Bailey, D.H.; Swarztrauber, P.N., 1991: The fractional Fourier transform and applications. SIAM Rev., 33, no. 3, 389–404.

P.N. Swarztrauber

Williamson, D.L.; Drake, J.B.; Hack, J.J.; Jakob, R.; Swarztrauber, P.N., 1992: A standard test set for numerical approximations to the shallow water equations in spherical geometry. J. Comput. Phys., 102, no. 1, 211–224.

D.L. Williamson

Medeiros, B.; Williamson, D.L.; Hannay, C.; Olson, J.G., 2012: Southeast Pacific Stratocumulus in the Community Atmosphere Model. Journal of Climate, 25(18), 6175–6192.

B. Medeiros

Variant path: Medeiros → Lauritzen or Williamson → Jablonowski → Stout → Harary → Erdős

Erdős Number

Shortest Connection — Er(4)

Four-step connection

Five-step Connections — Er(5)

Berkeley Chain

UCLA Chain

NCAR Chain

Further Reading