Erdos Number Page

Paul Erdos (from the film N is a Number: A Portrait of Paul Erdos, by George Paul Csicsery)

Those of us familiar with publishing scientific papers in journals may be interested to hear about the great mathematician, Paul Erdos. With more than 450 collaborators, Erdos wrote over 1,500 papers, more than any mathematician who ever lived.

Many of Erdos's mathematical collaborators were prolific themselves. This situation has led many mathematicians to say 'I have an Erdos Number of 2', meaning they wrote a paper with someone who had once written a paper with the great Erdos. Anyone who writes a paper with someone with an Erdos Number of 2 receives an Erdos number of 3, and so on. Small Erdos numbers are very prestigious, possessed by only the world's most brilliant mathematicians, making 'Erdos Numbers' an entertaining topic at mathematical cocktail parties, and the subject of some careful, but light-hearted, study.

Prompted by my mathematician friend, Richard Green (who has an Erdos number of 3) , I recently discovered that I had an Erdos number of 9 (now 3; details below, for anyone interested), as do many other members of the UCLA Brain Mapping Division. Although not of great importance (like saying 'my grandmother's piano teacher was Beethoven's grandson'), I wonder whether most of the world's scientists, working in fields widely different than mathematics, are somehow indirectly linked to Erdos. Update [March 2004]: Bill Roscoe, my college tutor in Mathematics, has pointed out a shorter path. See below. Many thanks! - Paul. Update 2 [July 2007]: Craig Brozinsky, of UC Davis, kindly pointed out a shorter path via Brian Wandell, giving me an Erdos number of 5. This reminded me that we have written a paper with the Fields Medalist ST Yau, so my Erdos number is 3. Also, one of my research assistants, Kiralee Hayashi, who is also an actress, has an Erdos-Bacon number of 6 (Bacon number 3, Erdos number 3 ). (She was in Wasabi Tuna (2003) with Jason London, who was in The Rage: Carrie 2 (1999) with Rachel Blanchard, who was in Where the Truth Lies (2005) with Kevin Bacon.)

- Paul Thompson
UCLA Lab of Neuro Imaging thompson@loni.ucla.edu
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NEW SEQUENCE OF PAPERS:

Ronald Graham (Erdos number 1) wrote a paper with Paul Erdos (Erdos number 0), called On Sums of Fibonnacci Numbers

Shing Tung Yau (Erdos number 2) wrote On Sampling Markov Chains with Ronald Graham

Paul Thompson (Erdos number 3) wrote this paper (and several others) with Shing-Tung Yau:
Wang YL, Gu X, Hayashi KM, Chan TF, Thompson PM, Yau ST (2005). Brain Surface Parameterization using Riemann Surface Structure. Medical Image Computing and Computer Assisted Intervention, 2005;8(Pt 2):657-65, 2005. [indexed in Medline].

BILL ROSCOE'S SEQUENCE OF PAPERS (new name on each paper is in bold type):

P. Erdos (Erdos Number=0)- A.M. Rudin (1) - A.W. Roscoe (2) - A. Rosenfeld (3) - A. Pentland (4) - C. Nastar (5) - N. Ayache (6) - P. Thompson (Erdos Number=7)

Erdos P, Rudin ME. A non-normal box product, in infinite and finite sets.

Collins PJ, Reed GM, Roscoe AW, Rudin ME, A Lattice of Conditions and Topological Spaces.

Kong TY, Roscoe AW, Rosenfeld A (1992). Concepts of Digital Topology, Topology Appl. 46, 219-262.

Dickinson SJ, Pentland AP, Rosenfeld A (1992). From Volumes to Views: An Approach to 3D Object Recognition, Proc. CVGIP 55(2):130-154, March 1992.

Moghaddam B, Nastar C, Pentland A (1996). Bayesian Face Recognition Using Deformable Intensity Surfaces, IEEE Proc. CVPR 1996.

Nastar C, Ayache N (1993). Fast Segmentation and Tracking of Deformable Objects, IEEE Proc. ICCV, Berlin, 1993.

Pitiot A, Toga AW, Ayache N, Thompson PM (2002). Texture-Based MRI Segmentation with a Two-Stage Hybrid neural Classifier, IEEE World Congress on Computational Intelligence and Neural Nets, Honolulu, HI, May 12-17 2002.

OLD SEQUENCE OF PAPERS:

Paul Erdos's collaborator Gabor Szego (Erdos Number 1) published the following work in 1958:

2. Ulf Grenander (Erdos Number 2) and Gabor Szego.
Toeplitz forms and their applications, Berkeley, University of California Press, 1958.

3. Proc Natl Acad Sci U S A 1993 Dec 15;90(24):11944-11948 Mathematical textbook of deformable neuroanatomies.
Miller MI (Erdos Number 3), Christensen GE, Amit Y, Grenander U

4. Radiology 1996 Jun;199(3):787-791 Hippocampal MR imaging morphometry by means of general pattern matching.
Haller JW, Christensen GE, Joshi SC, Newcomer JW, Miller MI, Csernansky JG, Vannier MW

5. AJNR (Am J Neuroradiology) 1994 Nov;15(10):1861-1869 Craniosynostosis: diagnostic imaging with three-dimensional CT presentation.
Vannier MW, Pilgram TK, Marsh JL, Kraemer BB, Rayne SC, Gado MH, Moran CJ, McAlister WH, Shackelford GD, Hardesty RA

6. Ann Neurol 1978 Aug;4(2):104-111 Cerebral hemodynamics and metabolism in pseudotumor cerebri.
Raichle ME, Grubb RL Jr, Phelps ME, Gado MH, Caronna JJ

7. J Neurophysiol 1991 Sep;66(3):735-743 Somatotopic mapping of the primary motor cortex in humans: activation studies with cerebral blood flow and positron emission tomography.
Grafton ST, Woods RP, Mazziotta JC, Phelps ME
(Acknowledgment: Many thanks to Roger Woods for noting that this paper creates a shorter series than I had before!)

8. Journal of Computer Assisted Tomography 1998 Jan;22(1):139-152 Automated image registration: I. General methods and intrasubject, intramodality validation.
Woods RP, Grafton ST, Holmes CJ, Cherry SR, Mazziotta JC

9. Journal of Computer Assisted Tomography 1997 Jul;21(4):567-581 Detection and mapping of abnormal brain structure with a probabilistic atlas of cortical surfaces.
Thompson PM (Erdos Number 9 (!)), MacDonald D, Mega MS, Holmes CJ, Evans AC, Toga AW

Paul Thompson
UCLA Lab of Neuro Imaging thompson@loni.ucla.edu
HOMEPAGE
PUBLICATIONS