The Erdös number is used in mathematics to show that mathematics is a strongly interlinked science. Build a graph where each mathematician is a vertex and a connection edge between two vertices indicates that these two mathematicians have published a joint paper. Then, the Erdös number of a given mathematician is the minimal number of edges (=joint papers) you need to reach Erdös from that person. Erdös was a famous mathematician with about 1000 publications and around 100 different coauthors (the ones with Erdös number 1)
0. Paul Erdös
M. Aigner,P. Erdös, D. Grieser: On the representing number of intersecting families. Arch. Math. (Basel) 49 (1987), no. 2, 114-118.
1. Daniel Grieser
H. Uecker, D. Grieser, Z. Sobirov, D. Babajanov, D. Matrasulov: Soliton transport in tubular networks: transmission at vertices in the shrinking limit. Phys. Rev. E (3) 91 (2015), no. 2, 023209, 8 pp.
2. Hannes Uecker
A. Mielke, G. Schneider, H. Uecker: Stability and diffusive dynamics on extended domains. In "Ergodic theory, analysis, and efficient simulation of dynamical systems, Springer, Berlin, 2001", 563-583.
3. Alexander Mielke
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Before 2015 my Erdös number was 4, as obtained from Math Reviews Collaboration Distance calculator on 30/9/2004.
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0. Paul Erdös
Paul Erdös & David Preiss: Decomposition of spheres in Hilbert spaces. Comment. Math. Univ. Carolinae 17 (1976), no. 4, 791--795.
1. David Preiss
David Preiss & Vladimír Sverák: Derivatives of type $1$. Real Anal. Exchange 12 (1986/87) 354--360.
2. Vladimír Sverák
Vladimír Sverák & Tomáš Roubíček: Nonexistence of solutions in nonconvex multidimensional variational problems. J. Convex Anal. 7 (2000) 427--435.
3. Tomáš Roubíček
Tomáš Roubícek & Alexander Mielke: A rate-independent model for inelastic behavior of shape-memory alloys. Multiscale Model. Simul. 1 (2003) 571--597
4. Alexander Mielke
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ERDÖS number 5 was found without a search machine from:
(Maybe 5 was the optimal number before 2003. It was valid at least after 1996.)
0. Paul Erdös
M. Cates, P. Erdös, N. Hindman, B. Rothschild: Partition theorems for subsets of vector spaces. J. Combinatorial Theory Ser. A 20 (1976), no. 3, 279--291.
1. Bruce Rothschild
Martin Golubitsky, Bruce Rothschild: Primitive subalgebras of exceptional Lie algebras. Pacific J. Math. 39 (1971), 371--393.
2. Martin Golubitsky
Ian Melbourne, Pascal Chossat, Martin Golubitsky: Heteroclinic cycles involving periodic solutions in mode interactions with ${\rm O}(2)$ symmetry. Proc. Roy. Soc. Edinburgh Sect. A 113 (1989), no. 3-4, 315--345.
3. Ian Melbourne
Ian Melbourne, Guido Schneider: Phase dynamics in the real Ginzburg-Landau equation. Math. Nachr. 263/264 (2004), 171--180.
4. Guido Schneider
A. Mielke, G. Schneider: Attractors for modulation equations on unbounded domains---existence and comparison. Nonlinearity 8 (1995), no. 5, 743--768.
5. Alexander Mielke
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alternatively from Golubitsky
3. Pascal Chossat
P. Chossat, G. Iooss: Primary and secondary bifurcations in the Couette-Taylor problem. Japan J. Appl. Math. 2 (1985), no. 1, 37--68.
4. Gerard Iooss
G. Iooss, A. Mielke: Bifurcating time-periodic solutions of Navier-Stokes equations in infinite cylinders. J. Nonlinear Sci. 1 (1991), no. 1, 107--146
5. Alexander Mielke
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alternatively from Golubitsky
A. Vanderbauwhede, M. Krupa, M. Golubitsky: Secondary bifurcations in symmetric systems. Differential equations (Xanthi, 1987), 709--716, Lecture Notes in Pure and Appl. Math., 118,
3. Andre Vanderbauwhede
A. Vanderbauwhede, B. Fiedler: Homoclinic period blow-up in reversible and conservative systems. Z. Angew. Math. Phys. 43 (1992), no. 2, 292--318.
4. Bernold Fiedler
G. Dangelmayr, B. Fiedler, K. Kirchgässner, A. Mielke: Dynamics of nonlinear waves in dissipative systems: reduction, bifurcation and stability. Pitman Research Notes in Mathematics Series, 352. Longman, Harlow, 1996.
5. Alexander Mielke
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alternatively from Golubitsky
M. Golubitsky, J.W. Swift, E. Knobloch: Symmetries and pattern selection in Rayleigh-Bénard convection. Phys. D 10 (1984), no. 3, 249--276.
3. Edgar Knobloch
G. Dangelmayr, E. Knobloch: Hopf bifurcation with broken circular symmetry. Nonlinearity 4 (1991), no. 2, 399--427.
4. Gerhard Dangelmayr
5. Mielke