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 mathematics 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 & Tomás Roubícek: Nonexistence of solutions in nonconvex multidimensional variational problems. J. Convex Anal. 7 (2000) 427--435.

**3. Tomás Roubícek**

Tomas 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

Cates, M.; Erdös, P.; Hindman, N.; Rothschild, B. Partition theorems for subsets of vector spaces. J. Combinatorial Theory Ser. A 20 (1976), no. 3, 279--291.

1. Bruce Rothschild

Golubitsky, Martin; Rothschild, Bruce Primitive subalgebras of exceptional Lie algebras. Pacific J. Math. 39 (1971), 371--393.

2. Martin Golubitsky

Melbourne, I.; Chossat, P.; Golubitsky, M. 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

Melbourne, Ian; Schneider, Guido Phase dynamics in the real Ginzburg-Landau equation. Math. Nachr. 263/264 (2004), 171--180.

4. Guido Schneider

Mielke, Alexander; Schneider, Guido 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

Chossat, P.; Iooss, G. Primary and secondary bifurcations in the Couette-Taylor problem. Japan J. Appl. Math. 2 (1985), no. 1, 37--68.

4. Gerard Iooss

Iooss, G.; Mielke, A. 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

Vanderbauwhede, A.; Krupa, M.; Golubitsky, M. Secondary bifurcations in symmetric systems. Differential equations (Xanthi, 1987), 709--716, Lecture Notes in Pure and Appl. Math., 118,

3. Andre Vanderbauwhede

Vanderbauwhede, André; Fiedler, Bernold Homoclinic period blow-up in reversible and conservative systems. Z. Angew. Math. Phys. 43 (1992), no. 2, 292--318.

4. Bernold Fiedler

Dangelmayr, Gerhard; Fiedler, Bernold; Kirchgässner, Klaus; Mielke, Alexander 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

Golubitsky, M.; Swift, J. W.; Knobloch, E. Symmetries and pattern selection in Rayleigh-Bénard convection. Phys. D 10 (1984), no. 3, 249--276.

3. Edgar Knobloch

Dangelmayr, Gerhard; Knobloch, Edgar Hopf bifurcation with broken circular symmetry. Nonlinearity 4 (1991), no. 2, 399--427.

4. Gerhard Dangelmayr

5. Mielke