While I’m not strictly speaking a mathematician, I always wondered what my Erdős Number would be. The Erdős number of an author is calculated the following way: Paul Erdős has number 0, people who have coauthored a paper with him have a number 1, people who co-wrote papers with people with a number of 1 have a number of 2, etc.
So I took advantage of this snowy Sunday to search for a path between Paul Erdős and myself. If you have published mathematical papers, you just need to search for yourself on the collaboration distance tool. But as I have not published any mathematical paper, I had to try out the various people I wrote papers with, and see what would come out. I then had to look for the people they wrote with to find a better path. I found the following four step path:

1. Paul Erdős → Stanley M. Selkow: Random graph isomorphism.
2. Stanley M. Selkow → Giovanni Coray: Order independence in local clustering algorithms.
3. Giovanni Coray → André Schiper: Une structure de contrôle à deux niveaux pour la programmation heuristique parallèle.
4. André Schiper → Matthias Wiesmann: Beyond 1-safety and 2-safety for replicated databases: Group-safety

The first five step path I had found was the following:

1. Paul Erdős → Shmuel Zaks: Minimum-diameter cyclic arrangements in mapping data-flow graphs onto VLSI arrays
2. Shmuel Zaks → Gerard Tel: Optimal synchronization of ABD networks
3. Gerard Tel → Bernadette Charron-Bost: Synchronous, asynchronous, and causally ordered communication
4. Bernadette Charron-Bost → André Schiper: Uniform consensus is harder than consensus
5. André Schiper → Matthias Wiesmann: Beyond 1-safety and 2-safety for replicated databases: Group-safety

But there is at least another 5 step possibility:

1. Paul Erdős → Ronald L. Graham: On sums of Fibonnaci numbers.
2. Ronald L. Graham → John L. Bruno: Computer and job-shop scheduling theory.
3. John L. Bruno → Divyakant Agrawal: Relative serializability: an approach for relaxing the atomicity of transactions.
4. Divyakant Agrawal → Gustavo Alonso: Advanced Transaction Models in Workflow Contexts.
5. Gustavo Alonso → Matthias Wiesmann: Understanding replication in databases and distributed systems.

I also found two different paths of length 6:

1. Paul Erdős → Fan Chung: On the product of the point and line covering numbers of a graph
2. Fan Chung → Patrick Solé: Patrick Multidiameters and multiplicities
3. Patrick Solé → Peter J. Olver: Generalized transvectants and Siegel modular forms
4. Peter J. Olver → Metin Arık: Multi-Hamiltonian structure of the Born-Infeld equation
5. Metin Arık → Gökhan Ünel: q-oscillators, the q-epsilon tensor and quantum groups
6. Gökhan Ünel → Matthias Wiesmann: Deployment and use of the ATLAS DAQ in the combined test beam

1. Paul Erdős → Alexander Rosa: Decompositions of complete graphs into factors with diameter two.
2. Alexander Rosa → Jean-Claude Bermond: Decomposition of complete graphs into isomorphic subgraphs with five vertices.
3. Jean-Claude Bermond → Michel Raynal: General and efficient decentralized consensus protocols.
4. Michel Raynal → Maria Gradinariu: Stabilizing mobile philosophers.
5. Maria Gradinariu → Xavier Défago: Fault-tolerant and self-stabilizing mobile robots gathering – feasibility study.
6. Xavier Défago → Matthias Wiesmann: Anonymous stabilizing leader election using a network sequencer.

Edit:
I found three new paths giving me a level four:

1. Paul Erdős → Shlomo Moran Extremal problems on permutations under cyclic equivalence
2. Shlomo Moran → Hagit Attiya Computing in totally anonymous asynchronous shared memory system
3. Hagit Attiya → André Schiper Structured derivation of semi-synchronous algorithms.
4. André Schiper → Matthias Wiesmann Understanding replication in databases and distributed systems

1. Paul Erdős → Pavol Hell Graph theory in memory of G. A. Dirac
2. Pavol Hell → Masafumi Yamashita Graph endpoint coloring and distributed processing
3. Masafumi Yamashita → Xavier Défago The gathering problem for two oblivious robots with unreliable compasses.
4. Xavier Défago → Matthias Wiesmann: Anonymous stabilizing leader election using a network sequencer.

1. Paul Erdős → Pavel Valtr Pavel Ramsey-remainder
2. Pavel Valtr → Ivan Stojmenović Whitesides, Sue The largest k-ball in a d-dimensional box.
3. Ivan Stojmenović → Julien Iguchi-Cartigny Localized minimum-energy broadcasting for wireless multihop networks with directional antennas
4. Julien Iguchi-Cartigny → Matthias Wiesmann: Collision Prevention Platform for a Dynamic Group of Asynchronous Cooperative Mobile Robots.

Edit:
Microsoft now has a tool to visualise such paths, which gives me four other paths of length four. Here is the embedded visualisation (requires Silverlight).