What is an Erdős number ?

 What is an Erdős number?

• It's a measure of the "collaborative distance" between a mathematician and the prolific Hungarian mathematician Paul Erdős, based on co-authorship of publications.
• It's a way to track the interconnectedness of mathematicians and their collaborative networks.

How is it calculated?

1. Erdős himself has an Erdős number of 0.
2. Anyone who co-authored a paper directly with Erdős has an Erdős number of 1.
3. Anyone who co-authored a paper with someone who has an Erdős number of 1 has an Erdős number of 2, and so on.
Opens in a new windowwww.researchgate.net
network of mathematicians with Erdős at the center, showing Erdős numbers

Key points:

• Lower Erdős numbers generally indicate a closer connection to the world of mathematics and a greater degree of collaboration.
• The average Erdős number is around 5, but it can range up to 13.
• Over 11,000 people have an Erdős number of 2.
• Having a finite Erdős number is considered a badge of honor among mathematicians.

Interesting facts:

• Albert Einstein has an Erdős number of 2.
• The actor Kevin Bacon has an Erdős–Bacon number of 6 (combining Erdős number and Bacon number, a similar concept for film collaborations).
• There are databases and websites dedicated to tracking Erdős numbers, such as the Erdős Number Project at Oakland University.

Beyond mathematics:

• The concept of Erdős numbers has been applied to other fields where collaboration is common, such as physics, chemistry, and computer science.
• It's a fascinating way to visualize and study the interconnectedness of researchers and the spread of ideas within a field.

Where I can find my Erdős Number ?

                 Go to the webpage 

https://mathscinet.ams.org/mathscinet/freetools/collab-dist 

The only person with Erdos $\#0$ is Erdos himself. Denote ${\text{E}}_0=\left\{\text{Erdos}\right\}$.

The set of persons with Erdos $\#1$ is the set of those persons who have at least one published paper with Erdos. Call this set ${\text{E}}_1$.

The set of persons with Erdos $\#2$ is the set of those persons who do not belong to ${\text{E}}_1$ and have at least one published paper with someone in ${\text{E}}_1$. Call this set ${\text{E}}_2$.

The set of persons with Erdos $\#3$ is the set of those persons who do not belong to ${\text{E}}_1\cup {\text{E}}_2$ and have at least one published paper with someone in ${\text{E}}_2$. Call this set ${\text{E}}_3$.

In general, you have Erdos $\#n$ if you do not belong to ${\text{E}}_1\cup {\text{E}}_2\cup \dots \cup {\text{E}}_{n-1}$ and have at least one published paper with someone in ${\text{E}}_{n-1}$. Call this set ${\text{E}}_n$.

My Erdős Number is 6.