Not sure if my recent paper "[Equivalence: an attempt at a history of the idea][1]" qualifies as one of the "best of Mathoverflow or papers inspired by Mathoverflow". But I am sure Mathoverflow was a force to keep me motivated for a journey that started 13 years ago into the long and rich history of equivalence. 

It was 4 years and 6 months ago that I asked on MO: "Who introduced the terms “equivalence relation” and “equivalence class”?" When I asked the question I was kind of full of myself to know nearly every corner of the relevant history, and the question was kind of let me find even that bit that I don't know. But, suddenly, there it was @Francois Ziegler's [answer][2] and then his comment to my own [answer][3]. Wow, it was much more than I asked. Basically, it opened up my eyes to something in front of me all the times, but I had failed to see it all the times. That answer was a new beginning for something that had started 6 years and a half year ago and continued for another 4 years and a half year!  
The paper has been dedicated to David Fowler for the reasons mentioned in the paper and [here][4]. But, I believe both Fowler and I should thank Francois for his short enlightening answer. Here is the abstract of the paper, hoping it deserves the name of David Fowler, Christopher Zeeman, Jeremy Gray, and Francois Ziegler who directly or indirectly, knowingly or unknowingly, encouraged me to finish my journey. 

> This paper proposes a reading of the history of equivalence in
> mathematics. The paper has two main parts. The first part focuses on a
> relatively short historical period when the notion of equivalence is
> about to be decontextualized, but yet, has no commonly agreed-upon
> name. The method for this part is rather straightforward: following
> the clues left by the others for the ‘first’ modern use of
> equivalence. The second part focuses on a relatively long historical
> period when equivalence is experienced in context. The method for this
> part is to strip the ideas from their set-theoretic formulations and
> methodically examine the variations in the ways equivalence appears in
> some prominent historical texts. The paper reveals several critical
> differences in the conceptions of equivalence at different points in
> history that are at variance with the standard account of the
> mathematical notion of equivalence encompassing the concepts of
> equivalence relation and equivalence class.




  [1]: https://link.springer.com/article/10.1007%2Fs11229-018-1674-2
  [2]: https://mathoverflow.net/a/135375/29316
  [3]: https://mathoverflow.net/a/135635/29316
  [4]: https://meta.mathoverflow.net/q/3598/29316