I am a masters student. I am interested in **short articles** which have counter examples and very few references. I want to write a short and interesting article.


**For example**; One of the best known shortest and best academic paper articles I read is *Counterexample to Euler's Conjecture on Sums of Like Powers* by L. J. Lander and T. R. Parkin (Bull. Amer. Math. Soc. **72** (1966) p 1079, doi:[10.1090/S0002-9904-1966-11654-3](https://doi.org/10.1090/S0002-9904-1966-11654-3)).
It has only one reference. It's really fascinating.


Is there any short articles in Mathematics and especially **in Analysis/Complex Analysis**? I am also looking at **Counterexamples books** for learning something and I searched open problems in Wikipedia and looked at undiscovered, newly valued and current topics.


So can you share these type of articles you read? I am curious about a good and interesting **short article topic**. What do you recommend to me about it? You can also give some references.\*\* Thanks for your ideas and answers.\*\*



Short research articles
[a bit too long for a comment]


I understand from the question that the aim is to find a research project based on the search for a counterexample. By construction, this will mean showing that some existing paper in the literature is mistaken. That is typically not a productive way to start a project in a new field, simply because (a) if the author of that paper is clueless then there is not much gained in showing them wrong by finding a counterexample,$^\ast$ while (b) if the author is an expert you are facing an uphill battle if you are just entering a field.


Typically, a more productive way to enter a field is to try to generalize/extend work of others, basically by exploring corners of the field they left untouched (or didn't bother to explore). You may find that this leads you to uncover an error/oversight in the paper you started from, but that would then be a byproduct of your research and not the primary motivation.


 $^\ast$ many questions here on MathOverflow can be readily dismissed by finding a counterexample, but that rarely becomes something worthy of a publication


