diophantus is for open discussions of academic papers
There are many situations when you want to comment an academic paper.
Sometimes people write their comments to authors. But often it doesn't work. Authors might not reply or might not be interested in the topic anymore. Also, often they cannot do anything about your comment (say, update a published paper). Moreover, other people having the same questions will not see the answers.
Another way is to write on your personal blog or in social media. But the problems are that it's unlikely that all people interested in your research area are reading your blog. Also, the comments are located in different places instead of one place right next to a paper.
On diophantus everyone interested in a paper is gathered in one place.
Everyone who is interested in a paper will see comments, notes, remarks, and answers in one place right next to a paper.
Another big topic is the lack of reviews. A published paper has at most 2-3 reviews, and sometimes papers published in the most prestigious journals turn out to be wrong. Researchers read papers and verify their results for themselves, but unfortunately this useful work is not shared with other people.
That's why we created the volunteer review system where you review, approve, or disapprove results from a paper. Every researcher who checks the results of a paper is encouraged to approve the results and show other people that they trust these results.
We hope that we'll see lots of volunteers helping with us to solve the crisis in modern mathematics where more and more papers are published but the results sometimes turn out to be wrong.