In mathematics, multiple authors are always listed alphabetically by family name; ie there is no &quot;first&quot; or &quot;second&quot; author.<p>In the situation you describe, the paper would probably be singly authored, and the author would write something like &quot;Thanks to my advisor _____ and to my colleagues ____ for many helpful discussions&quot; in an acknowledgments section.<p>If the contributions were more serious, then possibly the author would invite the others to co-author with him&#x2F;her, and the others would then either accept (and then help write the paper) or politely decline and say &quot;just mention me in the acknowledgments&quot;.<p>At least in my experience, co-authorship carries responsibilities: to help with the writing, the figures, references, dealing with editors and with submission to journals, speaking about the research at seminars&#x2F;conferences, etc.