Hide list fields upon creation of a SharePoint list item

Suppose you want to hide a SharePoint list field upon creation of a list item and to show it upon modification of that same list item. Suppose you want to hide another SharePoint list field upon modification of a list item and to show it upon creation of a list item in that same SharePoint list. This is something which cannot be achieved by using merely the out-of-the-box administration tools of SharePoint.