In the recent years, there has been a lot of talk and investment in the biotech space regarding life extension, with some saying that the eventual goal is to make us live forever. However, to strive to live forever could be interpreted as an attempt to take also of the tree of life and live forever, something which seems that G-d, blessed be He, doesn't want us to do as can be seen from Genesis 3:22 after the fall:
lest he put forth his hand, and take also of the tree of life, and eat, and live for ever
Therefore, would we be forbidden from trying to develop such technology, and perhaps could we, at best, try to develop life saving or life-extending technologies that make our lifespans longer by a reasonable amount as opposed to forever? What do the texts say about this?