To live longer.
Rarely, some people consider themselves as an idea, instead of a biological creature. Why do people do this? Well, because ideas spread, and things that spread last way longer.
In the sense of travelling vast distances in time, keeping ourselves functioning within our physical forms is simply impossible. The most we can do is to simplify ourselves to a point where we are just purely information.
Everything in the universe could be put in numbers and relations. We also assume that the same works with the lives of mortal beings.
In the context of self-preservation, the best method we have ever coined is photography. Essentially, projecting what we are at a given time and retaining that projection for a long period.
It's not like we could decode back what we were from a 2d imprint of us. But what if we know a method to capture stuff as what it is? What if we could capture ourselves in all the complexity, energies, reactions, states, transformations, movements, and everything that makes us into data?
No current tech can fully capture all energy states, quantum configurations, and historical materials at once. It's not only impossible currently, but also requires answering the Theseus's Paradox and defying the Heisenberg uncertainty principle.
But what if we made ourselves simpler? To the point we are optimized to be kept and rebuilt without needing to have groundbreaking advances in cryonics?
The simplest a person can get is to be an idea, a perspective, or a solution for a problem with multiple solutions. If we managed to figure out the fundamental concept of the reason for our existence, we could preserve the concept of what we are.
For example, automation is an idea; we don't need to teach someone to understand the concept of using tools to decrease their workload.
Exactly why we have patents over ideas, people might eventually rediscover it as an answer to a different question.
This literally means that the most durable form of existence is to be conceptual. That's it, maybe living longer means something totally different than physically living longer.
David Eagleman once said, "There are three deaths. The first is when the body ceases to function. The second is when the body is consigned to the grave. The third is that moment, sometime in the future, when your name is spoken for the last time."
The reason why laws and constants we know mention someone who found them could be because our life simply is about the stuff we do to the world around us, because the changes we make, the ideas we plant, stays.