I disagree. I've been keeping a journal for more than 10 years (started when I was 14 and am 25 now), where I report important events and more importantly reflect on them, and also on general concepts. Reading old entries can be very enlightening.
What comes out of it is that events are the "data", while personality/identity is the "software". The data is various, but the software is the same. The consistency of reasoning between now and then is incredible. When I read the setup of an old recounting, I start reacting to it while reading it from the point of view of my now-self, and then I see that the reflection of my old-self on this event to be very consistent with that. It's naive, uninformed and a bit rebellious (probably because of teenagehood), and sometimes because of that it completely misses the point, but the direction of reflection is the same. It's not alien, it makes sense.
We're reacting to events by using our software on related data. The value of experience entirely lies in the data, which can sometimes create entire shifts in perspective, but the software is the same. If you read an old journal you'll see that most reactions are the same, and for those which differ you can point out exactly what piece of data was missing in comparison to today's perspective.
A classic case of two steps forward, one step backward. Google knew this would be a big change for the tech community and devised a release strategy accordingly.
The most definitive version of a proof one can imagine is when the proof has been expressed via a formal language and a proof assistant checks that each step of the proof complies with axioms or already proven theorems from a library (which, in this case, are simple rewrite rules in the formal grammar). The [Mizar System](https://en.wikipedia.org/wiki/Mizar_system) is an example of that.
The question of formally proving Wiles' theorem is [discussed here](http://www.cs.rug.nl/~wim/fermat/wilesEnglish.html). Currently there exists no tool powerful enough to formalize such proof. It's considered a challenging problem in computer science.
What comes out of it is that events are the "data", while personality/identity is the "software". The data is various, but the software is the same. The consistency of reasoning between now and then is incredible. When I read the setup of an old recounting, I start reacting to it while reading it from the point of view of my now-self, and then I see that the reflection of my old-self on this event to be very consistent with that. It's naive, uninformed and a bit rebellious (probably because of teenagehood), and sometimes because of that it completely misses the point, but the direction of reflection is the same. It's not alien, it makes sense.
We're reacting to events by using our software on related data. The value of experience entirely lies in the data, which can sometimes create entire shifts in perspective, but the software is the same. If you read an old journal you'll see that most reactions are the same, and for those which differ you can point out exactly what piece of data was missing in comparison to today's perspective.