I hate the concept of the “Immortal Wunderkind”
The Immortal Wunderkind is a character who has immortality, and over their immortal lifespan, has become a genius and expert on an absurd range of topics and fields of study. They can speak a 100 languages, they’re an expert in all scientific fields of study, they were present and have firsthand accounts of every major historical event relevant to the plot, they are endlessly charismatic and intelligent and wise.
A classical example of this type of character is Vandal Savage.
Now, I like this trope. It’s fun and there is a lot you can do with it narratively. But I HATE the people who *believe* in it.
Every time the discussion of immortality comes up (especially the topic of immortality as a curse or blessing) a bunch of people show up that assume that, given an immortal lifespan, they would become an Immortal Wunderkind themselves.
These folks often hand waive any potential downsides or risks of immortality by stating that, as a Wunderkind with infinite time, they’d be able to solve or avoid any potential issues! They’d be able to figure out how to make other people immortal so they aren’t lonely and don’t have to deal with loss! They’d figure out how to back up their consciousness or body hop so they can never get trapped in a hole! They’d push humanity forward to solve our existential issues like climate change and so on. They’d even figure out how to dodge the heat death of the universe!
And to that I say… no you won’t.
If virtually anyone on the planet became immortal right now, today, they would simply not be exceptional in this way.
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#1 Your brain isn’t built for it
We don’t have infinite memory, and our memories are extremely imperfect. The human brain cannot even store one lifespan of memories effectively: you are going to run out of room. You're not going to be endlessly accruing knowledge and skills. You're going to be constantly accruing knowledge and skills while bleeding knowledge and skills in equal measure. This goes for soft skills like wisdom, patience, mental stability, stress management, etc. as well.
Maybe at some point we develop technology that allows us to expand the limits of our neurology; increasing memory capacity, creating perfect memory, increasing neuroplasticity or letting you download information directly into your mind. If such a technology is created, your immortal ass isn't going to benefit from it any more than anything else; you won't have a leg up because you have an extra 100 years of outdated knowledge as a starting point.
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#2 You are not going to keep up
If you, average Joe schmoe, became immortal and dedicated your life to learning everything there is to know about medicine, you would be perpetually behind on 99% of fronts. A doctor that graduated med school in 2016 has had half of what they learned become obsolete. Knowledge and expertise is not something you gain and keep, it is something you must actively maintain.
Every field of science and study is constantly evolving and being pushed forward by thousands of brilliant minds: unless they all stopped right now for you, Joe schmoe, you would never catch up even as these minds passed and were replaced by new ones.
Not to mention if your plan is to push any specific field of inquiry forward, that's going to involve decades of research where you'll fall behind on everything else. The only time you'll be at the top is if the rest of humanity goes extinct.
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#3 You still have to be smart to start with
No amount of time can make you smart, it can only make you knowledgeable. Critical thinking is something that can be cultivated but you're not going to develop a generalized super-brilliance that is applicable to all subjects and fields of expertise just because you've been around a thousand years.
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#4 You aren't guaranteed a solution for every problem
Even if you have infinite knowledge, infinite time, and infinite resources there's no guarantee that you'll be able to do anything. Just because the possibility of a solution, based on our current understanding, is above 0% doesn't mean you, Joe schmoe, will be able to find it before our universe dies.
There is so much magical thinking about "intelligence" and how it can be applied to solve problems, but you can't just use 100 billion years to hand waive how you'll solve avoiding the heat death of the universe or whatever.
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The ugly truth is that basically all of us, given an immortal lifespan, would not be any more of a "wunderkind" than the most brilliant minds and exciting people alive today. In order to be exceptional you need to actively pursue the exceptional, every day. And if you aren't doing that now, you probably won't do that with infinite time to procrastinate with.