If we're looking for the most elegant possible proof of a theorem (whatever that means), any sufficiently short proof is much more likely to be it than any sufficiently long proof.
Could you try to make that statement more precise? Because I don't believe it.
If you take the shortest possible proofs to all provable theorems of length less than N, both the maximum and the average length of those proofs will be extremely (uncomputably) fast-growing functions of N. To see that, imagine Gödel-like self-referential theorems that say "I'm not provable in less than 3^^^^3 steps" or somesuch. They're all true (because otherwise the axiom system would prove a false statement), short and easy to formulate, trivially seen to be provable by finite enumeration, but not elegantly provable because they're true.
Another way to reach the same conclusion: if "expected length of shortest proof" were bounded from above by some computable f(N) where N is theorem length in bits, we could write a simple algorithm that determines whether a theorem is provable: check all possible proofs up to length f(N)*2^N. if the search succeeds, say "yes". If the search fails, the shortest proof (if it exists) must be longer than f(N)*2^N, which is impossible because that would make the average greater than f(N). Therefore no shortest proof exists, therefore no proof exists at all, so say "no". But we know that provability cannot be decidable by an algorithm, so f(N) must grow uncomputably fast.
One of biases that are extremely prevalent in science, but are rarely talked about anywhere, is bias towards models that are mathematically simple and easier to operate on. Nature doesn't care all that much for mathematical simplicity. In particular I'd say that as a good first approximation, if you think something fits exponential function of either growth or decay, you're wrong. We got so used to exponential functions and how convenient they are to work with, that we completely forgot the nature doesn't work that way.
But what about nuclear decay, you might be asking now... That's as close you get to real exponential decay as you get... and it's not nowhere close enough. Well, here's a log-log graph of Chernobyl release versus theoretical exponential function, plotted in log-log.
Well, that doesn't look all that exponential... The thing is that even if you have perfect exponential decay processes as with single nucleotide decay, when you start mixing a heterogeneous group of such processes, the exponential character is lost. Early in time faster-decaying cases dominate, then gradually those that decay more slowly, somewhere along the way you might have to deal with results of decay (pure depleted uranium gets more radioactive with time at first, not less, as it decays into low half-life nuclides), and perhaps even some processes you didn't have to consider (like creation of fresh radioactive nuclides via cosmic radiation).
And that's the ideal case of counting how much radiation a sample produces, where the underlying process is exponential by the basic laws of physics - it still gets us orders of magnitude wrong. When you're measuring something much more vague, and with much more complicated underlying mechanisms, like changes in population, economy, or processing power.
According to IMF, world economy in 2008 was worth 69 trillion $ PPP. Assuming 2% annual growth and naive growth models, the entire world economy produces 12 cents PPP worth of value in entire first century. And assuming fairly stable population, an average person in 3150 will produce more that the entire world does now. And with enough time dollar value of one hydrogen atom will be higher than current dollar value of everything on Earth. And of course with proper time discounting of utility, life of one person now is worth more than half of humanity millennium into the future - exponential growth and exponential decay are both equally wrong.
To me they all look like clear artifacts of our growth models, but there are people who are so used to them that they treat predictions like that seriously.
In case you're wondering, here are some estimates of past world GDP.