Possible solution to the Fermi paradox: there is no paradox. The normal approaches find that there should be a very large number of civilizations by plugging point estimates into the Drake Equation, but multiplying point estimates (as opposed to probability distributions) with each other gives you misleading results.
As a toy example, if you multiply nine factors together to get a probability of life per star, each of the factors a random real number drawn uniformly from [0, 0.2] and the point estimate for each being 0.1, then the product of the point estimates is 1 in a billion. This would translate to an expected 100 life-bearing stars, given 100 billion stars. But if you instead combine the probability distributions, you get a median number of 8.7 life-bearing stars (the mean is still 100).
Going through the literature to estimate reasonable prior distributions for different values in the Drake Equation, you get much more pessimistic estimates for the probability of life in the universe; the priors chosen by the authors suggest a 40% a priori chance for life only emerging once. We really might just be alone.