Sometimes it's useful to remember the mistakes of the past in the context of today and exactly how tough it is to learn and know something. Those that thought the sun revolved around the earth were just as smart as we are today. It was only after careful study of the nuanced motion of the light dotting the night time sky that we were able to differentiate that some were planets and that some of them exhibited apparent retrograde motion. (Image to the right is an illustration of apparent retrograde motion.) Then, having made those observations, creating descriptions of the experiments which were repeatable to make the case to others and spread the knowledge.
The powers of data analysis brought to us by modern computing technology opens up a whole new class of problems to new levels of scrutiny. (The image to the left is an illustration of the four color theorem proved by computer in 1976.) Interestingly, there are still philosophical objections to mathematical proofs that depend partially on exhaustive computer powered computation. The main argument being that humans can't verify it logically so we can't trust it as proven. It requires a replacement of logical deduction with faith in the ability of the computer to accurately operate. I think the concept of black-box advancement of science is interesting. If you approach it with a willingness to engage in the process, risks of computer error in computer assisted proofs can be mitigated by using heterogeneous systems to replicate the proof. Varieties of architectures and software is something we don't have a shortage of.
Distributed processing and the promise of cloud based computation (buzz words aside) bring even more capability and variety to computational proofs. Being involved in this advancing field, I haven't seen anybody really engaging with this. We are barely scratching the surface of what's possible with making computers work together. The next few years promise to be an exciting time.