So here's the issue I have with this. We have a mathematical proof that the decimal expansion (or indeed an expansion in any integer basis) of pi is infinite. For one, pi is an irrational number, and therefore it cannot possibly be finitely represented. If you know basic calculus and have a piece of paper I could convince you of this right now, this instant. Again, we have a proof of this fact. An infallible series of logical steps that lead to an inevitable conclusion. You see, when a sound mathematical proof turns out to lead to the wrong conclusions, the damage doesn't end in something as trivial as "a constant we thought was irrational is in fact rational" - that I could live with. We can patch that up. In essence, to offer evidence contradicting a mathematical proof is to claim that one step in its reasoning is wrongly inferred. But there is no doubt in my mind - nor in the mind of anyone who's studied math for long enough - that any of the dozens of classical proofs of the irrationality of pi are all correctly inferred, and all of the logical steps in them are correctly argued for. To find evidence against this would be to find evidence against the basic principles of human reasoning. We would have to acknowledge the most absolute absurdities. Doublethink to a degree not even Orwell would be comfortable endorsing. A and not A. 1 = 2. What would such a world even look like? It's ridiculous and impossible.
Or so we thought. Turns out we were wrong. The mathematicians, the philosophers, the educators. Pi is finite. A and not A. Somebody raise Aristotle from the grave because he conned us, he conned us bad. We called countless conferences - we verified with the steps over and over - the greatest minds of our generation made their career debating this. The proofs seemed sound to us - pi is an irrational number. It can be shown with a simple chain of reasoning that anyone with the most average intelligence can understand, given enough time. But here the calculations were sitting before us and they showed us time and time again that at some point, at a digit place larger than any of us could imagine, pi terminates, and it ends with the number 9. We did not have the mathematical machinery, of course, to calculate the expansion of pi in its entirety - even the number of digits in pi would take far, far more than the amount of atoms in the universe to express in decimal notation - and for all practical means and purposes pi was as not-finite as we would have liked it to be. But here the facts were standing before us and the facts were that pi is a rational number with a finite decimal expansion.
The first generation of mathematicians took it the hardest. Some quit their occupation for more "practical" pursuits. The older generation mostly chose solace in retirement. Pioneers tried to patch up the issue but - after a few hundred years they gave up too. The theoretical physicists soon followed. Then came the philosophers and the intellectuals. The post-modernists looked at it as a triumph. The analytics turned continental. The continentals were welcomed in universities again.
Here was a world where X was not X, where 1 was 2 and where pi was both rational and irrational. A world where every statement could be asserted. Nothing was certain anymore, and everything was and everyone were equally correct. The intellectuals who dedicated decades in university to studying the deeper truths of the universe were no smarter or more qualified to talk of it than the class idiot. We no longer had anything to rely on, nor any common point of thinking to argue from. Every truth was false and every falsehood was said to be true; God was real and God was false; pigs could fly, Nessie was real, and Sasquatch was seen dipping in the lakes of Nebraska. The shockwave that begun in the highest ranks of the ivory tower of academia trickled down its height and soon everyone was affected by the absurdity. The concept of knowing, and of belief, had stopped making sense, and the very way we understood the language we use to talk of these things had changed.
And you know what? It wasn't that bad. After a few months the hype had been all but forgotten by the media. The engineers and scientists were shaken - but they continued their work still, if with less trust in the theorems and formulae they previously worked with. The face of science had changed and we were traversing new and exciting grounds. Technology continued to progress, as did experimental science, and society continued to function with no Spaghetti monsters (or actual Sasquatches) in sight. The mathematicians did not forget about this but as time passed theoretical mathematics was driven into obscurity, sometimes associating itself with literary criticism. Still, social activism would change. We became more tolerant, more spiritual and mystical. No longer able to rely on our own minds we began reviving arts that were passe in our generation - and soon palm readers and prophets and saints flooded the streets. The world opened its doorways and it reintroduced itself to us.
Yet it was the world we had always known. Our society was changed by our discovery - but in the end it was a discovery that took place entirely in our minds. The stars did not change their colors, the sun still rose in the morning, and the leaves on the trees kept changing with the seasons. It wasn't so much the discovery of the rationality of pi that shook us, but the discovery of our own irrationality. But we adapted, as our species is prone to do, and we kept walking forward.