Boris Alexeev (currently at OAI) has formalized the existence of a complex structure on S\^6 based on Claude's arguments. It compiles and the code is quite clean and efficient. It's good to have proof of the result and Levent should have probably waited to have a formalization done before announcing. My understanding is that people at the labs generally take their internal models' claims at face value, and given none of the results so far have been wrong I suspect as the models continue to progress most people will end up like this as well. Despite that I think formalization still should be an important step in this new age of math we are entering given just how good models are getting at it, as this is probably the most impressive formalization I have seen so far.