During the early parts of the cold war of the 20th century, we saw two almost independent developments of computational complexity, in the west and in the then USSR. There was little communication between the two groups, and countless theorems proven twice, most notably the seminal NP-complete papers of Cook and Levin. To understand more, I recommend the two articles about the early days of complexity by Juris Hartmanis and by Boris Trakhtenbrot.
Russia's invasion and relentless bombing in Ukraine have quickly separated the east and the west again.
Our first concern needs to be with Ukraine and its citizens. We hope for a quick end to this aggression and Ukraine remaining a free and democratic country. Ukrainian cities have undergone massive damage, and even in the best possible outcome it will take years if not decades to fully rebuild the country.
Terry Tao has been collecting resources for displaced mathematicians due to the crisis.
We've cut off ties with Russia institutions. In our world, major events to be held in Russia, including the International Congress of Mathematics and the Computer Science in Russia conference are being moved online. I was invited to workshops in St Petersburg in 2020 and 2021, both cancelled due to Covid, and was looking forward to one in 2022, which if it happens, will now happen without me.
The music world has has cancelled some stars, most notably Valery Gergiev and Anna Netrebko, due to their close ties to Putin. It's rare that we do the same to mathematicians for political reasons though not unheard of. I suspect most of our colleagues in Russia oppose the war in Ukraine, or would if they had accurate information of what was going on. I have several Russian friends and colleagues including two I travelled to Moscow in 2019 to honor and would hate to be disconnected from them.
It's way too early to know how this will all play out. Will we see a quick Russian retreat? Not likely. Will we see a situation that sees a mass migration of Ukranian and Russian mathematicians and computer scientists to Europe and North America, like in the 1990's? Possibly. We will see a repeat of the cold war, disconnected internets and science on both sides happening in isolation? I hope not but we can't rule it out.