A company announces it has solved in 88 hours a problem that has been open for decades. There are two easy reactions: to believe, because the pace of progress makes anything plausible; or to reject, because it is a company with an interest in the announcement. These two reactions have one thing in common: they spare us from waiting. That is precisely what must not be done.
On Friday we covered an announcement of this kind, saying that we would not come down on one side. Here is why, and what that assumes.
The principle, and how it is misread
The formula is well known: an extraordinary claim requires extraordinary evidence. It is correct, and it is constantly misapplied.
It does not mean that one should be harder to convince depending on the scale of the claim — that would be a bias, not a method. It means that the more a claim contradicts what we thought we knew, the more evidence is needed to revise.
The difference matters. In the first case, one decides in advance not to believe. In the second, one sets out what would change one's mind.
It is that enumeration which distinguishes methodical caution from posturing scepticism. Someone who doubts without being able to say what would convince them is not doubting: they are refusing.
The four questions that replace opinion
Faced with a claim, four questions allow one to take a position without having to believe anything.
What can someone else verify? This is the first and most useful. A formalised proof can be verified by anyone with the software. A result described in a press release cannot. The difference is not one of degree, it is one of kind.
Who benefits from the announcement, and when? This is not an argument against — interested parties are often right — but it indicates where to focus attention. An announcement made before a funding round or a stock market listing deserves the same scrutiny as any other, with particular attention to the timing.
What exactly does the claim say? This is where most misunderstandings lie. We stressed this for this week's announcement: demonstrating that a singularity can appear does not answer the same question as demonstrating that it never appears. A precise claim is not less impressive; it is simply smaller than a headline.
How long before we know? This is the question most often missing. If the answer is "months", then taking a position today has no informative value, whatever confidence is placed in it.
There is a serious argument against this stance, and it must be heard. Waiting has a price: while judgement is suspended, decisions are made, funding is directed, opinion takes shape. Whoever says "we don't know yet" systematically loses attention to whoever asserts. This is a real asymmetry of public debate, and it explains why caution is so rarely rewarded. It is nonetheless the right method: to have been right three months later is better than to have been wrong straight away, even if nobody notices.
What history suggests
Spectacular mathematical announcements have a high failure rate, and it almost never comes from bad faith.
A proof can be sound in its architecture and wrong in one link, as we recalled regarding the process by which proofs come to be accepted. The first work on Fermat's theorem contained a gap discovered during review. The author was deceiving no one: he had not seen it.
This is the purpose of institutional delays. They are not intended to flush out fraudsters, but to give different eyes the time to find what one pair of eyes did not see.
What formal verification changes, and what it does not
Precision is needed here, because this is the new element in this case.
A formalised proof eliminates an entire class of errors: logical gaps. That is considerable, and it should shorten technical review by several months.
It does not eliminate the other two classes. The statement may not correspond to the question. And the result may be correct without being what one thinks it is.
In other words, formal verification shifts where one needs to look. It does not remove the need to look.
What to take away
The answer to the question in the title is neither yes nor no: it is not yet, and knowing how to say what one is waiting for.
This stance is uncomfortable because it offers nothing to comment on. Yet it has a rare advantage: it is revisable. Someone who has set out their criteria can change their mind when those criteria are met, without contradicting themselves.
It is probably the most useful thing one can cultivate in the face of a stream of announcements that exceeds any capacity for verification. Not to distrust everything, which is exhausting and lazy, but to know, for each claim, what would make it credible. Most of the time, the answer is simple: someone else tried to break it and did not succeed.