It seems possible that mathematical breakthroughs are no longer being published, as they are now trade secrets/matters of national security. I wasn't surprised when Tao was beaten by a hedge funder.
2. It's not just my opinion, and
3. I didn't say they're "well ahead" unilaterally.
This isn't unique to finance; industry labs in tech also often have novel results in applied mathematics and computer science that are ahead of academia and other industry labs. You don't have to believe me but it's not exactly a controversial topic. Not everything is published or patented.
But I read your claim as saying that there are broad methods and approaches that they hide. And that's, while possible, more peculiar. Most of the tech industry labs don't keep their theoretical research secret. Practically anything that could be published is.
As for 3, the way you described the "rediscovery" made it sound like those Labs were a number of steps ahead, so I hope you pardon my misunderstanding.
Like I said in the original comment: this isn't (to my knowledge at least) pure mathematics that's being kept secret. But there are absolutely families of techniques and algorithms whose applications to finance are nontrivial, non-incremental and very well guarded.
In other words, techniques that are broadly applicable to the field, or techniques that maybe spawn a family of related techniques, but appear to be useful only in a specific subdomain.