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Dan_Moore comments on But Somebody Would Have Noticed - Less Wrong
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While I don't think that "someone would have noticed" is always a fallacy, I do think that we humans tend to underestimate the chance of some obvious fact going unnoticed by a large group for a prolonged period.
At a computer vision conference last year, the best paper award went to some researchers that discovered an astonishing yet simple statistic of natural images, which surprised me at first because I thought all the simple, low level, easily accessible discoveries in computer vision had long since been discovered.
A different example- one of the most successful techniques in computer vision of the past decade has been graph cuts, where you formulate an optimization problem as a max flow problem in a graph. The first paper on graph cuts was published in 1991 iirc, but it was ignored and it wasn't until 2000 that people went back to it, whereupon several of the field's key problems were immediately solved!
I agree, with respect to (e.g.) math. People reason that "someone would have noticed" implies that there is no undiscovered low-hanging fruit in math.
My skepticism of this conclusion is based on my perception of how mathematicians work. They are fairly autonomous, working on the things that interest them. What is interesting to mathematicians tends to be the large problems. They swing for the fences, seeking home runs rather than singles.
Plus, there are unfashionable areas of math. A consensus that certain areas of math have been fully explored (nothing new remains) has developed, but not in a systematic way. So, it's not clear whether this consensus is accurate, because politics (for lack of a better term) were involved in its formation.
It's only reasonable to be confident that 'someone would have noticed' if someone knowledgeable about what they are looking at actually looks in that direction.