Generally because that’s how mathematics tends to work - people publish a partial result & then they or others build on it to improve that result in various ways[1]. The authors are also usually embedded in a wider community of mathematicians who act as a pre-publication bullshit filter by asking pointed questions at seminars & that kind of thing.

It’s quite rare for a genuinely novel solution to a major problem in mathematics to spring up out of nowhere in the literature.

[1] Think of, eg, the Twin Prime conjecture (that there are infinitely many pairs of primes only 2 integers apart). For decades there was no progress on this problem, before Yitang Zhang published a paper last year proving that there were infinitely many primes less than a finite bound apart (70 million in his case). Then a horde of matheaticians attacked the problem using his & other new approaches to progressively reduce that large bound down to the point where it’s now been proven that there are infinitely many primes < 246 apart (according to the polymath group - I’m not sure whether this is a published result yet). The twin prime conjecture is in sight!