We are transitioning in mathematics from an era of proof scarcity to an era of proof abundance, but our mathematical infrastructure and culture has not yet adapted to this. As mentioned previously, there is now a strong (and growing) impedance mismatch between the three core components of mathematical problem solving: proof generation, proof verification, and proof digestion.

An early sign of this transition could be seen in the chaotic response to the initial "First Proof" challenge, in which many more potentially viable solutions to the given problems were produced than could be readily verified or digested, either by experts or by automated tools. And now we are seeing the same impedance mismatch at the Erdos problem website, where (since the release of GPT 5.5, as well as the highly publicized recent solution to Erdos problem #1196) there is now an unprecedented backlog of nearly twenty claimed full or partial solutions "pending assessment": https://github.com/teorth/erdosproblems/wiki/AI-contributions-to-Erd%C5%91s-problems . (Prior to this recent surge, this category contained one or two solutions at a time at best.) (1/5)

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As a crude first approximation, the problem-solving component of mathematical research (which, one should stress, is not the *only* aspect of such research) can be decomposed into three subcomponents:

1. Proof generation (finding a solution to a given problem);
2. Proof verification (checking that a proposed solution actually works); and
3. Proof digestion (understanding the essence of a solution, placing it in context with previous literature, summarizing and explaining it effectively, and gaining insights on other related problems and topics).

Until recently, all three of these subtasks were rather difficult and time-intensive to perform; but a human mathematician (or a collaboration between several mathematicians) who had invested the effort to both generate a proof and verify it usually gained enough understanding into the structure of that proof that they could also digest it effectively. Because of this, our community has been generally content to emphasize the proof generation and verification aspect of problem solving, as the proof digestion tended to be created naturally as an organic byproduct of these first two aspects. This was also convenient for assessing proof efforts, as the generation and verification tasks had well-defined objectives, whilst proof digestion was a more subjective and open-ended process. [Though "the ability to present the result at a research conference and take questions" is a rough first approximation of a metric for whether a proof has been digested,] (1/3)

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