The author mentions the classification of finite simple groups primarily in order to

show that a proof no individual has read entirely is not unique to machine methods.

argue that collaborative proofs are more reliable than computational ones.

illustrate a result that has since been found to contain errors.

contrast pure mathematics with the applied problems computers are used on.

The author regards the demand that a proof be explanatory as

a disguised objection to the use of computers in mathematics.

a requirement that any acceptable proof must satisfy.

unreasonable, given how many important theorems have opaque proofs.

legitimate, but a claim about a proof's value rather than its correctness.

According to the passage, the element of a machine proof most easily overlooked is

the number of configurations the program must examine.

the formal statement given to the machine, which must be shown to express the informal theorem.

the hardware on which the program is executed.

the time required to complete the computation.

It can be inferred that proof assistants built on a small auditable kernel have been more persuasive than ad hoc programs because they

produce arguments that a human reader can follow from beginning to end.

have been used to verify a greater number of published theorems.

reduce the portion of the tool that must be trusted without inspection.

remove the need to formalize the statement being proved.

The final sentence, that no one "has ever taken none of it on trust", functions primarily to

deny that machine proof introduces any distinctive risk.

place the machine case on a continuum with ordinary mathematical practice rather than outside it.

suggest that mathematical certainty is unattainable in principle.

concede that the objections raised in the first paragraph were correct after all.

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What a Machine Proof Proves

PRACTICE

100:00+4 −1MCQ Single Answer

Reading Passage

When the four colour theorem was settled in 1976, the settlement satisfied almost nobody. The proof reduced the problem to a catalogue of roughly nineteen hundred configurations and then checked each one by computer, a task no person could perform in a lifetime. Mathematicians who objected were not suggesting the result was false. Their complaint was that the argument could not be surveyed — read, followed, and judged by a human reader — and that it delivered no understanding of why four colours suffice. A proof, on this view, is not merely a certificate of truth but an explanation, and a catalogue explains nothing. The objection is harder to sustain than it first appears. Unsurveyability is not peculiar to machines. The classification of finite simple groups runs to something like ten thousand pages distributed across hundreds of papers by dozens of authors, and no individual has read the whole of it; confidence rests instead on a distributed social process of checking, which is not self-evidently more reliable than running a verified program twice on different hardware. The demand for explanation is on firmer ground, but it is a demand about what makes a proof valuable rather than about what makes it correct. Mathematicians want illuminating arguments for excellent reasons, and a theorem whose only known proof is opaque is a standing invitation to find a better one. That is a statement about mathematical taste, not about whether the theorem holds. What machine proof genuinely changed is where trust sits. Checking a human argument means checking reasoning; checking a machine argument means checking a tool — the program, the compiler beneath it, and, most easily overlooked, the formal statement fed in, which must be shown to say what the informal theorem says. This is a real risk and a different one, and it explains why proof assistants built on a small auditable kernel have persuaded sceptics that ad hoc programs did not. The question was never whether machines can establish theorems. It is which link in the chain a mathematician consents to take on trust, and no one has ever taken none of it on trust.

The primary purpose of the passage is to