PrepTest 49, Section 2, Question 22
A mathematical theorem proved by one mathematician should not be accepted until each step in its proof has been independently verified. Computer-assisted proofs generally proceed by conducting a vast number of calculations�surveying all the possible types of instances in which the theorem could apply and proving that the theorem holds for each type. In most computer-assisted proofs there are astronomically many types of instances to survey, and no human being could review every step in the proof. Hence, computer-assisted proofs involving astronomically many types of instances should not be accepted.
A mathematical theorem proved by one mathematician should not be accepted until each step in its proof has been independently verified. Computer-assisted proofs generally proceed by conducting a vast number of calculations�surveying all the possible types of instances in which the theorem could apply and proving that the theorem holds for each type. In most computer-assisted proofs there are astronomically many types of instances to survey, and no human being could review every step in the proof. Hence, computer-assisted proofs involving astronomically many types of instances should not be accepted.
A mathematical theorem proved by one mathematician should not be accepted until each step in its proof has been independently verified. Computer-assisted proofs generally proceed by conducting a vast number of calculations�surveying all the possible types of instances in which the theorem could apply and proving that the theorem holds for each type. In most computer-assisted proofs there are astronomically many types of instances to survey, and no human being could review every step in the proof. Hence, computer-assisted proofs involving astronomically many types of instances should not be accepted.
A mathematical theorem proved by one mathematician should not be accepted until each step in its proof has been independently verified. Computer-assisted proofs generally proceed by conducting a vast number of calculations�surveying all the possible types of instances in which the theorem could apply and proving that the theorem holds for each type. In most computer-assisted proofs there are astronomically many types of instances to survey, and no human being could review every step in the proof. Hence, computer-assisted proofs involving astronomically many types of instances should not be accepted.
Which one of the following is an assumption on which the argument relies?
The use of the computer to assist in the proof of mathematical theorems has greatly simplified the mathematician's task.
Most attempts to construct proofs of mathematical theorems do not result in demonstrations that the theorems are true.
Computers cannot be used to assist in generating proofs of mathematical theorems that involve only a very limited number of steps.
Any mathematical proof that does not rely on the computer cannot proceed by surveying all possible types of instances to which the candidate theorem might apply.
The use of an independent computer program does not satisfy the requirement for independent verification of each step in a proof that is extended enough to be otherwise unverifiable.
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