PrepTest 133, Section 2, Question 5
The area of mathematics called "gauge field theory,"(52 more words not shown)
Which one of the following(8 more words not shown)
- AApplications of some(18 more words not shown)
- BMathematicians are sometimes(14 more words not shown)
- CThe discoveries of(16 more words not shown)
- DThe nineteenth century(12 more words not shown)
- EMathematics tends to(9 more words not shown)
Reading the argument
We don't need to know how gauge field theory works. We need to notice when it was developed and when people found a use for it.
The first example gives us mathematical work from the nineteenth century that was only recently applied to quantum mechanics. The second gives us another delay: Gauss investigated differential geometry long before Einstein used one of its developments, tensor analysis, to explore general relativity.
Different mathematical subjects, same pattern. Work happens first; a particular useful application comes much later. The unfamiliar names can make this feel harder than it is, but we can follow that timeline without being able to do any of the mathematics.
What we’re looking for
We're asked what the examples illustrate. I'd predict that mathematicians can develop something well before people realize how to apply it. Stay with that delayed payoff, rather than trying to rank the importance of the discoveries or explain the science behind them.
Working the answers
- ACorrect
Some applications aren't recognized until long after the mathematical theories or techniques are discovered. That's the delay both examples illustrate. Gauge field theory existed before its recent use in quantum mechanics, and differential geometry preceded the use of tensor analysis in general relativity.
Here, an application being 'unrecognized' means that people haven't yet identified that use for the mathematics. It doesn't mean the mathematician failed to win recognition or an award. Read the word as part of the claim about applications, and it fits the examples.
- B
Did Gauss predict Einstein's use of the mathematics? We aren't told that. Discovering something that later proves useful is different from anticipating what future scientists will do with it. B would fit an example of a mathematician calling that future use in advance. These examples give us later applications without that prediction.
- C
Using earlier mathematics doesn't establish that modern physics would have been impossible without it. Perhaps a later scientist could have developed the needed mathematics independently or found a different way to solve the problem. The examples show that earlier work proved useful, not that it was the only possible route to these discoveries.
- D
We have two examples from the nineteenth century, but no comparison with the mathematical achievements of other periods. Perhaps another century produced even more major discoveries. The passage illustrates a delay in application, not an unusually productive historical era.
- E
Earlier discovery followed by later application doesn't measure how quickly entire fields advance. We haven't compared the rate of progress in mathematics with chemistry, geology, or every other physical science. E turns two timelines into a broad ranking the examples don't support.
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