Self-study
The area of mathematics called "gauge field theory," though investigated in the nineteenth century, has only relatively recently been applied to problems in contemporary quantum mechanics. ████████████ █████████ ███████ ████ ██ ████████████ ███ ████████████ ██ █████ ██ ███ █████ ██████████ ████████ ████ ██████ ████████ ██████████ ████ ███ ██ ███ ██████████ ██████ █████████ ███ ███ ███████████ ███████████ ███ █████████ ███████ ███████████
Summary
Gauge field theory is an area of math that, although investigated in the 19th century, has only recently been applied. Differential geometry is another area of math that was investigated in the 19th century, which was a long time before Einstein determined that one of its offspring, tensor analysis, was appropriate for the theory of general relativity.
Strongly Supported Conclusions
Some fields of math may be applicable many years after they are first investigated.
Some fields of math relevant to a problem may have been discovered many years in the past.
5.
Which one of the following ██ ████ ███████████ ██ ███ ████████ █████████ ██████
a
Applications of some ███ ████████ ██ ██████████ ██ ███████████ ███ ████████████ █████ ████ █████ ███ █████████ ██ █████ ████████ ██ ███████████
Strongly supported. The stimulus presents examples of areas of math that were first investigated many years before they were used for certain applications. This is evidence that those particular applications were unknown for a long time.
b
Mathematicians are sometimes ████ ██ ██████████ █████ ████████ ██ █████ ███████ ████ █████ ██████ ██ ██████ ███████████
Unsupported. The stimulus doesn’t suggest that any mathematician was able to anticipate which parts of their subject would be useful to future scientists. We don’t have any statements indicating the expectations or thoughts from mathematicians about the future.
c
The discoveries of ██████ ███████ █████ ███ ████ ████ ████████ ███████ █████ ████████████ ████████ ████ ██ ███ ██████████ ████████
Unsupported. Although we know that the math fields discussed in the stimulus were useful for certain problems related to physics, that doesn’t imply that modern physics wouldn’t have been discovered without those fields.
d
The nineteenth century ██████ ███ █████ █████ █████ ██ █ ██████ ██ █████ ████████████ ████████████
Unsupported. The stimulus doesn’t compare the 19th century with other centuries regarding the level of mathematical achievement.
e
Mathematics tends to ███████ ████ ███████ ████ ███ ██ ███ ████████ █████████
Unsupported. The stimulus doesn’t compare math to other fields regarding the speed of its advancement.