#5 - The area of mathematics called "gauge field theory,"

[Administrator]

Complete Question Explanation

Must Be True. The correct answer choice is (A)

This stimulus involves a discussion of mathematical theories and their applications. The “gauge
field theory” was investigated in the nineteenth century, but the theory wasn’t applied to quantum
mechanics until fairly recently. Another area of mathematics, differential geometry, was also
investigated by Gauss, well ahead of Einstein’s application of related, “offspring” concepts to his
theory of general relativity.

The question stem asks which one of the answer choices is best illustrated by the examples
presented. In an effort to prephrase this answer choice, we should note that the main link between the
two examples presented in the stimulus is that they both reflect mathematical discoveries which were
applied to concepts a long time after they were initially conceived.

Answer choice (A): This is the correct answer choice. New theories are often applied long after
their initial discovery—this reflects the concept prephrased above, and the example of Gauss’
investigation of differential geometry, the offspring of which was later applied by Einstein to the
exploration of general relativity.

Answer choice (B): The author of the stimulus alludes to the point that there are sometimes wide
spans of time between the conception of a mathematical idea and its application, but there is no
reference made to any such specific anticipation on the part of the mathematicians.

Answer choice (C): It is not clear that modern discoveries in physics would have been impossible
without 19th century mathematical advances—even though they may have facilitated the later
discoveries, this does not necessarily mean that the modern discoveries would have been impossible
without earlier advances. Rather, the examples in the stimulus are offered to refl ect the lapse that
sometimes occurs before an idea is applied.

Answer choice (D): While it may be true that the nineteenth century stands out as a period of great
mathematical progress, there is no way to know based on the information provided; since the
stimulus contains no reference whatsoever to the degree of progress during any other time periods,
there is no basis for such comparison. Since we cannot conclude that the nineteenth century held any
such distinction based on the stimulus, this cannot be the correct answer choice.

Answer choice (E): While mathematics might advance more quickly than other sciences, this is not
illustrated by the information contained in the stimulus. If anything, the stimulus points out the time
lapse between conception and application, indicating that mathematics in some cases advances rather
slowly, but there is no basis for comparison to other fields.

[jared.xu]

I got this question wrong and did not choose A, the right answer, because I had language issues in the answer. A states: "Applications of some new theories or techniques in mathematics are unrecognized until long after..." This implies that scientists have repeatedly applied the theories or techniques, and that their efforts, their applications, have not been recognized until Einstein and the people doing quantum mechanics. Whereas in the stimulus states: "the area of mathematics called "gauge field theory," though investigated in the nineteenth century, has only relatively recently been applied to problems..." What this implies is that the theory has not been applied until relatively recently. This disparity seems to indicate that A is wrong. Are we supposed to somehow subordinate the meaning of "has only relatively recently been applied" under that of "applications are unrecognized." They just do not seem to be the same thing. Thank you in advance for replying.

[Nikki Siclunov]

The statement "applications of some new theories or techniques in mathematics are unrecognized until long after the discovery of those theories or techniques" does not imply that scientists have repeatedly tested these theories or techniques. I think you are reading into this a bit too much

(A) simply means that their applications were not fully understood (i.e. "unrecognized") until long after. This is consistent with the facts presented in the stimulus: clearly, if the theories mentioned were only recently applied to contemporary problems, the application of these theories was not recognized until long after their discovery. This is so because every theory mentioned was discovered long before its appropriate application.

[cardinal2017]

Hi, I just want to add a bit of my explanation/interpretation on the staff's reply.

I got this Q wrong, too, and chose (C) after thinking between (A) and (C).

So let my automatic writing of how I understood this question explain.
That was because I chose (A) at first, but then I saw this verb 'unrecognized' doesn't necessarily fit in with what the Stimulus says---applications just didn't exist, not that it exists and just unrecognized, or not 'known/famous' to the world. Also, I suspected on this 'applications in mathematics' as well because I found the applications in the stimulus were all in physics as compared to math.

But, come to read of it again, now I see that what (A) mentions is not the applications are 'of mathematics' in itself, or it is a math. Rather, it means that the applications are from the math as in that what is stated is the 'apps of new theories in math' ---so that the theories are the ones in math, not necessarily the applications.

Also, the meaning of 'unrecognized' can be used when something is, actually, 'unrealized.' I thought it is a prerequisite that something needs to exist before it gets 'unrecognized' or not (i.e. recognized) but, perhaps in the LSAT, it seems not.

=========>So let's get into this attractive answer (C).

Before I realized the point, I was pretty confused why (C) isn't a better/best illustrating answer here.

But what was wrong with (C) was the subject of the sentence, 'the discoveries of modern physics.'

(C) is right in every aspect except this part (I think).

What would not have been possible w/o the math advances of 19th century was, not the 'discoveries' of modern physics', but the application of those mathematical theories 'TO' the modern physics.

Cleared/

[Clay Cooper]

Hi Cardinal2017,

Thanks for your post. I like your thorough reasoning. Let me just add my own take on why C is wrong; I think it is simple (if difficult).

The question asks us: the examples above best illustrate which one of the following?

And answer choice C claims: the discoveries of modern physics would have been impossible without the mathematics of the nineteenth century.

Do the examples we are given prove this? Not at all - all that they prove is that nineteenth century mathematics did, in fact, play some role in modern physics. What do we know about what would have been possible in a (hypothetical) world in which these 19th century mathematics didn't exist? Nothing at all; therefore, we cannot claim, as C does, that anything about modern physics would have been impossible in such a world. In other words, the simple fact that these mathematics were in fact used in the modern discoveries, does not necessarily mean that the mathematics were required for the discoveries.

I hope that helps! Remember, with a principle question like this, one very effective way to think about it is in terms of proof and proving. What are you claiming to have proved (here, the answer choice), and what proof do you have of your claim (here, the examples in the stimulus)? If your proof doesn't match what you're claiming to have proved, you're in trouble.