Question 36·Hard·Text Structure and Purpose
Since 2016, mathematician Eugenia Cheng has hosted public “math-art” salons in which she explains abstract category theory by way of baking demonstrations, classical piano performances, and whimsical cartoons. In her most recent book, The Joy of Abstraction, Cheng extends this method: every formal proof is followed by a brief children’s tale that echoes the same logical structure, allowing readers to move back and forth between rigorous mathematics and imaginative narrative. By entwining these seemingly incompatible genres, Cheng contends, the book dismantles the barrier that often makes higher mathematics feel remote from everyday experience.
Which choice best states the main purpose of the text?
For main-purpose questions, first read the entire passage, then briefly summarize it in your own words: “This paragraph is mainly about…”. Pay special attention to the first and last sentences, since they often frame the overall purpose. Next, scan the choices and eliminate any that introduce elements the passage never discusses (such as a full historical timeline, data-based evaluation, or a strong argument taking sides). Finally, choose the option that best matches your summary of what the author is doing overall, not just a single detail or phrase from the middle of the passage.
Hints
Look at the beginning and end of the paragraph
Reread the first sentence and the last sentence: what do they say Cheng is doing, and what result does the author claim this has?
Decide what kind of writing this is
Ask yourself: is the paragraph mainly telling a story over time, judging the success of something, or describing a particular person’s approach to a problem?
Watch for ideas that are not in the text
Check whether the paragraph ever talks about multiple programs, gives data, or sets up a debate between two teaching methods. If an answer choice depends on those things, be suspicious.
Match the choice to the overall focus, not a detail
Avoid picking an answer just because it mentions a familiar word like “category theory” or “proofs.” Make sure the choice describes why the author is writing about Cheng at all.
Step-by-step Explanation
Identify the task: main purpose
The question asks for the main purpose of the text, which means you should focus on what the paragraph is doing overall, not on any single detail or phrase. Think: if you had to summarize why the author wrote this paragraph in one sentence, what would you say?
Summarize the paragraph in your own words
Quickly restate the key ideas:
- Cheng hosts public “math-art” salons using baking, music, and cartoons to explain abstract category theory.
- Her book continues this method: each formal proof comes with a matching children’s tale.
- Readers can move between strict math and imaginative stories.
- The author says that by combining these genres, the book removes a barrier that makes higher math feel distant from everyday life.
Overall, the paragraph is describing what Cheng does and what effect that approach is meant to have.
Check each answer against that summary
Now compare your summary to the choices:
- One type of answer might be about history over time.
- Another might be about judging or evaluating a broad category like “programs.”
- Another might claim the paragraph takes sides in an argument (for example, saying one teaching method is better than another).
- One should simply match the idea that the paragraph describes Cheng’s way of presenting abstract math and what it tries to accomplish.
Eliminate any answer that adds something the passage never does (like a timeline of developments or a debate about which method is better).
Select the answer that matches the description and goal
Only one choice matches the paragraph’s focus on describing how Cheng uses creative methods (salons, music, cartoons, children’s tales) to help people engage with abstract category theory and reduce the sense that higher math is “remote from everyday experience.” That choice is C) To illustrate how one mathematician attempts to make abstract concepts more accessible.