A.I. Explanation:

Correct answer: anecdotes

Explanation: The term 'anecdotes' refers to short, interesting stories about real incidents or people, which fits well in the context of discussing Gauss's childhood and his remarkable abilities. It aligns grammatically as a plural noun that complements the verb 'are' in the sentence, indicating multiple stories about his precocity.

Meaning: Anecdotes are brief, entertaining stories about real events or people, often used to illustrate a point or provide insight into someone's character.

Wrong options:

• applications: Applications refer to practical uses or implementations of concepts, which does not fit the context of storytelling about Gauss's childhood.
• legends: Legends imply traditional stories that may not be entirely factual, which could misrepresent the factual nature of Gauss's childhood experiences.
• rumours: Rumours suggest unverified information or gossip, which does not convey the same level of credibility as anecdotes in this context.

Correct answer: discoveries

Explanation: The word 'discoveries' refers to the act of finding or learning something for the first time, which is appropriate in the context of Gauss's groundbreaking mathematical work. It fits grammatically as a plural noun that aligns with the verb 'made,' indicating multiple significant findings he achieved during his teenage years.

Meaning: Discoveries are new findings or insights that have been uncovered, particularly in a scientific or mathematical context.

Wrong options:

• inventions: Inventions refer to the creation of something new, typically a device or process, which does not accurately describe Gauss's mathematical contributions as he was not inventing but discovering existing mathematical truths.
• researches: Researches imply systematic investigations into a subject, which does not fit the context of Gauss's achievements as he was making significant findings rather than conducting research in a formal sense.
• studies: Studies refer to the act of examining or analyzing something, which does not capture the essence of Gauss's groundbreaking contributions as discoveries do.

Correct answer: corrected

Explanation: The verb 'corrected' indicates the action of fixing an error, which is appropriate in the context of Gauss identifying and rectifying a mistake in his father's payroll calculations. It fits grammatically as the past tense of the verb, aligning with the narrative of his early achievements.

Meaning: Corrected means to fix or make right an error or mistake, highlighting Gauss's early mathematical abilities at a very young age.

Wrong options:

• effected: Effected means to bring about or cause something to happen, which does not accurately describe the action of fixing an error in this context.
• caused: Caused implies being the reason for something happening, which does not fit the context of actively fixing an error in calculations.
• improved: Improved suggests making something better, which does not specifically convey the action of fixing an error, as 'corrected' does.