Final answer:
The claim that farming originated in the Americas approximately 10,000 years ago is false. Agriculture in this region developed later than in the Fertile Crescent and other areas of the Old World.
Step-by-step explanation:
The statement that farming in the tropical lowlands of Central and South America began around 10,000 years ago is false. According to various sources, agriculture developed in the western hemisphere significantly later than in the Fertile Crescent, India, China, and New Guinea. The earliest evidence of agriculture in the Americas is from northeastern Mexico around 6500 BCE, and in the Andes Mountains around 3000 BCE. In contrast, the Fertile Crescent saw the emergence of agriculture around 11,000-10,000 years ago. Consequently, New World farming did not originate at the same time as food production in Europe.