Final answer:
Number theory is a mathematical discipline focused on the properties of natural numbers, integral to various fields including cryptography, and serves as the language of nature, allowing for verifiable truth through logical systems.
Step-by-step explanation:
Number theory is a mathematical discipline that is primarily concerned with the properties that are exhibited by the natural numbers. This branch of mathematics delves into patterns, relationships, and problems associated with integers and is integral to various fields, including cryptography and computer science. Number theory can involve different techniques ranging from elementary methods to sophisticated tools of abstract algebra and analysis.
Mathematics, often described as the language of nature, is unique in its logical structure and its ability to model physical quantities and phenomena through mathematical models. This distinct way of understanding enables scientists and mathematicians to come to conclusions that are verifiable through evidence and logic. Mathematics claims about the natural numbers can be determined to be true or false by using the rules of mathematical systems, much like science tries to explain natural or human-made phenomena with observation and experimental investigation.