Theorems for Free!

Theorems for Free! is a concept in mathematics that suggests we can sometimes obtain useful conclusions or results without directly proving them rigorously. This is often seen in areas like combinatorics or number theory, where certain patterns or results seem evident, and we rely on intuitive reasoning or established knowledge. It emphasizes that some truths can be accepted based on their simplicity or consistency with other principles, allowing mathematicians to focus on more complex problems while leveraging these intuitive insights. Essentially, it's about recognizing that not every statement requires a full formal proof to be useful or valid.