Large Language Models (LLMs) have revolutionized AI, but reasoning remains a challenge. Think of solving a complex math problem—while LLMs can generate text, they don't always grasp the underlying logic needed for step-by-step problem-solving. Researchers are tackling this with preference optimization on reasoning traces, a technique that essentially teaches LLMs to prefer correct reasoning paths. Imagine showing an LLM two ways to solve a problem, one correct and one flawed. This method, called PORT, trains the model to recognize and favor the right approach. Interestingly, the training doesn't require new data. The research creatively uses existing reasoning datasets, introducing intentional errors, like slightly changing numbers in intermediate steps, to create examples of incorrect paths. This allows the model to learn from its mistakes. Experiments with models like Falcon2-11B and Mistral-7B demonstrated significant improvements in accuracy on math word problems. This work highlights the potential of preference optimization in enhancing reasoning abilities, suggesting that focused efforts in developing high-quality reasoning datasets could be the key to unlocking more advanced AI reasoning capabilities. This approach has exciting implications for real-world applications like automated problem-solving and personalized education. However, challenges remain, including the computational cost of training and potential limitations in generalizing to non-mathematical reasoning tasks. Future research may explore other error-generation methods and expand the scope of this technique to other reasoning domains, ultimately aiming to bridge the gap between human-like reasoning and the current capabilities of LLMs.