When discussing the implications of economic models, it's crucial to remember that just because a model's predictions are accurate, it doesn't mean the underlying assumptions capture reality.

Mathematics has a theoretical and experimental component, with recent advancements allowing for more experimental approaches in the field.

Mathematicians care about whether something holds true 100% of the time, unlike most fields where 99.99% suffices. This is crucial in fluid dynamics, where we need to understand if there are special initial states that could lead to blow-up scenarios.

In medical diagnostics, models can demonstrate impressive reasoning capabilities, mapping symptoms to correct medical cases effectively.

Even with handcrafted models, you can still understand and prove things about your solution, ensuring guarantees on the results.

Mathematics allows you to change the rules of the problem, which is not possible in other fields like engineering, where fixed requirements exist.

AI models can perform basic mathematical operations and demonstrate reasoning through their circuits, but they can also fake complex calculations.

Machine learning models excel at static problems, like analyzing radiological reports, but they falter when predicting future events, which is crucial for investing.

AI systems like AlphaProof are on the right track and will continue to improve, suggesting that the future of mathematics could be transformed by AI.