Mathematical Reasoning

- Overview

Mathematical reasoning is the ability to apply logical thinking to a mathematical problem to develop a solution. 

Mathematical reasoning involves:

• Quantifying information: Turning generic information into data
• Using deductive reasoning: Reasoning from premises to reach a logically certain conclusion
• Drawing logical conclusions: Based on evidence or stated assumptions
• Making connections: To work out the correct strategy to use in reaching a solution

Some types of mathematical reasoning include: Deductive reasoning, Inductive reasoning, Analogical reasoning, Abductive reasoning, Cause-and-effect reasoning, Critical thinking, Decompositional reasoning. 

Mathematical reasoning is different from logical reasoning. Mathematical reasoning is the ability to solve mathematical problems and understand mathematical concepts by using mathematical techniques.

- Mathematical Reasoning in AI

Mathematical logic is a foundational framework that enables AI algorithms to reason, analyze, and make decisions. 

Mathematics provides the theoretical foundation and computational tools for AI and machine learning. AI and machine learning use mathematical concepts to help machines mimic human behavior and learn from data. 

For example, AI chatbots use linear algebra to convert words into numerical vectors for analysis and understanding. Linear algebra is the cornerstone of AI, machine learning, and data science. It involves the study of vectors, matrices, and linear transformations.

Mathematical reasoning is the process of applying logical thinking to a situation to derive the correct problem-solving strategy. It's difficult to codify and even more difficult to quantify. 

AI has the potential to aid new mathematical discoveries. In 2019, computer scientist Christian Szegedy predicted that a computer system would match or exceed the problem-solving ability of the best human mathematicians within a decade.