How to think like a mathematician and to stop viewing the solutions

Summary

In this video, the speaker discusses how to think like a mathematician, emphasizing the importance of systematic and mechanical thinking. They compare math to music, explaining that success in both fields requires mastering underlying techniques and algorithms rather than simply 'flowing' through problems. The speaker highlights a step-by-step approach to problem-solving and advises starting from the end of a physics question to simplify the process. They also discuss the challenges of YouTube content creation, explaining the need for a membership model to maintain visibility due to over-uploading, offering access to podcasts and audiobooks for members.

Takeaways

• 😀 Math should be approached mechanically, like playing a musical instrument, focusing on each step rather than trying to flow through it.
• 😀 To think like a mathematician, focus on learning algorithms and the mechanics behind solving problems, similar to learning piano or guitar.
• 😀 The key to solving math and physics problems is understanding the process rather than simply memorizing solutions.
• 😀 When approaching physics questions, start from the end and work backwards. This helps cut down on unnecessary processing and mental distractions.
• 😀 In math, every problem follows an algorithm. If you don’t know the algorithm, you won’t be able to solve the problem.
• 😀 The process of elimination is crucial for solving math problems, ensuring you choose the correct method by ruling out incorrect options.
• 😀 Reading a physics question front to back can confuse you. Instead, focus on what is being asked at the end and work backwards.
• 😀 Understanding the mechanics of math (like the alphabet for writing) is essential for progressing in problem-solving.
• 😀 Math is a systematic process; you need to know the rules and techniques before applying them to solve problems.
• 😀 You don’t need to understand every detail of a problem immediately. Focus on applying known theorems and formulas step-by-step to find the solution.
• 😀 Watching solutions on platforms like YouTube provides the end result, but the real learning comes from doing the research and solving problems yourself.

Q & A

What is the main theme of the speaker's advice on learning math and physics?

The main theme of the speaker's advice is that learning math and physics should focus on understanding the mechanical and systematic processes behind solving problems, rather than just memorizing solutions. The speaker compares this process to learning a musical instrument, emphasizing the importance of mastering the mechanics before achieving fluency.

How does the speaker compare learning math to playing a musical instrument?

The speaker compares learning math to playing an instrument by explaining that, like music, math requires a mechanical understanding of steps and processes. In music, a musician doesn't just flow through a piece but follows specific mechanical steps like hitting keys or strings in a precise order with exact timing, which is similar to following algorithms in math to reach a solution.

What role does 'inertia' play in the way people approach learning, according to the speaker?

The speaker uses the concept of 'inertia' to describe how people tend to follow the path of least resistance when learning, often opting to memorize solutions instead of understanding the underlying principles. This behavior can lead to relying on pre-determined answers instead of engaging with the problem-solving process.

What is the speaker's perspective on using YouTube videos for learning math and physics?

The speaker views YouTube videos as potentially detrimental if used as the main source of learning, because they often show the end result without teaching the process. The speaker advocates for engaging in the problem-solving process oneself to gain experience, rather than just watching others' solutions.

Why does the speaker suggest starting at the end of a physics question?

The speaker suggests starting at the end of a physics question to avoid prematurely trying to solve it, which could lead to confusion or missteps. By focusing on what the problem is asking for, and working backwards through the equations, the solver can more effectively identify the right approach and reduce unnecessary mental effort.

What is the process of elimination in problem-solving, and why is it important?

The process of elimination is a problem-solving technique where you first identify what cannot be done, narrowing down the possible solutions. It’s important because it prevents wasting time on incorrect methods and ensures a more efficient approach by eliminating less likely options before focusing on the correct one.

How does the speaker suggest approaching a math question systematically?

The speaker suggests a systematic approach to math problems: first, identify the relevant formula, theorem, or definition; then, set up the problem; execute the solution; and finally, finalize the answer. This method ensures clarity and precision in solving mathematical problems.

What does the speaker mean by math being 'algorithmic'?

When the speaker describes math as 'algorithmic', they mean that math problems follow a set, step-by-step process (or algorithm) that must be learned and applied. The focus should be on learning the correct algorithms, as opposed to trying to understand the entire conceptual depth of a problem without first mastering the basic steps.

How does the speaker differentiate between solving physics problems in class versus real-world problems?

The speaker points out that physics problems in class are often simplified, and the goal is to apply learned equations and concepts to find a solution, typically following a set algorithm. In contrast, real-world problems may not have clear-cut solutions and require more flexibility and deeper analysis.

What is the speaker’s approach to learning and using algorithms in math and physics?

The speaker emphasizes the importance of learning algorithms in math and physics. They believe that knowing the correct algorithm for solving a problem is essential, and once the algorithm is mastered, solving similar problems becomes more intuitive and efficient. The key is not understanding every detail but being able to follow the steps accurately.