Stop Trying To Understand

Summary

The speaker emphasizes the importance of not getting stuck on understanding every detail in mathematics, sharing personal experiences and advice. They suggest that it's okay to not fully grasp concepts immediately and recommend moving on when stuck, as revisiting them later can often lead to clarity. The speaker also discusses the struggle of students with understanding and the importance of managing time effectively, especially in the context of mathematical studies. They conclude by encouraging learners to persevere without getting hung up on every problem.

Takeaways

• 😀 It's important to not spend too much time on a single problem, as it can lead to frustration and wasted effort.
• 🤔 Sometimes, moving on from a difficult concept and returning to it later can lead to a better understanding.
• 📚 Students often struggle with understanding the 'why' behind mathematical formulas and derivations, which can hinder their learning process.
• 🕒 Time management is crucial, especially in subjects like mathematics that can be very time-consuming.
• 🔄 Revisiting past material can often make it easier to understand, as familiarity and new perspectives can clarify complex ideas.
• 🚫 It's not necessary to understand everything in a class; partial understanding is still valuable and better than none at all.
• 🤷‍♂️ Not understanding a concept does not mean you are incapable or less intelligent; it's a normal part of the learning process.
• 💡 Half understanding can be a stepping stone to full understanding, so it's okay to move on when you're stuck and come back later.
• 🎓 Even as a college student, the speaker understood only about 60-70% of what was taught, which is a reminder that complete understanding is not always possible or necessary.
• 👨‍🏫 The speaker's advisor's advice to not spend too much time on one problem is a lesson in efficiency and the importance of moving forward.
• 📈 The concept of understanding varying degrees of material can be applied to grading, where a 'C' grade could mean understanding 70% of the material.

Q & A

What advice did the speaker's advisor give them about working on math problems?

The advisor advised not to spend too much time on any one problem because it could be a waste of time.

What was the speaker's initial reaction to the advisor's advice?

The speaker initially thought it was great advice and appreciated the advisor's perspective.

What mistake did the speaker make after not taking the advisor's advice?

The speaker spent about 50 hours working on a math problem that had a typo, realizing it was a waste of time.

Why does the speaker suggest that students sometimes need to move on from a problem they can't solve?

The speaker suggests moving on to manage time effectively and because revisiting the problem later might make it easier to understand.

What issue does the speaker identify that many students face when learning mathematics?

Many students get hung up on understanding 'why' behind formulas and derivations, which can lead to frustration and wasted time.

How does the speaker describe their experience with learning to find the inverse of a matrix?

The speaker struggled with finding the inverse of a matrix due to making silly mistakes and not fully understanding the process despite staying up late to practice.

What is the speaker's view on the necessity of understanding everything taught in a class?

The speaker believes it's not necessary or even possible to understand everything taught in a class, and that it's more important to manage time and focus on what's in front of you.

What example does the speaker give about a concept that was difficult for them and others to understand?

The speaker mentions learning mathematical induction with inequalities as a concept that was difficult for both themselves and their students.

How does the speaker reflect on their own understanding of the material when they were a college student?

The speaker estimates they understood about 60 to 70% of the material taught in their classes, which they felt was low but still allowed them to perform well.

What does the speaker suggest is an appropriate response when faced with a difficult problem in mathematics?

The speaker suggests not spending too much time on one problem, but rather moving on and revisiting it later when it might be easier to understand.

What is the speaker's recommendation for managing time when working on math problems?

The speaker recommends spending a limited amount of time on each problem, revisiting them periodically, and not getting hung up on a single problem for too long.