Abstract Mathematology (UH, IS MATH REAL?) with Eugenia Cheng | Ologies with Alie Ward

Intro

In this episode of “Ologies with Alie Ward,” Alie Ward interviews mathematician Eugenia Cheng to explore the abstract and fascinating world of mathematics. They discuss the nature of math, its applications, and the emotional side of learning and teaching it. Eugenia Cheng’s book “Is Math Real?” serves as a guide to understanding the intricacies of math and debunking common misconceptions. Join Alie and Eugenia as they dive into the weird and artsy side of mathematics.

Main Takeaways

Mathematics as a Lifestyle

• Math stems from a root meaning simply to learn.
• Math is not just numbers, but a lifestyle.
• Math is weirder and more artsy than you think.

Abstract Mathematics vs. Applied Mathematics

• Pure mathematics is more of a name to distinguish it from applied mathematics.
• Abstract mathematics is the same as pure mathematics.
• Abstract mathematics uncovers logical structures for their own sake.
• Applied mathematics solves problems in the concrete world using techniques from pure mathematics.
• The distinction between abstract and applied math is not always clear-cut.

Empowering People through Math

• The book “Is Math Real?” explores questions about the nature of mathematics.
• The book validates and empowers people who have felt stupid or inadequate about math.
• The author received emails from grown adults who were weeping in their cars because they finally felt validated.
• The author had been building up a catalog of questions that people have really wanted to ask about math.

Emotional Side of Math

• There’s tons of emotion in math, humans are emotional creatures and when we’re communicating math, we need to communicate it with emotions.
• Feelings are always true as a basic starting point, but sometimes there are other things going on as well.
• Math shouldn’t have any emotions in it, but all human experiences have emotions in them.
• Teaching without showing the emotional side doesn’t make it go in as deeply.

Teaching Math and Making it Engaging

• Contextual problems in math lessons can make no practical sense at all.
• Having emotional experiences when doing something makes you remember it more deeply.
• Linking math to topics that people already have feelings about can make them care more.
• Linking math to relatable topics can make it more interesting and engaging.

The Beauty of Mathematics

• Abstract mathematics can be difficult to learn and understand.
• One plus one does not always equal two, it depends on the scenario.
• Math does not come from only one side of the brain, it involves both logical and creative thinking.
• Plasticity of the brain allows for compensation and learning new skills.

History and Cultural Influences

• Different cultures have used different number systems based on their fingers or other factors, such as base 8 or base 20.
• The base 10 system has been used for a long time and was eventually adopted in Europe around 1000 years ago.
• Some ancient cultures used base 60, which is why we have 60 minutes in an hour and 60 seconds in a minute.
• The number 60 is a good number to use because it has a lot of factors and can be divided into many handy units.

Challenging Assumptions and Misconceptions

• Math challenges received wisdom and assumptions, which is important in life as well.
• Critical thinking skills are essential in math and life to avoid making unnecessary assumptions.
• Most people agree that the way math is taught needs to change, but there is disagreement on how to do it.
• Teaching basic appreciation and allowing teachers more autonomy to teach the things they care about is more successful than aiming to teach people content.

The Fascinating World of Numbers

• Zero has troubled people for thousands of years about whether it should count as a number.
• Zero is a helpful number to have around because it allows us to represent nothing and make negative numbers.
• Imaginary numbers were invented to solve the problem of not being able to take the square root of a negative number.
• Imaginary numbers are called that because they were imagined into existence, and they can be useful in solving certain mathematical problems.

The Intricacies of Patterns and Sequences

• The Fibonacci sequence is a mathematical sequence that appears in nature.
• The Fibonacci sequence starts with 1 and is created by adding the two previous numbers together.
• The Fibonacci sequence can be seen in things like the spiral patterns of seashells and the arrangement of leaves on a stem.
• The Fibonacci sequence was not actually discovered by Fibonacci, but named after him.

Mathematics for All

• Math is for everybody and can be used to understand all parts of the world.
• Celebrate the questions that children ask and don’t be afraid if it’s a question you don’t know how to answer.
• Overcoming people’s misconceptions about math is the biggest challenge.
• Most mathematicians find everything very difficult and think they’re stupid.

Summary

Mathematics as a Lifestyle

Mathematics is not just about numbers; it is a way of thinking and living. It delves into the weird and artsy aspects of life, uncovering logical structures and patterns that may not be immediately apparent. Abstract mathematics, also known as pure mathematics, explores these structures for their own sake, while applied mathematics uses these techniques to solve real-world problems. However, the distinction between abstract and applied math is not always clear-cut.

Empowering People through Math

Eugenia Cheng’s book “Is Math Real?” addresses the common feelings of inadequacy and stupidity that many people experience when it comes to math. The book validates and empowers individuals by answering questions they have always wanted to ask about math. It has received overwhelming responses from adults who finally feel understood and validated in their struggles with math.

Emotional Side of Math

Mathematics is not devoid of emotions; it is a subject that can elicit deep feelings. Teaching and learning math should involve acknowledging and embracing these emotions to make the content resonate more deeply. Contextual problems and relatable topics can make math more interesting and engaging, allowing individuals to form emotional connections with the subject.

The Beauty of Mathematics

Abstract mathematics can be challenging to learn and understand, but it offers a unique perspective on the world. It requires both logical and creative thinking, engaging both sides of the brain. The plasticity of the brain allows for compensation and the acquisition of new mathematical skills. Different cultures have influenced the development of number systems, with base 10 becoming widely adopted in Europe. The Fibonacci sequence, a mathematical sequence found in nature, showcases the beauty and efficiency of patterns.

Challenging Assumptions and Misconceptions

Mathematics challenges assumptions and received wisdom, emphasizing the importance of critical thinking skills. There is a consensus that the way math is taught needs to change, but there is disagreement on the best approach. Teaching basic appreciation and allowing teachers more autonomy to teach what they care about has shown greater success than focusing solely on content. Overcoming misconceptions and changing people’s perceptions of math is a significant challenge.

The Intricacies of Numbers and Sequences

Numbers like zero and imaginary numbers have sparked debates throughout history. Zero is a crucial number for representing nothingness and enabling the concept of negative numbers. Imaginary numbers were invented to solve the problem of taking the square root of negative numbers. While they may not have physical reality, they have proven useful in solving mathematical and even physical problems. The Fibonacci sequence, named after Fibonacci but not discovered by him, appears in various natural phenomena, highlighting the presence of patterns and sequences in the world.

Mathematics for All

Mathematics is not exclusive to a select few; it is for everybody. It can be used to understand and analyze different aspects of the world. Celebrating the curiosity and questions of children and embracing the unknown fosters a positive and inclusive learning environment. Overcoming misconceptions and instilling a growth mindset are essential in making math accessible to all individuals.

Conclusion

Mathematics is a fascinating and diverse field that extends beyond numbers and equations. It is a lifestyle, a way of thinking, and a means to understand the world. By embracing the emotional side of math, challenging assumptions, and making it engaging and relatable, we can empower individuals to overcome their fears and misconceptions. Math is for everybody, and it is through curiosity, critical thinking, and a growth mindset that we can unlock its beauty and applicability in our lives.