Why Do People Hate Mathematics? Efim Zelmanov (Fields Medal 1994)
TLDRIn a captivating discussion at the Heidelberg Laureate Forum, Yim Zelmanov, a renowned mathematician, shares his perspective on why some people may dislike mathematics, emphasizing that it's often due to its compulsory nature and the challenge it presents. He argues that mathematics is about problem-solving, not memorization, and that the joy comes from overcoming difficulties. Zelmanov also delves into the beauty of mathematics, comparing it to an art form, where beauty is associated with simplicity and structure. He discusses his work on the Burnside problem and the excitement of approaching and solving complex mathematical problems. The conversation touches on the interplay between pure and applied mathematics, the potential applications of abstract concepts, and the importance of unity within the field. Zelmanov's mathematical genealogy, the distinction between pure and applied mathematics, and his preference for traditional blackboards over modern tablets are also explored. The discussion concludes with Zelmanov's views on the nature of mathematical discovery versus invention, his stance on whether zero is a natural number, and his fondness for all numbers equally.
Takeaways
- π Mathematics is a foundational subject for all technology and engineering courses, which is why it is often a mandatory part of education for many students.
- π The obligation to take math courses, even for those not interested in the field, can lead to a dislike for mathematics.
- π§ββοΈ Some people are attracted to mathematics because of its difficulty and the sense of achievement that comes from solving complex problems.
- π‘ Mathematics is not about memorization but about problem-solving, which can be a source of joy when a problem is finally solved.
- π΅οΈββοΈ When working on a difficult problem, it's important to consider what new approaches or insights you can bring to the table that others have not.
- π¨ Mathematics can be both a science and an art, with mathematicians often discussing the beauty of a solution or problem.
- πΌ Just as in music or art, mathematicians develop a sense of what is beautiful through exposure to and study of the works of great mathematicians.
- π The speaker believes that the separation between pure and applied mathematics is not ideal and advocates for unity within the field.
- π Many mathematical concepts initially considered abstract or pure have later found real-world applications, such as in cryptography.
- π³ The speaker's mathematical genealogy traces back to influential mathematicians like Gauss and Newton, highlighting the interconnectedness of mathematical thought.
- β The speaker does not have a preference for zero as a natural number unless it is defined as such by a mathematical law or convention.
- π The speaker prefers using both traditional blackboards and whiteboards over tablets for mathematical work, valuing the tactile and visual aspects of these tools.
Q & A
Why does Yim zelmanov believe that people hate mathematics?
-Yim zelmanov suggests that people hate mathematics because it is often made obligatory for students pursuing various fields, similar to how people might hate music if it were declared obligatory. Additionally, he mentions that mathematics can be difficult, which may contribute to the negative perception.
What does Yim zelmanov think about the difficulty of mathematics attracting people to the subject?
-Yim zelmanov acknowledges that some people are attracted to mathematics precisely because of its difficulty. He likens the struggle and eventual triumph over a mathematical problem to an exciting and beautiful experience.
How does Yim zelmanov describe the process of solving a mathematical problem?
-According to Yim zelmanov, solving a mathematical problem is not about memorizing or reading; it's about engaging with the problem-solving process. He emphasizes the joy that comes from solving a problem oneself, without looking at the solution in a book.
What was Yim zelmanov's personal experience with the struggle of solving a mathematical problem?
-Yim zelmanov shares that it took him a year of 'frontal attack' to solve a problem, constantly thinking about it day and night. He mentions feeling exhausted rather than euphoric when he finally solved it, suggesting that the excitement came later.
How does Yim zelmanov perceive the relationship between mathematics and art?
-Yim zelmanov views mathematics as both a science and an art. He explains that mathematicians often discuss the beauty and ugliness of mathematical concepts, much like artists and musicians do, and that the pursuit of beauty is a decisive factor in mathematical work.
What does Yim zelmanov think about the beauty in mathematical solutions?
-Yim zelmanov believes that the beauty in a mathematical solution is subjective and comes from the structure and elegance behind it. He compares this to how students of music or art develop their taste by learning from the masters.
How did Yim zelmanov approach the Burnside problem?
-Yim zelmanov had a different approach to the Burnside problem, which he believed was possible to solve due to his unique perspective. He had the idea for the solution before deciding to tackle the problem.
What is Yim zelmanov's view on the current state of the bounded Burnside problem?
-Yim zelmanov does not believe that we are close to solving the bounded Burnside problem. He suggests that a dramatically new idea is needed, as even a supercomputer won't help with problems that are algorithmically undecidable.
What is Yim zelmanov's opinion on the interaction between mathematics and computer science?
-The transcript does not provide a direct answer to this question. However, Yim zelmanov does mention the importance of mathematics in technology and engineering, implying a strong connection between mathematics and computer science.
How does Yim zelmanov feel about the division between pure and applied mathematics?
-Yim zelmanov prefers unity and has always pushed for it within mathematics departments. He does not believe in the strict separation of pure and applied mathematics, advocating for a more integrated approach.
What is Yim zelmanov's view on the mathematical genealogy project?
-Yim zelmanov is aware of the mathematical genealogy project and finds it interesting. He acknowledges that his genealogy leads to prominent mathematicians like Gauss and Newton.
Which mathematical notation does Yim zelmanov prefer for calculus?
-Yim zelmanov admits to using both Newton's notation (f prime or F dashed) and Leibniz's notation (dy/dx) without much thought, but he expresses a slight preference for dy/dx.
Does Yim zelmanov have a favorite number?
-Yim zelmanov does not have a favorite number; he likes all numbers equally.
What is Yim zelmanov's preference between blackboards, whiteboards, and tablets?
-Yim zelmanov is more used to blackboards and prefers them over whiteboards and tablets. He appreciates the traditional feel and noise of chalk on a blackboard.
Outlines
π Understanding the Perception of Mathematics
In this paragraph, Yim Zelmanov discusses the reasons why people may dislike mathematics, emphasizing that it is a foundational subject for technology and engineering. He suggests that the obligation to take math courses, even for those not interested in the field, contributes to the negative perception. Zelmanov also highlights the beauty and excitement of overcoming mathematical challenges, comparing the process to the pursuit of art and the development of taste, much like in music or painting.
π€ The Beauty and Difficulty of Mathematical Problems
The speaker delves into the nature of mathematical problem-solving, arguing that it's not about memorization but about the joy of solving problems. He shares his personal experience of working on a problem for a year, which was exhausting but ultimately led to a sense of accomplishment. The conversation also touches on the debate of whether mathematics is an art or a science, with the speaker suggesting it's both, especially for those deeply involved in it.
π The Evolution and Relevance of Mathematical Concepts
This section explores the historical evolution and application of mathematical concepts. The speaker points out that subjects once considered purely abstract, like finite fields, have found real-world applications, such as in financial transactions. There's a discussion about the division between pure and applied mathematics and the importance of unity within the field. The speaker also reflects on his mathematical genealogy and the influence of historical mathematicians like Gauss and Newton.
π Final Thoughts and Invitation to Learn More
The final paragraph serves as a conclusion to the interview, with the speaker encouraging viewers to search for more information about the guest's work online. There's a reminder for viewers to subscribe for more content, and a note of thanks from the host for watching the video.
Mindmap
Keywords
π‘Mathematics
π‘Difficulty
π‘Problem Solving
π‘Beauty in Mathematics
π‘Bounded Burnside Problem
π‘Mathematical Genealogy
π‘Pure vs. Applied Mathematics
π‘Euler's Formula
π‘
π‘Galois Theory
π‘Algorithmically Undecidable
π‘Blackboards vs. Whiteboards
Highlights
Mathematics is a prerequisite for all Technology and Engineering courses, which may contribute to the obligation and difficulty students face.
The struggle and eventual triumph over difficult mathematical problems can be exciting and beautiful.
Mathematics is not about memorization but about problem-solving, which can bring joy when a problem is solved independently.
The speaker's personal experience with solving the Burnside problem involved a year of intense focus and exhaustion.
The pursuit of beauty in mathematics is akin to the pursuit of beauty in music or art, with mathematicians developing a sense of what is aesthetically pleasing.
The speaker's approach to the Burnside problem was based on a different approach, highlighting the importance of innovation in problem-solving.
The Burnside problem was popular in the Soviet Union and the speaker's work was somewhat related, showing the influence of academic environment.
The bounded Burnside problem remains unsolved, requiring a dramatically new idea, indicating the ongoing nature of mathematical inquiry.
Mathematics and computer science have a significant interaction, with mathematical theorems underpinning modern technologies like cryptosystems.
The speaker appreciates the beauty of Euler's formula and its profound implications in mathematics.
The division between pure and applied mathematics is seen as potentially detrimental, with the speaker advocating for unity in the field.
The mathematical genealogy project traces academic lineage, revealing connections between mathematicians and their advisors.
The speaker prefers the notation dy/dx over f'(x) or F dashed, showing a personal preference in mathematical notation.
Zero's classification as a natural number is a matter of convention, with the speaker indicating flexibility in its categorization.
The question of whether mathematics was discovered or invented is left open by the speaker, reflecting the complexity of the issue.
The speaker does not have a favorite number, expressing equal appreciation for all numbers in mathematics.
A preference for blackboards over whiteboards or tablets is noted, highlighting the traditional aspects of mathematical work.
Transcripts
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