Summary of Charla de Divulgación Matemática

00:00:00 - 00:50:00

Ana discusses how to give a mathematics lecture to students, and how this can help them understand the subject better. She also talks about how Wittgenstein believed that language was a tool for understanding reality, and how this can apply to mathematics.

• 00:00:00 The speaker presents a philosophy of mathematics talk focusing on the question of whether mathematics is created or discovered. She reviews various philosophical positions on the matter, and then presents her own view that mathematics is created. She invites the audience to explore this idea through philosophical analysis and the study of ontology and epistemology.
• 00:05:00 In this video, claramente, we talk about creating something. We have this idea of building something to bring it towards its creation, rather than the other way around. We consider discovery, which implies more than simply carrying out a project--something that is already observed--but something that is already there, observing what kind of thing it is. Then, we go to each of these verbs in order to attempt to understand what we want to answer this question: what do we do when we create, well, we generate the existence of something new. Then, the creation process is sensitive to time; we see that, before we can create, we may have tools, knowledge, and position to start. During the creative process, what we do is create and generate something completely new, different from our tools and materials but what does that mean in and of itself--a product, in and of itself? For example, we may imagine many tools, imagine the materials that could be part of the creation of a computer, for example. We can't have metal, plastic, code from all different types of parts, and so on. However, we have the verb discover. Discovery involves knowing something that was previously ignored. We use tools that help us
• 00:10:00 In this video, Charla de Divulgación Matemática, two different philosophical stances on the existence of mathematical objects are described: the Platoist view that they exist as abstract objects, and the Aristotelian view that they exist as instances of particular objects. Next, we discuss the third position, which is the Platonic view that they exist independently of any particular objects. Finally, we discuss the Platoist view that mathematical objects have no spatial or temporal dimensions.
• 00:15:00 Mathematicians are independent of the mind and language, which means that for Plato, mathematics are something that happens only in our minds and then clearly, like they don't have temporal dimensions, only exist in our minds for Plantonists, abstract objects in mathematics exist in some abstract way and can be represented in the world space-time, but they're not exactly that. Their essence is complete and are independent of agents, like you and me, as well as our neighbor. They're not dependent on language either, which is why the concept of number 3, for example, doesn't depend on how we talk in Spanish here, say 3 or 3 in any other language. The concept of stress, for example, according to Platonists, is abstract and can be talked about in different languages because there is agreement among Platonists on this point, abstract objects in mathematics exist independent of our language. That's why we say that mathematics is this universal language very well. As we have seen dishes, we also have anti-Platonist schools of thought during the flowering of science. There were many philosophical movements that distanced themselves from Platonism, considered it an old, somewhat archaic theory, and there was like this pressure to move away from these strange
• 00:20:00 In this video, David Hilbert explains how mathematics is based on symbolism, and how various schools of thought have influenced the way we understand the subject. He also discusses the Plato-inspired anti-Platoism, and how it has been criticized for not being adequate for the kinds of mathematical activity scientists require. Finally, he provides an updated, more complex version of the Platonic theory, which relies on reason and intuition.
• 00:25:00 The video discusses the Plato-based hypothesis that mathematics are either self-created or discovered according to Plato's philosophy. The video discusses the epistemology and ontology of this hypothesis, and how they might help us answer the question of whether mathematics are created or discovered. The video then goes on to talk about two different types of learning methods, deductive and inductive, and how they apply to the question of whether mathematics are created or discovered. Finally, the video talks about how science can use either type of learning method to arrive at conclusions about mathematics.
• 00:30:00 This video discusses the properties of logical structures and how these structures are used to create mathematical theorems. However, some of us may not be as "rich" with regard to this knowledge, as it seems to be false or superficial. We can be critical of this representation of mathematics within sciences in many ways. For example, we could say that there is a method that is not used by all deductive sciences, and that there are some non-deductive sciences. This method is experience-based and involves spatial and temporal perceptions. For example, if we have this system of truth, we have a sequence of numbers: 14, 7, 10. We see that in each situation, we find a pattern, and that the numbers are not increasing by three units. Instead, they are increasing by three units each time. This is based on each small experience we have. So, we create a general formula from these particular instances, which would help us answer this question: "What is the sequence of numbers 14, 7, 10?" We can also use inductive methods to help us teach mathematics in different pedagogies. Space-time is indeed true, but teachers and students are not the only ones who know this. We can work with this idea by
• 00:35:00 In this YouTube video, a Charla de Divulgación Matemática is presented in which various aspects of the philosophy of mathematics are discussed. Among these are anti-Platonism, the three Platonic schools of thought, and contemporary theories within the Platonic tradition. The video then switches gears to discuss learning methods for mathematics, focusing on deductive and inductive methods. However, it is not clear exactly how deductive and inductive methods can be said to speak to what kinds of things are within mathematics, as they seem to be used in a similar way to inductive methods when working with mathematics. Nevertheless, this video provides a useful introduction to Platonic philosophy for those new to it.
• 00:40:00 This video discusses the difference between inductive and deductive reasoning, and provides an example of each. The presenter then asks a question about the effectiveness of one method over the other. The answer depends on the individual's goals.
• 00:45:00 Wittgenstein believed that language was a representation of the world, and that mathematics is a particularly effective language for representing reality. This video summarizes Wittgenstein's philosophy, focusing on his idea that language is a tool for understanding reality. Wittgenstein also argues that it is difficult to think about something that doesn't exist, and that the principles of mathematics are just as applicable to non-mathematical concepts as they are to mathematics itself. Finally, the presenter provides a summary of the main points of Wittgenstein's philosophy.
• 00:50:00 This video is a presentation by a group of people about mathematics, and one of the people speaking is Ana. She discusses how to give a mathematics lecture to students, and this is the first of many such lectures that the group will be holding monthly. Thank you, Ana, and thank you to everyone who tuned in to this presentation. We'll see you next time.