Yes, there is a need to rethink the function of history in mathematics to better understand the cultural, social, and political contexts in which mathematical ideas and practices have developed.

## So let us take a deeper look

The function of history in mathematics is worth rethinking to gain a deeper understanding of the cultural, social, and political contexts in which mathematical concepts and practices evolved. Historians of mathematics have been exploring this topic for decades, uncovering previously overlooked aspects of mathematical development and shedding light on how mathematical knowledge has been shaped by societal and political factors.

As mathematician Morris Kline once said, “Mathematics is man’s own handiwork, subject to the same fallacies and flaws as any other human endeavor.” Therefore, understanding the historical context of mathematical development is central to comprehending the evolution of mathematical concepts and techniques. For instance, the history of mathematics in ancient Greece sheds light on the foundations of geometric thinking and the role of mathematics in Greek culture and society.

Moreover, examining the social and political contexts of mathematical development illuminates the ways in which mathematical knowledge intersects with broader societal issues. Mathematics has often been used to reinforce power imbalances and support political agendas. For instance, non-Euclidean geometry was initially rejected by many mathematicians because it challenged the dominant worldview of the time, which privileged Euclidean geometry. This shows that mathematical knowledge is not neutral and objective, but rather, deeply influenced by factors such as culture, politics, and power.

Here are some interesting facts that highlight the importance of understanding the historical context of mathematics:

- The development of calculus in the 17th century was shaped by the rise of capitalism and the need for tools to measure and analyze economic data.
- The way we write mathematical symbols, such as + and ×, has changed over time and varies across cultures.
- Mathematical concepts that were once seen as abstract and esoteric, such as game theory, have since become important tools in fields such as economics, political science, and biology.
- The history of women and marginalized groups in mathematics has been largely ignored, leading to the erasure of important contributions to mathematical development.

As the historian of mathematics Karen Parshall once wrote, “Understanding the historical development of mathematics and its role in society is essential to understanding the subject as a whole.” By reconsidering the function of history in mathematics, we can gain a richer and more nuanced understanding of this complex and fascinating field of study.

Table:

Historical Context | Example |
---|---|

Ancient Greece | Geometric thinking, role of math in society |

Rise of capitalism | Development of calculus |

Changing mathematical symbols | Variations across cultures |

Game theory | Application in other fields |

Marginalized groups in math | Erasure of important contributions |

**Answer in the video**

The video presents a rethinking of the foundations of mathematics and its practical consequences. It discusses the limitations of current mathematical concepts, including the notion of an infinite decimal expansion, and proposes new approaches for understanding numbers in different contexts. This includes considering real numbers as probabilistic entities made up of bits that can be computed sequentially. The video also delves into the history of mathematical inquiry and the challenges faced by mathematicians in developing new concepts and breaking away from traditional thinking. Ultimately, the video suggests replacing the concept of a set in foundational mathematics with computable mathematics and the notion of bits.

## You will probably be interested in these topics as well

**Why is it important to know the history of mathematics?** It helps students develop a deeper understanding of the mathematics they have already studied by seeing how it was developed over time and in various places.

**What do we learn from history of mathematics?**

The history of mathematics deals with the origin of discoveries in mathematics and the mathematical methods and notation of the past. Before the modern age and the worldwide spread of knowledge, written examples of new mathematical developments have come to light only in a few locales.

**How are math and history related?**

Response: 2) Math History Deepens Our Respect for Human Cultures and Collaboration Across Time. The story of math spans continents and centuries. For example, the insights of algebra and the numeral system we use today originated with the medieval Spanish Arabs.

Thereof, **How does incorporating history into mathematical instruction improve student learning?**

Response to this: These reasons are; **historical knowledge increases students’ motivation and helps them to develop a positive attitude towards mathematics**, seeing the obstacles experienced in the development of mathematics in the past allows them to see difficulties encountered in present, to solve problems from history helps the

In this manner, **Is the history of mathematics useful to teachers?**

Response to this: The ‘genetic principle’ and other ways in which the history of mathematics may be useful to teachers are examined; it is found that most of these are of limited value in the school situation. The claim is made that, in education, the main reason for studying the history of mathematics is to throw some light on the nature of the discipline.

One may also ask, **Can the history of mathematics reduce the divide between mathematicians and researchers?**

The answer is: The specialization that mathematics education research has undergone in the past decades has led to a sense of division and disconnection between mathematicians and mathematics education researchers. This chapter deals with the possibilities that the history of mathematics may afford to reduce the divide.

**Why do historians need a database?** The response is: History writing is leading the humanities to contribute to that new frontier of science called big data. So historians now have to get their heads around mathematics, too. While a database is never much more than an expression of arithmetic or linear algebra, the increasing amount of available data is calling for a more sophisticated approach.

Beside this, **What was mathematics education like in the early 20th century?**

Response: It is clear indeed that in the early 20 th century, research in mathematics education revolved around curricular problems and international cooperation, as the epoch-making articles published in L’Enseignement Mathématique in the first decades of the 20 th century make clear (see, e.g., Borel 1914; Bourlet 1910 ).