Reading+Riemann

What aspects of the learner profile can you identify in this reading? List examples of: thinker: [**Riemann, and generally any student in the universities working to excel in mathematics or science**], risk taker: [**When Riemann chose to stop studying theology and begin studying mathematics**], knowledgeable: [**Similar to thinker, generally anyone in the universities who study and hope to achieve great things in the fields of mathematics and sciences**], caring [**Gauss working to keep Riemann at Göttingen**], open-minded: [**people in the universities, willing to listen to the new theories created**], reflective: [**Any of the mathematicians after Riemann who thought about his lecture and how it would affect the field of geometry**], communicator: [**Riemann giving his inaugural lecture**], balanced [**?**] and inquirer: [**Gauss wanting to know how Riemann would handle presenting on a topic that he knew so little about**].

Why was Riemann an important figure in Mathematics? •	Riemann contributed significantly to the field of geometry (and mathematics in general).

What does the author state about the importance of Riemann's work with regards to changing our view of the world? •	“It opened new possibilities for modern science and mathematics, and fundamentally altered the way geometry and topology would develop.”

Describe the changing political structure of Europe at the time, and explain the increasing role of the university as an institution of significance with regards to the creation of knowledge. •	Riemann’s times were that of political turmoil. Many people that lived in rural areas moved into the cities and towns, and soon after there were uprisings that happened in these cities over such things as wages and poor living conditions. •	Universities began to grow in this period of turmoil. Mathematics and science kept advancing and this contributed to the growth of universities. As the universities were growing, as well, more and more knowledge was being created, specifically in the field of mathematics and science. How do universities work? •	Students would work to achieve a doctorate, which would allow them to assist in courses. The student would then do more work, not just tied to the thesis, and would submit a paper of their results (Habilitation paper) and would then present an inaugural lecture (Habilitation lecture). A small group of professors would judge the paper and the lecture given by the student. If the student passed the Habilitation, he could become an assistant professor (professor extraordinarus).

Write down any questions you have about the reading. •	Did not understand most of what Riemann said in regards to his lecture on geometry.

Write down any points of interest you would like to share. These can be related to math, creating knowledge, validity, or truth, history, social structures, culture, personal insights, thought processes of the author or those discussed. Anything you find interesting is worth sharing. •	It’s interesting how Riemann had to present on a topic he did not know much about, yet after presenting, he impacted the field of geometry and mathematics significantly. •	It’s also interesting to hear what he had to say (even though I did not understand some of it) as it makes you think about how much work he put into his inaugural lecture.

Read the section in Chapter 8 on the summary of Riemann's lecture on p. 99 and the Effect of Riemann's lecture following that. Any Questions, thoughts or ideas to share are expected. •	Why was Riemann's work so revolutionary? o	It laid new foundations in the field of mathematics. o	Contributed to much of modern science and mathematics. Proposed that spaces can be infinite in their dimensions. There is a significant difference between just a space and a space that has a geometry.