# Summer SAVY, Session 4 Day 5, Mathematicians in History (3rd -4th)

Dear SAVY Families,

I can’t believe that we have completed our time together in Mathematicians in History. This group of SAVY students impressed me in countless ways, and I am so grateful that I got to spend part of my summer learning with and from them.

To start our Friday, we spent the morning learning about our last two mathematicians: Carl Gauss and Sophie Germain. Gauss is known for being the founder of modern number theory, and he worked specifically with prime numbers. The SAVY mathematicians were quick to note that Gauss came from a poor family, which broke our previously noted pattern that the famous mathematicians came mostly from wealthy families. To model Gauss’ work, the SAVY mathematicians had to come up with strategies to solve two problems. The first was: How can you find the sum of the first 100 counting numbers? The second was: How can you find the sum of the first 50 odd numbers? The mathematicians used the habits of a scholar to persevere through this task. Gauss was a very well-liked mathematician by our SAVY mathematicians, as he, along with Newtown and Archimedes, is considered one of the three greatest mathematicians of all time.

Next, we studied Sophie Germain. The SAVY mathematicians were excited to study another woman and one of the few women whose work is recorded in early mathematics history. Germain worked with palindromes, a number that reads the same both forward and backward. We learned that most numbers can be turned into palindromes using the “reverse and add” method, however, some numbers require this to be done more than one time. The SAVY mathematicians were given eight numbers to determine how many steps it would take to turn the number into a palindrome. Finally, Germain also worked with number theory. The SAVY mathematicians were given a set of numbers and had to factor the number into primes. Many mathematicians were excited to use their known strategy of number trees to solve these problems.

This afternoon, we spent time creating a final poster presentation. The SAVY mathematicians were tasked with creating a poster about their favorite mathematician that we studied this week. On this poster, the mathematicians were required to include biographical information about their chosen mathematician, details of the mathematician’s contributions, the historical context for their mathematician, and connections to our generalizations of relationships. While all the mathematicians were given the same set of expectations, I was impressed with the creative angles they took this project from. After completing the posters, the mathematicians each had 3 minutes to present their poster. While some mathematicians were intimidated by this at first, I was proud of their bravery to stand up and share their ideas with the class. Some mathematicians did not complete their posters, so they may ask to complete these at home. We ended our day with a final closing circle, synthesizing all of our ideas from the week and revisiting our big question: is mathematics discovered or invented? Has your opinion changed on that question throughout the week? How many people do you have to ask to find two people with the same birthday? Pascal’s probability says only 23!

Questions to ask:

- Who was Carl Gauss? What were his contributions to mathematics?

- Who was Sophie Germain? What were her contributions to mathematics?

- How did Carl Gauss and Sophie Germain follow the noted patterns in the lives of the mathematicians we studied? How did they break those patterns?

- Who was your favorite mathematician that you studied this week? Why?

- Is mathematics discovered or invented? Did your opinion on that question change throughout the week?

- Archimedes, Newton, and Gauss are often called the three greatest mathematicians of all time. Do you agree or disagree? Why?

The SAVY mathematicians truly exceeded every expectation this week. I am so proud of their hard work and for dedicating a week of their summer to learning more about math. I know each of them will excel in their upcoming school year, and I hope to see all these mathematicians in a future SAVY class.

Sincerely,

Ms. Gruchot