Counting Sheep or Sums of Primes

 

(Image: Creative Commons — Attribution-ShareAlike 3.0 Unported — CC BY-SA 3.0 Washaweb on Iconfinder)

The other night, I had trouble getting to sleep. Instead of counting sheep, I challenged myself to adding the first n primes. The first 10 primes are 2, 3, 5, 7, 11, 13, 17, 19, 23, 29. Therefore, for the n=1 through 10, the sums of the first n primes are: 2, 5, 10, 17, 28, 41, 58, 77, 100, 129. 

I was interested in any pattern exhibited by the sequence. After n=10, I became less confident in my ability to add late at night and then a comforting thought hit me. I realized one could easily research if others had explored this sequence by going to the website of The On-Line Encyclopedia of Integer Sequences® (OEIS®). This site was written about in a prior post: Math Vacation: What is the next number in the sequence...? (jamesmacmath.blogspot.com).

With the thought that my inquiry into the sequence could easily be answered, I fell asleep. Mission Accomplished.

The next morning, I simply entered 2, 5, 20, 17 into the site’s search bar and the following answer came up: A007504 - OEIS, The sum of the first n primes. With this sequence are links also related to sequences and references to those who have researched the sequence.

I invite readers to explore this rich resource at OEIS.

 

Book Review: A divine language : learning algebra, geometry, and calculus at the edge of old age.

Alec Wilkinson, staff writer for The New Yorker magazine, recently wrote about his quest to study math later in life. Here is a link to his September 6, 2022, article: How Mathematics Changed Me | The New Yorker. He started his quest five years ago at age 65. He also writes about this in his book, A divine language : learning algebra, geometry, and calculus at the edge of old age. I have the book on order and look forward to reviewing it.

From his article, I understand much of what Wilkinson learned during his quest as I started this math blog late in my life. This blog started as a Covid project two years ago when I was 61. We both learned strangeness of different types of infinities, mystery of design of our world, and how God in unknowable.

11/8/2022 Update - my local library got this book, and I just finished it. Wilkinson included stories about many of my favorite mathematicians. I liked that he was able to interview Chris Ferguson, who won $1,000,000 in the World Series of Poker in 2000, shortly after earning his PhD from UCLA. 

Book Review: We Have No Idea, A Guide to the Unknown Universe by Jorge Cham and Daniel Whiteson

 

(Jacket design by Jorge Cham, Penguin Random House Riverhead Books)

If you are looking for an entertaining book on cosmology, We Have No Idea fits the bill. Authors Cham and Whiteson begin the book with a few chapters on what makes up the universe where we learn that it consists mostly of dark matter and dark energy. Fitting for the title of the book, scientists still know little about 95% of the universe.

To make the material easier to read, the book is generously illustrated by Cham with cartoon-style drawings.

Footnotes include science humor topics. For example, footnote 68 refers readers to the website: Has the Large Hadron Collider destroyed the world yet?

While providing a humorous example, I found their explanation of the difference of philosophical and scientific theories to be very easy to understand. Essentially, theories need to be testable to be deemed scientific.

 Another topic explored is string theory. Those who like the post, The Very Samll and the Very Big will like the chapter "How Many Dimensions are There?" 

Book’s website: We Have No Idea by Jorge Cham, Daniel Whiteson: 9780735211520 | PenguinRandomHouse.com: Books