Gem #7: Dewey’s "Democracy and education"

Yesterday, I mentioned John Dewey in my post about the latest issue of Journal of Curriculum Studies. This gave me an idea, and as a result I figured out that it would have been nice to add a work by Dewey in my gem-series. I know, it is not a famous book of mathematics or mathematics education, but Dewey’s theories have had great influence in educational research in general, and also in research in mathematics education. Therefore, I am happy to present today’s gem: “Democracy and Education”, by John Dewey. As usual, you can read it below, or download the pdf. Happy reading!

John Dewey – Democracy and Education: An Introduction to the Philosophy of Education

Gem #6: Napier’s logarithms

John Napier (1550-1617) John Napier (1550-1617) was a Scottish mathematician. He is most famous for having invented logarithms, and today’s featured book is precisely about that. Napier’s book is entitled “The construction of the wonderful canon of logarithms”, and it is an English translation of the original Latin book. The book is available as Flip Book, or you could download the PDF. You could also start reading it below, without leaving this blog 🙂

Napier’s wonderful world of logarithms

Gem #5: Russel’s Principles of Mathematics


The gem that I have decided to share with you today, is Bertrand Russel‘s book from 1903: “The Principles of Mathematics”.

You can download the pdf, or you can read it below. You can also check out this site, for another online version of the book. Enjoy!

The Principles of Mathematics (1903) – Bertrand Russell

Gem #4: Hardy’s Apology

This gem from the history of mathematics is more recent. It was published in 1940 by British mathematician G.H. Hardy. The book/essay was written when Hardy (then 62) felt that he no longer had the ability to contribute to the field of mathematics. A main theme in the book is concerning mathematical beauty, and he believed that the most beautiful mathematics was that, which had no application! Luckily, this book is also in the public domain, and you can read it in below (or download the pdf):

A Mathematician’s Apology

Gem #3: Newton’s Principia

Isaac Newton is arguably one of the greatest scientists (and mathematicians) of all times, and his Principia is one of the great works from the history of mathematics. Together with Leibniz, Newton is normally acknowledged as the founder of differential and integral calculus. If you want to download Principia to your computer, you can head over to the Internet Archive. The original was in Latin, but you can read an English translation below:

Newton’s Principia

Gem #2: Hilbert’s "The Foundations of Geometry"

David Hilbert (1862-1943) was one of the most important mathematicians of last century. He worked most of his life in Göttingen, which had a very important mathematics center at the time. Here, Hilbert was surrounded by excellent mathematicians like Felix Klein, John von Neumann, Ernst Zermelo, Emmy Noether and more.

One of Hilbert’s achievements was to initiate a shift towards a more modern axiomatic method in mathematics, and in particular in geometry. In relation to this, he proposed a research project, called “Hilbert’s program”, which aimed at formulating a solid and complete logical foundation for mathematics. Hilbert’s “The Foundations of Geometry” is therefore one of the most important modern works in mathematics, although his program did not succeed. The book is therefore a natural follow-up for Gem #1: Euclid’s “The Elements” (which is regarded as one of the most important mathematics texts ever, and in particular related to geometry). If you want to download the book in pdf format, you can go to the Gutenberg Project. Otherwise, you can read it here:

David Hilbert – The Foundations of Geometry

Gem #1: Euclid’s Elements

When I was a student, I was lucky enough to study in a school which had a very good library of books related to mathematics and mathematics education. Nowadays, you can study many of the great classical texts online. In 2009, I am going to share with you several gems that I have found online. In my quest for these texts on mathematics/mathematics education, a natural first stop is with one of the greatest mathematical texts of all times: The Elements, by Euclid.

Here is the text:
Euclid Elements

You can also download (or read online) this great book in Google Books. See these two links for two versions of the text.

Happy new year, and happy reading!