Understanding e to the pi i - "An intuitive explanation as to why e to the pi i equals -1 without a hint of calculus. This is not your usual Taylor series nonsense." (via via; reddit; previously) [more inside]
I was surprised to learn that few people knew that almost all maths was written rhetorically before the 16th century, often in metered poetry. Even our wonderful symbol for equality – you know, those two parallel lines – was not used in print before 1575.
Recently Emily Graslie, of the fantastic natural history tumblr and youtube series TheBrainScoop, was asked a question about whether she had personally experienced sexism in her field. Her response is fucking amazing.
Inside is her goldmine of awesome female science educators online with channels that focus on Science Technology Engineering and Math. My work day is fucked.[more inside]
Avogadro Project - The International Avogadro project relates the kilogram to the mass of a fixed number of atoms by measuring the number of atoms in a sphere of silicon. I'll leave this here.
Using computer systems for doing mathematical proofs - "With the proliferation of computer-assisted proofs that are all but impossible to check by hand, Hales thinks computers must become the judge." [more inside]
The origins of plus and minus signs - "There be other 2 signes in often use of which the first is made thus + and betokeneth more: the other is thus made – and betokeneth lesse."
What is the smallest prime? "It seems that the number two should be the obvious answer, and today it is, but it was not always so. There were times when and mathematicians for whom the numbers one and three were acceptable answers. To find the first prime, we must also know what the first positive integer is. Surprisingly, with the definitions used at various times throughout history, one was often not the first positive integer (some started with two, and a few with three). In this article, we survey the history of the primality of one, from the ancient Greeks to modern times. We will discuss some of the reasons definitions changed, and provide several examples. We will also discuss the last significant mathematicians to list the number one as prime."
There were ways to find the tangent to a curve, and the area under one, in an ad hoc manner before the birth of calculus. It was even known that these two were inverses of each other.
Larry Gonick is a veteran American cartoonist best known for his delightful comic-book guides to science and history, many of which have previews online. Chief among them is his long-running Cartoon History of the Universe (later The Cartoon History of the Modern World), a sprawling multi-volume opus documenting everything from the Big Bang to the Bush administration. Published over the course of three decades, it takes a truly global view -- its time-traveling Professor thoroughly explores not only familiar topics like Rome and World War II but the oft-neglected stories of Asia and Africa, blending caricature and myth with careful scholarship (cited by fun illustrated bibliographies) and tackling even the most obscure events with intelligence and wit. This savvy satire carried over to Gonick's Zinn-by-way-of-Pogo chronicle The Cartoon History of the United States, along with a bevy of Cartoon Guides to other topics, including Genetics, Computer Science, Chemistry, Physics, Statistics, The Environment, and (yes!) Sex. Gonick has also maintained a few sideprojects, such as a webcomic look at Chinese invention, assorted math comics (previously), the Muse magazine mainstay Kokopelli & Co. (featuring the shenanigans of his "New Muses"), and more. See also these lengthy interview snippets, linked previously. Want more? Amazon links to the complete oeuvre inside! [more inside]
A Brief History of Mathematics is a BBC series of ten fifteen-minute podcasts by Professor Marcus du Sautoy about the history of mathematics from Newton and Leibniz to Nicolas Bourbaki, the pseudonym of a group of French 20th Century mathematicians. Among those covered by Professor du Sautoy are Euler, Fourier and Poincaré. The podcasts also include short interviews with people such as Brian Eno and Roger Penrose.
Learn how to operate the world's first fully electronic digital computer in this helpful instructional video. No, not ENIAC - the Atanasoff Berry Computer. Here's an operator's manual. More information about the reconstruction.
Trigonometric Delights. This book is neither a textbook of trigonometry—of which there are many—nor a comprehensive history of the subject, of which there is almost none. It is an attempt to present selected topics in trigonometry from a historic point of view and to show their relevance to other sciences. It grew out of my love affair with the subject, but also out of my frustration at the way it is being taught in our colleges.
The MacTutor History of Mathematics archive is an astounding collection of historical material on mathematics, especially biographies. (Previously: 1 2 3 4.)
The MacTutor History of Mathematics archive from the University of St. Andrews' School of Mathematics and Statistics.
Women Mathematicians. With numerous biographies and photographs, this website indexes the many contributions that women have made to the field of mathematics. From Pythagoras' wife Theano and martyr Hypatia, also notable are the first female computer programmer and the first female Ph.D. recipient.