February 20, 2015 — Hector Zenil, Special Projects Group

When I was invited to join the Turing Centenary Advisory Committee in 2008 by Professor Barry Cooper to prepare for the Alan Turing Year in 2012, I would have never imagined that just a few years later, Turing’s life and work would have gained sufficient public attention to become the subject of a Hollywood-style feature film, nor that said movie would go on to earn eight Oscar nominations.

Imitation game nominations using Wolfram|Alpha

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February 9, 2015 — Jenna Giuffrida, Content Administrator, Technical Communications and Strategy Group

We are once again thrilled by the wide variety of topics covered by authors around the world using Wolfram technologies to write their books and explore their disciplines. These latest additions range from covering the basics for students to working within specialties like continuum mechanics.

Books

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January 15, 2015 — Oleksandr Pavlyk, Kernel Technology

January 16, 2015, marks the 360th birthday anniversary of Jacob Bernoulli (also James, or Jacques).

Input 1 through Output 4

Jacob Bernoulli was the first mathematician in the Bernoulli family, which produced many notable mathematicians of the seventeenth and eighteenth centuries.

Jacob Bernoulli’s mathematical legacy is rich. He introduced Bernoulli numbers, solved the Bernoulli differential equation, studied the Bernoulli trials process, proved the Bernoulli inequality, discovered the number e, and demonstrated the weak law of large numbers (Bernoulli’s theorem).

Jacob Bernoulli's mathematical achievements

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October 21, 2014 — Ed Pegg Jr, Editor, Wolfram Demonstrations Project

For today’s magic show:
A century ago,
Martin Gardner was born in Oklahoma.
He philosophized for his diploma.
He wrote on Hex and Tic-Tac-Toe.
The Icosian game and polyomino.
Flexagons from paper trim,
Samuel Loyd, the game of Nim.
Digital roots and Soma stairs,
mazes, logic, magic squares.
Squaring squares, the golden Phi.
Solved the spider and the fly.
Martin GardnerPenrose Tilings and Wieringa Roofs
Tiling with PentominosHamiltonian Tours on Polyhedra

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October 6, 2014 — Jenna Giuffrida, Content Administrator, Technical Communications and Strategy Group

Authors turn to Wolfram technologies to elucidate complex concepts, from physics to finance. Here is a roundup of the latest publications that feature the Wolfram Language and Mathematica.

New books group #1

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October 1, 2014 — Richard Asher

The Nobel Prize in Physics ceremony is upon us once again! With the 2014 winner set to be revealed in Stockholm next week, we at Wolfram got to wondering how many of the past recipients have been Mathematica users.

We found no less than 10 Nobel Prize–winning physicists who personally registered copies of Mathematica. That’s at least one in every eight Physics laureates since 1980! And anecdotal evidence suggests that nearly every Nobel laureate uses Mathematica through their institution’s site license.

Frank Wilczek Wolfgang Ketterle John Forbes Nash, Jr.

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August 12, 2014 — Stephen Wolfram

Every four years for more than a century there’s been an International Congress of Mathematicians (ICM) held somewhere in the world. In 1900 it was where David Hilbert announced his famous collection of math problems—and it’s remained the top single periodic gathering for the world’s research mathematicians.

This year the ICM is in Seoul, and I’m going to it today. I went to the ICM once before—in Kyoto in 1990. Mathematica was only two years old then, and mathematicians were just getting used to it. Plenty already used it extensively—but at the ICM there were also quite a few who said, “I do pure mathematics. How can Mathematica possibly help me?”

Mathematics

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August 6, 2014 — Devendra Kapadia, Mathematica Algorithm R&D

What is the sum of all the natural numbers? Intuition suggests that the answer is infinity, and, in calculus, the natural numbers provide a simple example of a divergent series. Yet mathematicians and physicists have found it useful to assign fractional, negative, or even zero values to the sums of such series. My aim in writing this post is to clear up some of the mystery that surrounds these seemingly bizarre results for divergent series. More specifically, I will use Sum and other functions in Mathematica to explain the sense in which the following statements are true.

Using Sum

The significance of the labels A, B, C, and D for these examples will soon become clear!

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July 30, 2014 — Wolfram Blog Team

Kenzo Nakamura uses Mathematica to create Escher-inspired mathematical art. His trademark piece, Three-Circle Mandala, depicts a large circle covered by three smaller, repeating circles that form a Sierpinksi gasket.

When Nakamura began using Mathematica, he didn’t originally intend to use it for his artistic endeavors. He found the program by chance at a seminar while looking for the right tool to help him write his master’s thesis.

Now, in addition to using Mathematica for technical and operations research, Nakamura uses it to create Mathematica-derived visual illusions. Although his works are static drawings, their infinite properties create the illusion of movement.

Watch Nakamura discuss using Mathematica to create his drawings, and see a few of his creations.


(YouTube in Japanese)

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May 22, 2014 — Bernat Espigulé-Pons

Without doubt, the golden ratio is nowadays considered the most mysterious, magical, and fascinating number that exists:
GoldenRatio. As we will see in this post, this number still has many interesting properties that can be investigated, some even dating back to the works of the ancient Greeks Pythagoras and Euclid, the Italian mathematician Leonardo of Pisa, and the Renaissance astronomer Johannes Kepler. Though it might sound strange, I will unveil new geometric objects associated with the golden ratio, which are the objects that illuminated my way when I attempted to map an unknown region of the Mathematical Forest.

The following findings aren’t a mere accident; I’ve been working hard to grasp a glimpse of new knowledge since high school. After seeing Hans Walser‘s drawings of golden fractal trees in 2007, I was convinced that there was still space for exploration and new discoveries. Though I had to wait quite a while, I finally found the right tools: Mathematica, combined with Theo Gray‘s “Tree Bender” Demonstration. After gathering some intuition and a rudimentary knowledge of the Wolfram Language, I encountered my first insights. For example, here is one of the first self-contacting golden trees that I discovered when I created my own version of “Tree Bender” in order to explore ternary trees (trees with three branches per node):

Ternary trees

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