January 15, 2015 — Oleksandr Pavlyk, Manager of Probability and Statistics, Mathematica Algorithm R&D
January 16, 2015, marks the 360th birthday anniversary of Jacob Bernoulli (also James, or Jacques).
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).
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.
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.
October 1, 2014 — Richard Asher, Public Relations
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.
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?”
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.
The significance of the labels A, B, C, and D for these examples will soon become clear!
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)
May 22, 2014 — Bernat Espigulé-Pons, Consultant
Without doubt, the golden ratio is nowadays considered the most mysterious, magical, and fascinating number that exists:
. 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):
February 12, 2014 — Vitaliy Kaurov, Technical Communication & Strategy
An original gift can make people feel much warmer, especially in the icy weather affecting so many places this winter—including our headquarters. Valentine’s Day is a good excuse to get a little creative in the art of gift making. And for me, “getting creative” long ago became synonymous with programing in the Wolfram Language. It is that medium that compels me to treat programming as art, where one can improvise, easily pulling magical rabbits out of a hat.
So what shall we make? I think the best gift is a DIY one—especially if it says a lot without even making a sound. Below you see a 3D-printed silver earring in the shape of a sound wave recorded while a person is saying “I love you.”
February 10, 2014 — Crystal Fantry, Manager, Education Content
We are happy to announce the Mathematica Summer Camp 2014! This camp, for advanced high school students entering grades 11 or 12, will be held at Bentley University in Waltham, Massachusetts July 6–18. If you are ready for two weeks of coding fun, apply now on our website. Students who attend the camp have a unique opportunity to work one-on-one with Wolfram mentors in order to build their very own project in Mathematica.