September 30, 2016 — John McGee, Applications Developer, Wolfram Technology Group
A Mersenne prime is a prime number of the form Mp = 2p – 1, where the exponent p must also be prime. These primes take their name from the French mathematician and religious scholar Marin Mersenne, who produced a list of primes of this form in the first half of the seventeenth century. It has been known since antiquity that the first four of these, M2 = 3, M3 = 7,
M5 = 31 and M7 = 127, are prime.
August 26, 2016 — Zach Littrell, Technical Content Writer, Technical Communications and Strategy Group
We are constantly surprised by what fascinating applications and topics Wolfram Language experts are writing about, and we’re happy to again share with you some of these amazing authors’ works. With topics ranging from learning to use the Wolfram Language on a Raspberry Pi to a groundbreaking book with a novel approach to calculations, you are bound to find a publication perfect for your interests.
July 14, 2016 — Connor Flood, Consultant, Wolfram|Alpha Math Content
An idea, some initiative, and great resources allowed me to design and create the world’s first online syntax-free proof generator using induction, which recently went live on Wolfram|Alpha.
July 6, 2016 — Zach Littrell, Technical Content Writer, Technical Communications and Strategy Group
The population of Wolfram Language speakers around the globe has only grown since the language’s inception almost thirty years ago, and we always enjoy discovering users and authors who share their passion for Wolfram technologies in their own languages. So in this post, we are highlighting foreign-language books around the world that utilize Wolfram technologies, from a mathematical toolbox in Japanese to an introduction on bioinformatics from Germany.
May 19, 2016 — Michael Trott, Chief Scientist
Some thoughts for World Metrology Day 2016
Please allow me to introduce myself
I’m a man of precision and science
I’ve been around for a long, long time
Stole many a man’s pound and toise
And I was around when Louis XVI
Had his moment of doubt and pain
Made damn sure that metric rules
Through platinum standards made forever
Pleased to meet you
Hope you guess my name
Introduction and about me
In case you can’t guess: I am Jean-Charles de Borda, sailor, mathematician, scientist, and member of the Académie des Sciences, born on May 4, 1733, in Dax, France. Two weeks ago would have been my 283rd birthday. This is me:
Nearly two hundred years after Friedrich Bessel introduced his eponymous functions, expressions for their derivatives with respect to parameters, valid over the double complex plane, have been found.
In this blog we will show and briefly discuss some formerly unknown derivatives of special functions (primarily Bessel and related functions), and explore the history and current status of differentiation by parameters of hypergeometric and other functions. One of the main formulas found (more details below) is a closed form for the first derivative of one of the most popular special functions, the Bessel function J:
April 7, 2016 — Wolfram Blog Team
Authors that choose to incorporate Wolfram technologies into their books are practitioners in a variety of STEM fields. Their work is an invaluable resource of information about the application of Mathematica, the Wolfram Language, and other Wolfram technologies for hobbyists, STEM professionals, and students.
September 10, 2015 — Ed Pegg Jr, Editor, Wolfram Demonstrations Project
This statement is in a math textbook, but it is horrifyingly wrong. A statement like “the letters A–Z cannot be matched up with the numbers 1–26″ would be similarly wrong. These two sets of the same size (here, 26) can be matched up as A1, B2, C3, …, Z26. Can the rational numbers be matched up with the integers? Both are infinite, which allows for the tricks of a technique called Hilbert’s hotel, a hotel with infinite numbered rooms that can always make room for one more guest. The Glencoe claim asks if the cardinality of the integers and rationals is the same. Both are , or Aleph-0, which Georg Cantor proved in the 1870s.
July 2, 2015 — Jenna Giuffrida, Content Administrator, Technical Communications and Strategy Group
We’re always on the lookout for new ideas and ways of using the Wolfram Language that our users produce and choose to write about in their books. In this quarter, we have applications that bridge the gap between art and geometry, and demonstrate intuitive data analysis. In addition to writing books, Wolfram welcomes authors to submit articles for publication in The Mathematica Journal, our very own in-house periodical.
June 28, 2015 — Giorgia Fortuna, Consultant, Advanced Research Group
Three months ago the world (or at least the geek world) celebrated Pi Day of the Century (3/14/15…). Today (6/28) is another math day: 2π-day, or Tau Day (2π = 6.28319…).
Some say that Tau Day is really the day to celebrate, and that τ(=2π) should be the most prominent constant, not π. It all started in 2001 with the famous opening line of a watershed essay by Bob Palais, a mathematician at the University of Utah:
“I know it will be called blasphemy by some, but I believe that π is wrong.”
Which has given rise in some circles to the celebration of Tau Day—or, as many people say, the one day on which you are allowed to eat two pies.
But is it true that τ is the better constant? In today’s world, it’s quite easy to test, and the Wolfram Language makes this task much simpler. (Indeed, Michael Trott’s recent blog post on dates in pi—itself inspired by Stephen Wolfram’s Pi Day of the Century post—made much use of the Wolfram Language.) I started by looking at 320,000 preprints from arXiv.org to see in practice how many formulas involve 2π rather than π alone, or other multiples of π.
Here is a WordCloud of some formulas containing 2π: