September 7, 2017 — Greg Hurst, Wolfram|Alpha Math Content Manager

See what is new in step-by-step solutions

In our continued efforts to make it easier for students to learn and understand math and science concepts, the Wolfram|Alpha team has been hard at work this summer expanding our step-by-step solutions. Since the school year is just beginning, we’re excited to announce some new features.

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August 25, 2017 — Michael Trott, Chief Scientist

Last week, I read Michael Berry’s paper, “Laplacian Magic Windows.” Over the years, I have read many interesting papers by this longtime Mathematica user, but this one stood out for its maximizing of the product of simplicity and unexpectedness. Michael discusses what he calls the magic window. For 70+ years, we have known about holograms, and now we know about magic windows. So what exactly is a magic window? Here is a sketch of the optics of one:

Magic window optics sketch

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May 25, 2017 — Devendra Kapadia, Kernel Developer, Mathematica Algorithm R&D

Calculus mathematician timeline

Derivatives of functions play a fundamental role in calculus and its applications. In particular, they can be used to study the geometry of curves, solve optimization problems and formulate differential equations that provide mathematical models in areas such as physics, chemistry, biology and finance. The function D computes derivatives of various types in the Wolfram Language and is one of the most-used functions in the system. My aim in writing this post is to introduce you to the exciting new features for D in Version 11.1, starting with a brief history of derivatives.

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February 24, 2017
Jeffrey Bryant, Research Programmer, Wolfram|Alpha Scientific Content
Paco Jain, Research Programmer, Wolfram|Alpha Scientific Content
Michael Trott, Chief Scientist

The movie Hidden Figures was released in theaters recently and has been getting good reviews. It also deals with an important time in US history, touching on a number of topics, including civil rights and the Space Race. The movie details the hidden story of Katherine Johnson and her coworkers (Dorothy Vaughan and Mary Jackson) at NASA during the Mercury missions and the United States’ early explorations into manned space flight. The movie focuses heavily on the dramatic civil rights struggle of African American women in NASA at the time, and these struggles are set against the number-crunching ability of Johnson and her coworkers. Computers were in their early days at this time, so Johnson and her team’s ability to perform complicated navigational orbital mechanics problems without the use of a computer provided an important sanity check against the early computer results.

Row[{Show[    Entity["Movie", "HiddenFigures::k39bj"][     EntityProperty["Movie", "Image"]], ImageSize -> 101], "  ",    Show[Entity["PopularCurve", "KatherineJohnsonCurve"][     EntityProperty["PopularCurve", "Image"]], Axes -> False,     Background -> LightBlue, ImageSize -> 120]}]

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December 28, 2016 — Kathryn Cramer, Technical Communications and Strategy Group

When looking through the posts on Wolfram Community, the last thing I expected was to find exciting gardening ideas.

The general idea of Ed Pegg’s tribute post honoring Martin Gardner, “Extreme Orchards for Gardner,” is to find patterns for planting trees in configurations with constraints like “25 trees to get 18 lines, each having 5 trees.” Most of the configurations look like ridiculous ideas of how to plant actual trees. For example:

One of Pegg's orchard plans

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December 22, 2016
Eric Weisstein, Senior Researcher, Wolfram|Alpha Scientific Content
Ian Ford, Pure Math Developer, Wolfram|Alpha Scientific Content

Graph of relationships between spaces


Building on thirty years of research, development and use throughout the world, Mathematica and the Wolfram Language continue to be both designed for the long term and extremely successful in doing computational mathematics. The nearly 6,000 symbols built into the Wolfram Language as of 2016 allow a huge variety of computational objects to be represented and manipulated—from special functions to graphics to geometric regions. In addition, the Wolfram Knowledgebase and its associated entity framework allow hundreds of concrete “things” (e.g. people, cities, foods and planets) to be expressed, manipulated and computed with.

Despite a rapidly and ever-increasing number of domains known to the Wolfram Language, many knowledge domains still await computational representation. In his blog “Computational Knowledge and the Future of Pure Mathematics,” Stephen Wolfram presented a grand vision for the representation of abstract mathematics, known variously as the Computable Archive of Mathematics or Mathematics Heritage Project (MHP). The eventual goal of this project is no less than to render all of the approximately 100 million pages of peer-reviewed research mathematics published over the last several centuries into a computer-readable form.

In today’s blog, we give a glimpse into the future of that vision based on two projects involving the semantic representation of abstract mathematics. By way of further background and motivation for this work, we first briefly discuss an international workshop dedicated to the semantic representation of mathematical knowledge, which took place earlier this year. Next, we present our work on representing the abstract mathematical concepts of function spaces and topological spaces. Finally, we showcase some experimental work on representing the concepts and theorems of general topology in the Wolfram Language.

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December 5, 2016 — Alyson Gamble, Wolfram Blog Team

Whatever their future fields, students need to learn computational thinking, a method of problem solving in which questions are framed in a way that can be communicated to a computer.


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November 14, 2016 — Kathryn Cramer, Technical Communications and Strategy Group

Today is the 300th anniversary of the death of Gottfried Leibniz, a man whose work has had a deep influence on what we do here at Wolfram Research. He was born July 1, 1646, in Leipzig, and died November 14, 1716, in Hanover, which was, at the time, part of the Holy Roman Empire. I associate his name most strongly with my time learning calculus, which he invented in parallel with Isaac Newton. But Leibniz was a polymath, and his ideas and influence were much broader than that. He invented binary numbers, the integral sign and an early form of mechanical calculator.

Leibniz portrait and notebook

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November 4, 2016 — Zach Littrell, Technical Content Writer, Technical Communications and Strategy Group

Here are just a handful of things I heard while attending my first Wolfram Technology Conference:

  • “We had a nearly 4-billion-time speedup on this code example.”
  • “We’ve worked together for over 9 years, and now we’re finally meeting!”
  • “Coding in the Wolfram Language is like collaborating with 200 or 300 experts.”
  • “You can turn financial data into rap music. Instead, how about we turn rap music into financial data?”

As a first-timer from the Wolfram Blog Team attending the Technology Conference, I wanted to share with you some of the highlights for me—making new friends, watching Wolfram Language experts code and seeing what the Wolfram family has been up to around the world this past year.

Images from the 2016 Wolfram Tech Conference

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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.

Marin Mersenne

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