Wolfram Computation Meets Knowledge


Current Events & History

Classical Ciphers to Digital Signatures Wolfram U Launches New Cryptography Course

Cryptography has been around since time immemorial, and in the modern technological age is an omnipresent, often invisible middleman that helps protect your data. As a field of study, it combines mathematics, computer science, physics and even linguistics. As a tool, it concerns informatics, business, finance, politics, human rights—any sector that deals with personal information or requires communication. In fact, it’s hard to imagine a sector that cryptography does not impact.
Current Events & History

Celebrating a Third of a Century of Mathematica, and Looking Forward

Celebrating a Third of a Century of Mathematica, and Looking Forward

Mathematica 1.0 was launched on June 23, 1988. So (depending a little on how you do the computation) today is its one-third-century anniversary. And it’s wonderful to see how the tower of ideas and technology that we’ve worked so hard on for so long has grown in that third of a century—and how tall it’s become and how rapidly it still goes on growing.

In the past few years, I’ve come to have an ever-greater appreciation for just how unique what we’ve ended up building is, and just how fortunate our original choices of foundations and principles were. And even after a third of a century, what we have still seems like an artifact from the future—indeed ever more so with each passing year as it continues to grow and develop.

In the long view of intellectual history, this past one-third century will be seen as the time when the computational paradigm first took serious root, and when all its implications for “computational X” began to grow. And personally I feel very fortunate to have lived at the right time in history to have been able to be deeply involved with this and for what we have built to have made such a contribution to it.

Current Events & History

Change Your Perspective on the History of Mathematics with These Eight Learning Journeys

Amid COVID’s first wave, I had the privilege to join forces with Eric Weisstein and his team at Wolfram Research to create the History of Mathematics Project, a virtual interactive gallery highlighting physical artifacts that are important to the history of mathematics, for the National Museum of Mathematics (MoMath) in New York City. Most of my mandatory confinement at home was spent navigating through online collections from world-class museums, locating outstanding mathematical artifacts and creating interactive and computational explanations for them.
Current Events & History

John Snow & the Birth of Epidemiology Data Analysis & Visualization

In 1854, there was a major cholera outbreak in Soho, a neighborhood in London that Judith Summers described as full of “cow-sheds, animal droppings, slaughterhouses, grease-boiling dens and primitive, decaying sewers.” At the time, the cause of the outbreak was unknown because germ theory was still being developed and disease transmission was not well understood. Miasma theory was the dominant hypothesis, and it proposed that diseases, including cholera and the plague, were spread by foul gasses emitted from decomposing organic matter.
Current Events & History

The Singular Euler–Maclaurin Expansion A New Twist to a Centuries-Old Problem

Of all mathematical operations, addition is the most basic: It’s what we learn first in school. Historically, it is the most ancient. While the simple task of getting the sum of two numbers is simple, sums of many numbers can easily turn into a challenging numerical problem if the number of summands is very large.

Current Events & History

Is Your Function Continuous? Squaring Away the New Function Properties in the Wolfram Language

The Wolfram Language has several hundred built-in functions, ranging from sine to Heun. As a user, you can extend this collection in infinitely many ways by applying arithmetic operations and function composition. This could lead you to defining expressions of bewildering complexity, such as the following:

&#10005 f = SinhIntegral[ LogisticSigmoid[ ScorerHi[Tanh[AiryAi[HermiteH[-(1/2), x] - x + 1]]]]];
You may then ask, “Is continuous?” or “Can be written as a composition of an increasing function with another function?” The powerful new tools for studying function properties in Version 12.2 provide quick answers to such questions—opening the doors for applying a network of theorems and ideas that have been developed by mathematicians during the last few centuries.
Current Events & History

The Solution of the Zodiac Killer’s 340-Character Cipher

In 2020, Melbourne, Australia, had a 112-day lockdown of the entire city to help stop the spread of COVID-19. The wearing of masks was mandatory and we were limited to one hour a day of outside activity. Otherwise, we were stuck in our homes. This gave me lots of time to look into interesting problems I’d been putting off for years.

I was inspired by a YouTube video by David Oranchak, which looked at the Zodiac Killer’s 340-character cipher (Z340), which is pictured below. This cipher is considered one of the holy grails of cryptography, as at the time the cipher had resisted attacks for 50 years, so any attempts to find a solution were truly a moonshot.

Current Events & History

Spherical Aberration Optics Problem Finally Solved Using the Wolfram Language

Solving a 2,000-Year-Old Mystery

It’s not every day that a 2,000-year-old optics problem is solved. However, Rafael G. González-Acuña, a doctoral student at Tecnológico de Monterrey, set his sights on solving such a problem—spherical aberration in lenses. How can light rays focus on a single point, taking into account differing refraction? It was a problem that, according to Christiaan Huygens back in 1690, even Isaac Newton and Gottfried Leibniz couldn’t sort out, and was formulated two millennia ago in Greek mathematician Diocles’s work, On Burning Mirrors.

But González-Acuña and his colleagues realized that today, they had the use of the Wolfram Language and its computational tools to solve this age-old problem. The result? A breakthrough publication that outlines an analytical solution to why and how lensed images are sharper in the center than at the edges, with 99.999999999% accuracy simulating 500 light beams.

As it happens, González-Acuña was recently at the Wolfram Summer School, and we had the opportunity to ask him a little bit about his work.

Current Events & History

Creating an Animated Historical Map Function for the Wolfram Function Repository

Mapping an Ancient Empire

Geocomputation is an indispensable modern tool for analyzing and viewing large-scale data such as population demographics, natural features and political borders. And if you’ve read some of my other posts, you can probably tell that I like working with maps. Recently, a Wolfram Community member asked:

“How do I make an interactive map of the Byzantine Empire through the years?”

To figure out a solution, we'll tap into the Wolfram Knowledgebase for some historical entities, as well as some of the high-level geocomputation and visualizations of the Wolfram Language. Once we’ve created our brand-new function, we’ll submit it to the Wolfram Function Repository for anyone to use.