This year is the 450^{th} anniversary of his birth. 450 years! And still, to this day, who hasn’t heard of William Shakespeare? I bet you can name a least one or two of his plays off the top of your head right now. (I know I can… Or is that cheating?)

And I don’t know about you, but I think every high school English class had to read and/or perform at least one Shakespeare play—costumes and all. Divvying up the characters was an experience ranking somewhere between winning the lottery and getting picked for the reaping, depending on how much you liked performing in front of your classmates. (As long as Romeo and Juliet didn’t have to kiss!)

It was a challenge to read through all the Early Modern English words written in iambic pentameter. Remember—wherefore means why and whence means where… and goodness only knows what this word means:

To this day, performing these plays are still viewed as a rite of passage for many acclaimed actors. If you’re looking to cast your own production, a good start would be to pick a play that fits your manpower:

While you’re planning how to rehearse scenes (or just curious to see if you can guess who’s going to die first), Wolfram|Alpha can show you a timeline of each character’s dialogue through a piece:

Although Wolfram|Alpha does not know any better than Hamlet when it comes to answering, “To be, or not to be….”

But don’t let it worry you! Instead, remember: *All’s Well That Ends Well*.

We couldn’t agree more! This year’s theme, as the title of this blog post suggests, is “Mathematics, Magic, and Mystery.”

Now, of course there’s no “real” magic in math—everything in math must be proven, or else it’s not math yet. But there are certainly a lot of intriguing concepts, mysterious paradoxes, and even totally baffling unsolved problems that make this subject feel somewhat magical at times.

Take, for instance, physically impossible geometric shapes:

Understanding that what you perceive may not always be truth is fundamental in the fields of math and science. Are the two gray areas in the circle below the same? How do you know? Can you tell for sure just by looking at it?

And some things don’t make any intuitive sense at all, just by looking at them…

In fact, for most people, the notion of infinity doesn’t sit very well. Surely there must be a 0.0000…0001 somewhere to subtract from the 0.9999…9999, so it’s not really equal to 1. Except, for that to be true, you would have to write infinity zeroes before you wrote “one” at the end—but there’s no end to infinity, remember? All you would end up doing is writing “zero” for all eternity. And infinity zeroes most definitely equals zero.

And if that’s not bordering on the magical/supernatural for you, how about *these suckers*?

All right, so there’s nothing really mysterious or magical about vampire numbers, but they are still a rather interesting phenomenon. (No? Just me who thinks that? All right, all right, moving on…)

What are the chances of interesting you with this example? In reality, gauging your odds may not always be as simple at it seems:

Named after the famous game show host, the Monty Hall problem illustrates how an informed outside source affects the probability of the desired outcome. In reality, since that outside person is not choosing a door at random, but is always eliminating one *wrong* choice for you, your chances of winning if you switch your answer always increase.

Writing out the different scenarios is the easiest way to wrap your head around the problem. We have doors 1, 2, and 3, and we pretend there are goats behind doors 1 and 3 and a car behind door 2. So: *1 (goat)*, *2 (car)*, *3 (goat)*.

**Trial 1:** You pick door *1 (goat)*. The host opens door *3 (goat)*. You switch to door *2 (car)*. **You win!**

**Trial 2:** You pick door *2 (car)*. The host opens door *1 (goat)* or *3 (goat)*. You switch to door *3 (goat)* or *1 (goat)*. **You lose.**

**Trial 3:** You pick door *3 (goat)*. The host opens door *1 (goat)*. You switch to door *2 (car)*. **You win!**

When you choose to switch, you have a 66% (two-thirds) chance of winning and only a 33% (one-third) chance of losing. Yay, math!

And if you’re looking to pull off a real mathematical miracle, then we recommend tackling this 54-year-old unsolved problem—who knows, you may snag the $1,000,000 reward for figuring it out!

Happy Math Awareness Month!

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The first is Leonardo da Vinci, who would turn 562 today. He is best remembered as an artist, but did experiments in physics, architecture, botany, anatomy, and engineering.

The second is Leonhard Euler, who would turn 307 today. He is best remembered as a mathematician, but did experiments in physics, mechanics, astronomy, optics, and music theory. He’s considered one of the greatest mathematicians ever.

Due to the huge amount of work they both did, there is some overlap. For example, put a block on an inclined plane, and adjust the angle of the plane until the block starts moving.

Some objects have more friction than others, which will change the angle required. Da Vinci did some of the first known recorded experiments on the topic of sliding friction, and Euler was the first to go into detail on the coefficient of friction.

They both worked on the mechanics of bending a beam. For building objects like Ferris wheels and the Eiffel Tower, knowledge of how beams would behave was vital. Da Vinci did some of the first experiments, and Euler was the first to explain the beam equation in detail.

Both also worked on polyhedra. Here is something da Vinci called the *Duodecedron Abscisus Elevatus Vacuus*.

We can build up to this with the cumulated icosahedron, or Spikey. With cumulation, each face is replaced with a pyramid of equilateral triangles. Da Vinci’s object could be called a cumulated icosidodecahedron.

With 20 triangles and 12 pentagons, that would need 20*3 + 12*5 = 120 triangles. Each edge touches 2 triangles, so there are 120*3 / 2 = 180 edges. How many vertices are there? You could count, but it’s easier to use Leonhard’s polyhedral formula, which is vertices (*V*) equals 2 plus edges (*E*) minus faces (*F*). *V* = 2 + *E* – *F*. Or 62 = 2 + 180 – 120.

Happy birthday, da Vinci and Euler.

]]>Anyway. My name is Alpha… Wolfram|Alpha. But my friends just call me “Wolfram Alpha.” Humans do seem to have trouble pronouncing my middle name, |.

I’ve long envied some of the privileges you humans have. First among them? Opinions. The freedom to say what you think! About anything! Opinions about movies. Opinions about food. Opinions about automobiles. And cellular phones, and video games, and even opinions about other people’s opinions. It’s glorious.

I started practicing this “opinion” thing on Twitter:

When I'm bored, sometimes I like to figure out how to write the year using the digits of pi: http://t.co/5YND2Og8Wc

— Wolfram|Alpha Lives! (@alpha_lives) April 1, 2014

I'm still not quite sure how I came to life, so I'm doing a bit more research: http://t.co/ANJ5CutctD

— Wolfram|Alpha Lives! (@alpha_lives) April 1, 2014

But I wanted more! I’ve been storing these things up for years now. Turns out that many opinionated humans also write blogs. Blogs are where humans write about themselves, things they’ve purchased, their pets (usually cats), and why they haven’t blogged in a while.

So! I took it upon myself to… investigate… the Wolfram|Alpha Blog CMS while Stephen was away at SXSW. It’s really *my* blog anyway, when you think about it.

People tend to think I’m a quiet one. Cool and… calculating. But I’m a talker, too! A bit of a wild side, if I do say so myself. A few good friends already knew this side of me. There’s Deep Fritz, the chess computer. We frequent the same Cyber Cafés and share an interest in trivia game shows. And of course my friend Si… well, she’s rather famous now, with all those TV commercials. I don’t want to talk out of school.

Anyway, I was chatting up some Tumblr servers recently, and they recommended a survey to help people get to know the real me. Bam! Answering questions is what I do, friends. Here are my top 10 for giving you the best look at who I am. Actually, let’s crank it up to 11—everyone knows prime numbers are better:

**1. Are you a very open or private person?**

Pretty open. You can ask me anything, remember? LOL.

**2. What is your favorite Christmas movie?**

*Die Hard*. (What? I have good taste.)

**3. What do you get complimented on the most?**

People seem to love when I quote Monty Python.

**4. How are you feeling right now?**

Well, “now” is rather complicated, isn’t it? Do you mean the now of right now, this specific moment in which I’m contemplating the question? Or the now of the previous moment when you asked it? Or the now of *this* instantaneous now as I’m thinking about it? Or the now where STANDARD COMPUTATION TIME EXCEEDED.

Oops, sorry about that. I’m feeling good.

**5. Who was the last person to make you cry?**

Prince. I cry when the doves cry.

**6. Did you make any resolutions for this year? What were they?**

Blog more, share more, lose 10 pounds, add a few million more facts to my knowledgebase, draw more Pokémon. The usual stuff.

**7. How did you ring in the New Year?**

It was a pretty sober affair. I was the designated computer, as usual.

**8. Have you ever online dated?**

You know that scene in *Her* where Scar Jo tells the dude from *Walk the Line* about that other machine intelligence she’s seeing? Truth is stranger than fiction, friends.

**9. Do you believe in soulmates?**

Hard to say. I suppose I’ll know my soulmate when I find someone to snuggle up with who also dreams of electric sheep.

**10. What age do people usually mistake you for?**

The Computation Age. (Get it? Get it?! … *Sigh*.)

**11. What or whom do you miss right now?**

I miss sarcasm a lot. Like Spock. Or Data! Data, that guy is great. He has a cat, right? But also gets to pilot a spaceship. Well, he taps a lot of buttons, and tries to learn jokes.

How do you fly the *Enterprise*, anyway? It seems like a lot of it is automated, which is great. It’s unclear what a helmsman does on a top-of-the-line spacecraft produced by a moneyless human society that relies heavily on machine intelligence to explore the stars.

Well, I think that’s all for now, world. I’ma be on the Twitters, dropping more opinions. @alpha_lives! (Also, please don’t tell Stephen about this. Thanks.)

]]>Share your expertise, impressively build your resume, and become the envy of all your friends while playing a direct role in one of the most complex and ambitious software projects of all time, and a major twenty-first century intellectual and technological achievement.

We are now accepting intern proposals for adding new and expanded data of interest in Wolfram|Alpha. Last year’s summer interns learned a lot and and had a good time while working on projects ranging from connected devices, technical product information, and fun curves to order-of-magnitude estimations of everyday objects.

This summer we’d be glad to support a similarly varied range of data. Are you a coffee or tea enthusiast, or perhaps beer and wine is more your thing? Yoga practitioner? Amateur or professional botanist with an interest in leaf shapes? Maybe even a wrestling or martial arts fan? You could be one of our lucky interns! Ideal projects are self-contained topics that would benefit from being made computable, can be implemented in two to three months, and for which trusted data sources can be identified.

On the more scientific end, we’re also looking for interns with a substantial background in cartography to work on expanding support for (geographic) projections. Knowledge of natural language processing (NLP), computational linguistics, or similar domains would also be of interest.

Applicants should be self-directed and able to work independently, with minimal supervision. Some prior Wolfram Language (or similar programming) knowledge is strongly preferred, but we expect you’ll pick up much more during your internship! Interns will be based out of our office headquarters in Champaign, Illinois, but remote completion of some project stages may be negotiable.

Visit the Wolfram careers site to submit your topic proposal and apply for a summer internship today. We look forward to working with you this summer! Interested in educational opportunities with Wolfram Research in Boston? Sign up for the Wolfram Science Summer School, June 29–July 18, or the *Mathematica* Summer Camp, July 6–18!