"Hey, everybody, Jillian Mason here. As promised, I'm back with more Jillians of Science Ideas. This is my seventh JSI podcast from orbit. In earlier episodes, we covered Goldaskian artificial gravity, the warp drive, Parallel Evolution, space warfare, Goldaskian DNA, and the basics of the Galactic language. Make sure to check those out, and remember to click Like because the computer can't see you smiling—or can it?" Jillian put what she thought was the right amount of humorously ominous tone into her delivery.

"This episode is on mathematics. Now, it's long been assumed that math is the same everywhere you go, and that when we met aliens, we'd probably use math to start out learning each other's language. But learning to count to ten or twelve is only the beginning. What else is out there? How do aliens do geometry? Algebra? Calculus? Well, let me explain how this gets hard.

"When I was a college sophomore, I asked one of my math professors whether there was a complete map of mathematics anywhere. All the mathematics human beings know, organized. I was hugely disappointed to find out that such a thing didn't exist—not even just for human math. Everybody can learn definitions and understand proofs, so it's not as if there are disagreements about the facts, but organizing it?

"To give you an idea of the kinds of problems that come up, think about this: How would you put algebraic formulas...in order? Words—we can put those in alphabetical order. You might think we could do the same with algebra, but...what about these?" At this point, she put up the first visual, with several wildly different formulas, including fractions, square roots and more. "I could put them in some order, but would it be a good one? And would you see it the same way? Could you find things if you looked them up in my system?

"And this is just the simple stuff! Human beings have made so much math that it's impossible for anyone to know it all. Now we've got alien mathematics from half a dozen worlds piled on top. What are we going to do with it all?" She leaned forward sympathetically, as if confiding a bad secret.

"It gets worse. You know how English majors think English is the best major, and physics majors think physics is the best, and so on? Math is so big, you've got rivalries like that just within math itself! Topologists think they're the coolest, and statisticians think they are, and so forth.

"This wouldn't be a problem, except that—as the aliens show—you can describe the same math in a lot of different ways. So the topologist can look at abstract algebra and say, 'Abstract algebra is just a part of topology!' And they can organize the way they do all math by thinking of it that way. Meanwhile the logicians are like, 'No, everything is a part of logic!', and they can actually make a case for viewing it that way, too!

"So we have this one, huge, complicated, wibbly-wobbly ball of interconnected theorems, lemmas, proofs, and definitions called 'Math', and then we have everybody looking at it from their own favorite angle and describing the giant spaghetti snarl of facts they way they see it. It's the old parable of the Three Blind Men and the Elephant. That's a classic, look it up when you're done watching this."

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"Now, the math we all learned as kids was put in that order for a reason, and we've mostly figured out how to teach the basics consistently. But once things get more advanced—hoo boy! Watch out!

"Well, Volume 1 of Basic Mathematics from the Arrurrans has just dropped, so anyone can download a copy and take a look. Human mathematicians are going to be all over that book like black on a goth. I was tempted to skip a podcast or two to study it myself, but things are still pretty exciting up here, and I want to keep everyone informed.

"So...I did sneak a peek at the first few pages, and Arrurrans apparently use base twelve arithmetic. In case you don't already know it, here's what that means..."

Jillian gave a brief explanation, and pointed her viewers at a few links to online videos that explained the ideas more thoroughly, with her usual difficulty ratings of Mild to Extra Spicy so that people knew which one they wanted to try watching first.

"...so it turns out that old myth of 'count the digits to identify people who are alien' has a tiny grain of truth to it, at least if you like nerdy jokes."

Jillian wrapped up with her usual plea to subscribe et cetera, and ended the recording. She then spent a good hour editing the five minute video to her satisfaction, then uploaded it, where it immediately started getting likes and views. In her early days, she had kind of gotten addicted to seeing those numbers climb, but by now she was jaded about it. She had more important things to think about—like the next broadcast.

She really wanted to do one about computer technology, including the translation tech being used to translate between the races. She was sure some paranoid people were rapidly learning the languages so that they could compare the direct statements with their translations. Alyssa had made some noises along those lines. That girl had a good eye for analysis, and Jillian was looking forward to picking the brains of the investigative reporter when they both had time.

Dr. Vickall interrupted her musings by showing up to give her a treatment, which was apparently a kind of body tune-up, to judge by the statements of the others who had already gone through the process. Certainly the billionaire looked years younger, though he was a lot moodier than before. He seemed to be watching TV shows instead of financial reports the way he had been earlier.

Jillian asked lots of questions, and Dr. Vickall had no objection to her recording the whole thing. After a while, she stopped and apologized. The red-skinned alien waved a hand dismissively.

"No, you ask good questions. Better ones that some others do," she added heavily. Jillian nodded. She had noticed the human doctors pestering her quite a bit. You'd think that they would put some care into not irritating their information source, she thought, but that would be sensible and logical, and unfortunately the best of us humans treat logic as a hobby to occasionally dabble in.

Then the good Doctor dropped the bombshell. "I have now learned enough about human physiology to adapt a process used on Goldaskians to increase intelligence. Would you have interest in such a treatment?"

Jillian's jaw dropped, while a calculating part of her mind said, Well, I know what another one of my podcasts is going to be about!

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