If the Doctor looked like a cat, his ears would be perked and his pupils wide, ready to pounce on whatever interesting things ran in front of his paw. But sadly he wasn't, so he settled for grinning widely and putting on his best 'I'm curious about you' eyes.
"…" said the alien on the left, and the alien on the right answered: "…"
Their mouths opened, but Martha didn't understand them. Or rather: she couldn't hear them, even though their mouths opened and closed as if they talked.
"So you're… what race exactly?"
"…" answered the alien, looking at the Doctor and waving his hand about as if it meant something. It towered over them by a good four feet, its lanky body weaving softly in the breeze. Its green-yellow antlers fluttered about in the wind. Grey lips joined the green-yellow skin and a red pattern slid of dots across its scales like a shower cubicle with the remaining drops clinging to the glass.
The alien possessed three eyes, two on the front and one on the back of the head. They all blinked out of sync.
It gestured at them in some kind of sign language Martha didn't understand, but the Doctor apparently did. He reached inside his suit jacket and brought out a piece of paper and a pen. He scribbled things down furiously, with the alien looking on, still flapping its mouth as if talking.
"Doctor?" asked Martha when the other alien looked on in interest at Martha. It licked its lips, which sent shivers down her spine. "Doctor, you think they're friendly?"
"Yeah, pretty sure. They haven't attacked us yet, have they?"
"Good point," conceded Martha. She made herself appear larger and more intimidating to the huge alien by squaring her shoulders and tilting her chin up, staring the alien in its eyes. It stopped licking its lips.
"What are you writing, anyway?" she asked as she kept on looking the alien in its eyes. It seemed to be the only way to stop it from licking its lips, because the moment she looked away it continued licking, like a cat which ate a can of tuna fish.
"Oh, just, y'know, numbers."
"Numbers?"
"Something like that, yeah."
Martha broke her staring contest with the alien and looked over to Doctor as he flipped the page and showed it to the alien. The whole page was filled with… numbers. At the top of the page the Doctor had written numbers from zero to nine, and underneath that he had begun with simple addition and subtraction. The numbers then moved on to multiplication and divisions.
"Why numbers?" asked Martha.
The Doctor held out pen and paper to the aliens and the one on the left gently took it, gripping the pen in its three-fingered hand. It looked at Martha for a second and then also began writing.
"Because if you don't understand them, you don't start with 'Hi I'm the Doctor'. Any space traveler can tell you that. You start with math."
More numbers flowed from the pen in the alien's hand and filled the pages, becoming ever more complex. The alien's handwriting was surprisingly readable, considering it possessed pincer-like fingers. Martha squinted her eyes at the many numbers and formulas which now enriched the paper, but slowly it crossed from high school math problems to a Good Will Hunting-level of math.
But the Doctor only grinned when the alien presented the paper back to him. He reached into his pocket again and retrieved a fresh piece of paper. With one glance at the alien's formulas he began to solve the various problems as fast as he could write. His handwriting looked a lot less neat, but when the alien nodded along with the answers, Martha felt a tension leave her shoulders. It looked like they would be able to communicate on some level.
"And… forgot to carry the one there, fixed, solved Riemann's hypothesis, and done."
The Doctor presented the piece of paper to the alien and it licked its lips as well as it read the various solutions. Its companion trod over and also read the formulas.
"There, now that we've established we're two sentient species, let's get down to business, shall we?" asked the Doctor, but of course he got no answer from the aliens. At least, no discernable answer. "Why can't I understand you?"
The Doctor pulled what Martha secretly called his 'I'm baffled but don't like to show it'-face.
"You're not telepathic, otherwise I'd have heard you. You're a sentient species, so you have language. Your gesturing is too imprecise to be sign language, so that must mean…"
"Maybe they talk through writing?" suggested Martha, but the Doctor didn't react to her. He furrowed his brown in thought but that didn't get him anywhere either.
The alien gestured towards the paper, then towards itself and its companion. Martha suppressed a snort at the thought that this alien might be a creature like the Doctor, and the one licking its lips at her the companion.
"You don't dance like the bees, you don't communicate through writing, you don't … make any sound at all! That's it!"
The Doctor raked a hand through his glorious hair as he babbled the solution to the problem.
"The TARDIS doesn't translate because we can't hear the translation! Its frequency is too high, even for me!"
The Doctor reached into his jacket and got out his trusted screwdriver, which happened to be soniced up. With a few clicks and a whirr Martha could hear the aliens speak.
"Sonic, my specialty," said the Doctor. He pressed his lips to the sonic screwdriver before he put it back into his pocket. Martha envied it for a second.
"Hi, I'm the Doctor, and this is Martha," introduced the Doctor himself to the aliens. They conversed a bit about who they were and what the aliens called themselves, what the Doctor and Martha were doing on the planet and how the weather was nice.
"There's been some mysterious disappearances around here," said the alien who had been licking its lips all the time. The Doctor grinned meaningfully at Martha and tentatively she grinned back. The TARDIS sure picked its landings spots with pinpoint precision. Maybe there existed a 'trouble-is-here' wavelength humans hadn't yet discovered, but the Doctor had. Martha wouldn't put it beyond him.
Still, before they got dragged into the next exhilarating and terrifying adventure, Martha had to clear one thing up.
"Why math? Why not do the whole sonic screwdriver bit right at the beginning?"
The Doctor waved the bit of paper around before he answered with a gleeful smile.
"Because math is truly the universal language."