Georg Petschnigg is distracted. He's trying to tell me about his company's new app—Paper for iPhone, an adaptation and re-thinking of the wildly celebrated iPad sketching app—but the gold Galaxy Note 5 sitting on the table keeps catching the CEO's eye. "Man, that would be a really nice form factor for this app," he says. A few minutes later: "I wish I could just—whoosh!—wave the magic hand" and move the app from the iPhone 6 in his hand to the Note 5.

The Note would be perfect. It has a big, high-res screen; a pressure-sensitive stylus; and a self-selecting set of users who buy the phone because it promises Maximum Productivity. And productivity, perhaps even more than the sketching or doodling FiftyThree's app has become known for, is what the new Paper is all about. Same goes for the new iPad Pro, by the way, or the new Apple Pencil, the stylus that mimics FiftyThree's device both in purpose and in name. But Petschnigg isn't worried—his company will support the new Pencil, too, and he hopes Apple's foray into stylus territory will be good for everyone. Plus, he thinks he's onto something better anyway.

"We've always been about capturing ideas," Petschnigg says. When FiftyThree decided it wanted to create something for the iPhone, they started to look at what people do differently on a phone. The team discovered two things: People spend a lot of time composing notes-to-self, and a lot of those notes are images. Not just pretty and well-composed photos, either: screenshots of text, pictures of signs, all sorts of hacky capture methods. "We started combining that," he says, "with this basic truth they'll teach you in design school. That is, if you want to remember an idea, you have to put text and images together."

Paper for iPhone is all about this combination of text and images. No matter where you are in the app, there's a small "+" icon at the bottom of the screen. Tap it, and you're staring at a blank note. You fill it with a photo or drawing, using all the same tools available in the iPad app. You can use Paper's many brush tools, its sophisticated color-picker, even the neat tool that figures out you were trying to draw a circle or square and straightens everything out for you. If you shot a photo, you can put a spotlight around the important stuff, If you want, you can even connect the Pencil stylus and work that way—though that's a lot more awkward on the smaller iPhone screen.

Or you just write. A caption, a description of the image you created—a few sentences, a paragraph, a to-do list. Maybe the most novel thing about Paper is the way it handles text formatting through gestures; you just swipe right on a line to turn it into a task or bullet point, or left to make it into a header. Making lists and taking notes in Paper makes other solutions feel ridiculous. Why have I been searching in nested menus, or poking through the extra row of keys above the keyboard, when I could just use my finger to move text where it goes? "This is going to become the new standard," Petschnigg says, and it's hard to argue. I'm not an artist—I just don't think that way—but having a more malleable way to take simple notes has been incredible.

Rather than stick with the "journals" metaphor Paper has always had, FiftyThree turned to "Spaces." They're more like neatly-stacked piles of paper strewn all over your desk, each one endlessly sortable and available for you to flip through. You start in the app's homescreen, which is just a scrollable list of your spaces; tap or swipe into one, and the individual pages come apart as if they're being spread out in front of you. Tap into one, and it's like it's being held up in front of your face. Swipe down, and everything shuffles back into the pile and you're back at your homescreen. There's a wonderful physicality to the animations, always carefully reminding you of where you are in the interface. There are some clunky spots—you can't swipe down to stop editing a note, you have to tap "Done"—but in general it's smooth and stylish.

FiftyThree

You can move notes around within and between spaces, and even export entire spaces to, say, Keynote presentations. Petschnigg showed me a space he'd created for a board presentation, sketching out two- or three-word slide ideas; he quickly dashed off the outline and sent it to the board for feedback, long before he started really building anything nice. On one slide is a diagram about his vision of the creative process: an arrow, going around every which way, curling around and over itself 20 times before finally moving vaguely off to the right. That's the metaphor, he says, for everything Paper is about. The process is messy, so they want to make it easy to capture everything, move it around, and then take a step back and see at a glance what you've been working on. "This is much more like your mobile wall of stickies," Petschnigg says. "That I can wrap my head around."

There are more than enough note-taking apps in the App Store, but Paper still feels refreshing. It'll be a drawing tool for people who like sketching, a digital version of the tiny Field Notes notebook in your breast pocket. For others, it'll be a more grokkable kind of note-taking app, where things are sorted by more than just chronology. It's a near-perfect mix of camera roll and journal, too.

It's just the beginning for FiftyThree, and there's a lot left to do. For starters, it needs to make the app sync with the iPad, or anything else for that matter, so your data doesn't feel trapped in this tiny device. And there's that Android thing—Petschnigg wants desperately to build Paper for the platform, he just needs the right developers to do it. But already, this feels simple, elegant, freeing. It feels like, well, like Paper did when it launched for the iPad in the first place. I don't have to do things the way the app dictates, in the order it dictates. I can just do whatever I want, and worry about where it goes later.