"We shall be able to witness and hear events: the inauguration of a president, the playing of a world series game, the havoc of an earthquake or the terror of a battle — just as though we were present," said Dr Tesla in 1926.
The device, Dr Tesla said, would be small enough to carry about in one's "vest pocket".
Vests aren't so common these days, but he's spot on with everything else. Smartphones — combining the traditional function of a phone with internet browsing, video and apps — have changed the way we relate to, and communicate with, the world.
So what future predictions can be made about our smartphones now they've been around for a while?
Many tech-heads say the smartphone's potential is yet to be fully realised — like futurist and honorary associate with Sydney University's digital cultures program, Mark Pesce.
In the first 10 years of the internet, it took us a while to work out "what the hell was going on" — and we're at the same kind of stage with smartphones, Mr Pesce said.
"If you think about how our expectations for what a smartphone is have changed in 10 years, the next 10 years will make that seem like nothing."
Ever more clever
Our phones already use artificial intelligence — when we use GPS to navigate, or ask a question of Siri or Alexa.
But the phones of the future will also be able to work out when we're sick, and act as sophisticated personal assistants communicating on our behalf, experts say.
Better biometric sensors — monitoring things like heart rate and blood pressure — could work in tandem with artificial intelligence to anticipate a stroke and contact emergency services, said Dr Christine Satchell, a Melbourne-based researcher in smart mobile platforms.
"There's a huge range of ways AI could impact on the health sector. It's potentially life-saving," she said.
Dr Satchell envisages a world where our smartphones act as executive assistants — screening calls, responding to emails, and making appointments on our behalf.
There is, however, a balance to be struck.
"You don't want it to be telling the truth all the time, because sometimes we're not sick in bed, or we're not already on our way," she said.
"How smart do you want it to be?"
Will the look of our phones change?
Bendy bodies, curved screens, wearables and holographic displays — promises abound when it comes to the form our future smartphones are going to take.
But most experts don't actually think the smartphone's shape will change that much — at least in the next 10 years.
While the screen size of popular smartphones continues to increase (from 3.5 to 5.5 inches between iPhone iterations, and 3.2 to 6.2 for Samsung) and square or curved corners go in and out of fashion, Dr Satchell said little else about the smartphone's form factor has changed.
"I think there is something critically compelling about the current shape that works for people in terms of fitting into pockets, fitting into handbags," she said.
Director of the University of Western Australia's Centre for Software Practice, Dr David Glance, said the smartphone's form factor has stayed the same for so long because of our love of video.
Until there's a superior way of tuning into a screen to watch video — or "until we have [brain] implants" — he said the phone's shape was likely to stay roughly the same.
The popularity of Pokémon GO — in which gamers on their phones traipsed the neighbourhood trying to capture monsters superimposed over the landscape — showed augmented reality (AR) could be successful.
But entertainment's just a small part of its future, Mr Pesce said.
Future smartphones could interface with high-tech glasses to overlay what we see with virtual data and images, projecting "a consensual hallucination into the real world," Mr Pesce said.
AR could help people do their jobs, learn new tasks, or guide tourists on a journey around the city.
"It's not just that you're not going to be lost somewhere, you're actually going to have an awareness of what's around you," Mr Pesce said.
An alternative route is phones so powerful we won't need accessories like glasses to enjoy augmented reality, according to Dr Glance.
"I've played around with the iOS AR kit [the latest AR kit for Apple mobiles] and that was quite phenomenal," he said.
Smartphone at the centre
We've moved from the desktop computer, then the laptop, to the smartphone as the central means by which many of us access news, connect with friends and family, and interact with the wider world.
But will the smartphone stay at the "centre" — as the main thing we use to interact with the digital world and manage all our other bits and pieces (including peripheral devices like headphones, speakers and Bluetooth headsets)?
"If history's taught us anything, the answer's no," Mr Pesce said.
He said as cloud computing and AI continue to develop, the smartphone may be eclipsed by other, more clever devices.
"The thing that replaces it may be that all these things on the periphery — whether they're glasses, or [earphones], or they're holographic projectors — these get so smart that they replace the need for having that thing in the centre."
In such a future, it could be a pair of glasses, displaying an augmented view of reality, through which we access the internet and contact friends, Mr Pesce said.