Last week, Apple reported that it now has reserves of $76 billion in cash, short term securities and long term securities. As many wags pointed out, that’s more than the cash-strapped U.S. government has left. On Tuesday, Apple also briefly surpassed Exxon Mobil to become the world’s most highly valued company, at more than $340 billion in stock-market valuation.

With tens of billions of dollars to throw around and super-high investor confidence, shouldn’t Apple reinvest in some cutting-edge R&D that could make it even more successful?

Apple has already shown the value of introducing unique new technologies for its products: the iPhone’s advanced touchscreen and the MacBook’s one-piece aluminum case, for example. Apple has also begun bringing CPU chip design and production closer to home, giving it another technological advantage.

So it wouldn’t be a stretch for Apple to spend some of its cash on bringing new technologies into existence that competitors couldn’t touch. Never mind buying Hulu or some other company. Here are five ways could Apple actually invent the future, and thwart other makers of phones, tablets, and computers.

5. Color screens that work in the sunshine

As much as I love printed books, I’d much rather tote a skinny little iPad for my on-the-go reading. But here in sunny Los Angeles, I can’t see the color screen when I try to read outdoors. There’s no way to read a book on a tablet at the beach, or in the park.

Of course mobile displays for reading in direct sunlight are already available, such as those on Amazon’s Kindle, but they’re only black-and-white, and they refresh at a painfully slow, page-turning speed. Now that a large chunk of my media consumption is in color, these displays don’t cut it. Surely a daytime color display isn’t impossible. With Apple’s spare cash, could a breakthrough be around the corner?

4. Wireless network quality

Before Steve Jobs unveiled the original iPhone in 2007, he and his company pulled off a feat most pundits would have considered impossible: They got AT&T to change the way its voicemail system worked. Instead of forcing users to listen to all messages in order—a throwback to cassette-tape answering machines, and also good for getting customers to run up their minutes—the iPhone let its users view all messages onscreen at once and play only those they tapped.

But iPhone owners still complain bitterly about the quality of wireless service. AT&T drops calls, and Verizon won’t let you make a voice call and use an Internet app at the same time. The audio quality of voice calls on any phone, through any carrier, seems to have gotten worse rather than better. If Apple could fix these issues, iPhone calls could become a premium feature rather than a joke. It might require a multi-billion-dollar investment in wireless network infrastructure, but we know who’s got the money to spend.

3. Hands-free interfaces

Yes, I’ve figured out how to swipe at the latest version of Mac OS X. But you know what would be even better? Being able to wave at my iPhone instead of having to fumble with the keypad. Once you’ve tried Oblong Technology’s hands-free interface, even a touchscreen seems dated.

The only problem is that Oblong’s system is still too expensive for the mass market. Apple is legendary for turning Xerox’s high-end mouse-and-menu workstations into affordable Macintoshes in the early 1980s. Couldn’t they do the same with a hands-free interface?

2. Education

Another form of R&D: Give your products to a whole bunch of kids. In 2002, Apple began helping the state of Maine leapfrog its students ahead of wealthier states by giving Maine’s schools a special deal on notebooks. Every seventh- and eighth-grader in Maine gets an Apple laptop that they can take home after school. Classrooms have wireless networks. Not only are the kids learning to use the tools they’ll someday encounter in real-world jobs, but they’re also being trained to prefer Apple over Windows. Apple has long focused on the educational market for both ideological and marketing reasons. Now would be a good time for a big national giveaway on MacBooks or iPads for future geniuses—and future customers.

1. Reinvent the battery

What’s the biggest problem with your phone, laptop, or music player? It runs out of juice when you’re nowhere near a power supply to recharge it. Even with a less thirsty CPU, energy-saving software, and premium batteries packed into as much internal space as possible, Apple’s products can’t hold enough power for a full day of heavy use for most customers.

Battery technology has advanced much more slowly than chips and displays. Apple’s approach to product design—don’t just think outside the box, replace the box entirely—could change the way mobile gadgets are powered. Is there a battery technology waiting to be discovered that blows past lithium-ion tech?

Could a new kind of battery be recharged without a special power adapter, or even without a wall socket? If my phone is about to conk out, could I get it to last a few minutes longer by shaking it? I’m fond of my Android phone, but its less-than-all-day battery life has caused me plenty of problems, and before day’s end I often run down both the battery in the phone and the spare battery I carry with me. If Apple offered an iPhone that I could use in the real world for a week without a recharge, I’d switch on the spot.

Of course, what has made Apple so special for decades isn’t fulfilling my wishes, but going beyond them. Dear Steve Jobs: Please bring me yet another gadget I would never have even thought of. Now more than ever, you can afford to do that.