Shares of Duolingo (DUOL 3.64%) are posting enormous gains today. The leading language-learning expert published stellar fourth-quarter results after Wednesday's closing bell, driving stock prices as much as 23.1% higher the next morning. It cooled down to a still impressive 16% gain by 1 p.m. ET.

Duolingo's Q4 by the numbers

Duolingo's fourth-quarter revenue rose 45% year over year, landing at $151 million. The bottom line swung from a $0.35 net loss per share to earnings of $0.26 per share. Your average analyst would have settled for earnings of roughly $0.17 per share on top-line sales near $148 million.

Furthermore, Duolingo's daily active users (DAUs) jumped 65% higher to 26.9 million names while the monthly active users (MAUs) increased 46% to 88.4 million.

That's an impressive quarter in any language. Muy bien, Duolingo. Sehr gut, indeed.

Beyond languages: Duolingo's vision for universal learning

The company is growing like wildfire and expanding its profit margins at the same time -- a rare and shareholder-friendly combination. But CEO and co-founder Luis von Ahn isn't sitting on his hands. Duolingo is experimenting with different prices and features in its three subscription tiers, tweaking the family plan's feature set, and exploring new subjects starting with music and math.

And von Ahn's long-term goals are even more ambitious.

"We have about 90% share of global online language learning MAUs. And yet, we still see so much more potential and opportunity ahead of us," he said on the earnings call. "There are hundreds of millions of language, math, and music learners out there who have yet to sign up for Duolingo, and we're working on winning them over."

The new subjects won't make meaningful contributions to Duolingo's top or bottom lines anytime soon, but they are great concept tests for a much larger business in the long run.

"If you rewind to 10 years ago and you look at language learning, these courses are just way ahead," von Ahn said. In other words, additional topics may evolve into solid business operations even faster than the original language courses did.

Eventually, Duolingo may cover digital learning in a plethora of non-language subjects such as geography, history, or physics -- any topic where deep user engagement with a lot of repetition makes sense.

But for now, Duolingo is focused on languages and giving the math and music courses the old college try.

Det är en bra plan, as they say back home in Sweden. It's a growth-oriented business plan supported by profitable operations, and I can't wait to see von Ahn's vision of a universal learning platform materialize.