AILSA CHANG, HOST:

All right. It's time now for our science news roundup from Short Wave, NPR's science podcast. I'm joined by the show's dynamic duo, Regina Barber and Emily Kwong. Hey, ladies.

REGINA BARBER, BYLINE: Hey, Ailsa.

EMILY KWONG, BYLINE: Hi, Ailsa - so good to be here.

CHANG: So good to be with you. All right, so you have brought us three science stories that caught your attention this week. What are they?

BARBER: We have these two amazing students who developed new math for proving the Pythagorean theorem.

KWONG: How animals eating overripe fruit in the wild may have affected evolution.

BARBER: And the discovery of a fossil that sheds new light on the life cycle of frogs.

CHANG: All right. Well, what I really want to do is relive eighth grade geometry class. So let us...

KWONG: Me too.

CHANG: ...Start (laughter) with the students tackling the Pythagorean theorem. What is their story?

KWONG: OK. So in 2022, two high school students shocked the math world by solving the Pythagorean theorem using trigonometry. And for doing this, Calcea Johnson and Ne'Kiya Jackson earned keys to the city of New Orleans.

CHANG: Whoa.

KWONG: And now they are published mathematicians. Calcea and Ne'Kiya published their work - five proofs and a method for finding at least five more - in the journal American Mathematical Monthly. It's super-prestigious, and seeing the paper online, Calcea started jumping up and down.

CALCEA JOHNSON: It's really great to see it not just on my own laptop because that's where it's been for a very long time (laughter).

CHANG: Wait. How old are they now?

KWONG: They're sophomores in college.

CHANG: That's incredible.

KWONG: Yeah. Yeah.

CHANG: OK. Can we just back up a little bit, though? - because the Pythagorean theorem, in case anyone needs a refresher course...

BARBER: (Laughter).

CHANG: It's about the three sides of a triangle that has one right angle, right?

BARBER: Yeah. So over 2,000 years ago, the Greek philosopher Pythagoras figured out the equation A squared plus B squared equals C squared.

CHANG: Equals C squared.

BARBER: Right.

CHANG: Yes.

BARBER: To calculate the length of a right triangle.

CHANG: I mean, I still chant it in my sleep. It was drilled deep into my soul 35 years ago.

KWONG: Was that a math cheer? Amazing. OK.

CHANG: Yes.

BARBER: Yeah. That theorem has been proven again and again with geometry and algebra, but it was once thought impossible to do with trigonometry. Like, only two other mathematicians had done it before Calcea and Ne'Kiya.

KWONG: And that's because trigonometry is, like, based on the Pythagorean theorem, so it's tricky to use trigonometry to prove it.

CHANG: Ah. I mean, this is kind of circular reasoning, right?

BARBER: Right, but Calcea and Ne'Kiya proved it could be done. They actually developed five proofs in total.

CHANG: Wow, little overachievers.

BARBER: Yeah. Calcea is particularly proud of the proof that involves this infinite series of little triangles, which looks like a waffle cone.

CHANG: Ooh, yummy, yummy. So wait. What's next for these two math superstars?

BARBER: They're in college. Calcea is studying environmental engineering at Louisiana State University, while Ne'Kiya is studying pharmacy at Xavier University. And Ne'Kiya had some advice for today's high schoolers. Finish what you start.

NE'KIYA JACKSON: I know there's moments where you're like, I don't want to do this for real. But in the long run, it might be something that could have mattered if you had just tried or kept with it.

BARBER: And that's certainly true for her and Calcea, who both wanted to thank their parents for all their support.

CHANG: Aww (ph), what good kids.

BARBER: I know - good kids.

CHANG: All right. So let's move on. We're going to talk about overripe fruit. Animals eat this. I mean, I do.

BARBER: I mean, I do, too. Ailsa, have you heard of something called the drunken monkey hypothesis?

CHANG: No, but this makes me want to hang out with some drunk monkeys.

BARBER: Same. LOL. OK, the drunken monkey hypothesis suggests that our human interest in alcohol may be due to the abundance of alcohol, especially ethanol, from all that rotting, naturally fermenting fruit in the wild...

CHANG: No way.

BARBER: ...Which animals have eaten throughout history.

KWONG: Yeah, but there was no consensus for this hypothesis among scientists who studied primates when the theory was proposed decades ago.

MATTHEW CARRIGAN: There was, like, 90% of primatologists who thought fermented fruit was very rare, and then there's 10%, a handful of primatologists, who thought it was so common to be uninteresting. And that was kind of, like, the divide.

BARBER: That's Matthew Carrigan, who's an author of a review paper, which is an article that looks at a lot of studies, that came out in the journal Trends In Ecology And Evolution.

CHANG: OK, so did they figure out how common it is for animals to eat fermented fruit?

BARBER: So this review paper claims that many animals consume large amounts of fruit to survive.

KWONG: And they are bound to encounter fermented fruit with low levels of ethanol, so consuming this specific kind of alcohol is most likely very common. Also, if you eat a lot of these fruits, that alcohol is going to make you tipsy.

BARBER: Yeah. And intoxication is dangerous out in the wild. Like, animals would be too vulnerable to predators or falling out of a tree. So Matthew says that our primate ancestors likely had to adapt to alcohol consumption and more or less become functional drinkers. They probably didn't have a choice.

CARRIGAN: And so it kind of flips the story on the head. Rather than being, you know, humans consuming alcohol to get drunk, to now, perhaps it's the other way around - that animals are either intentionally or can't avoid consuming ethanol they're going to be exposed to on a perhaps very routine basis.

CHANG: OK, so I have these monkeys to thank for how we evolved...

KWONG: Yeah.

CHANG: ...To be able to drink...

KWONG: Yeah.

BARBER: Yeah.

CHANG: ...And break down alcohol because our ancestors apparently could not avoid it.

BARBER: Yeah.

KWONG: Yeah. Yeah. Matthew says we still don't know for sure if, like, animals actually prefer fermented fruit, like, sometimes seek it out. There needs to be more studies on that. But scientists are seeing more and more evidence that this was an evolutionary advantage to have enzymes break down alcohol, which may have led to many human civilizations enjoying it.

CHANG: So interesting. OK. Well, we have to move on...

KWONG: Yeah.

CHANG: ...Now to another story about the animal world. I hear a new fossil of a frog has been found.

KWONG: You heard that right, though it is technically the fossil of a tadpole, the oldest-known fossil of a tadpole. Tadpole - that's the larval stage of a frog's life, you know, when they're just...

CHANG: Yeah.

KWONG: ...Little swimming polliwogs with a tail.

CHANG: Right, like, 'cause frogs are like butterflies or salamanders in that they go through metamorphosis from their larval to their adult stage, yeah?

KWONG: Yeah. We call this the biphasic life cycle.

BARBER: Back to this, like, really cool fossil. This tadpole fossil is 161 million years old, from the middle to late Jurassic period. And it's incredibly intact, like, which is shocking because tadpoles are really delicate. They're made mostly of cartilage. And also, the tadpole stage only lasts a few months before the tadpole transforms into that adult frog. So it's been very hard for scientists to find tadpole fossils that are this well-preserved.

KWONG: Mariana Chuliver is the lead author of a new paper about this in the journal Nature. She said when she saw the fossil, she knew immediately what it was.

MARIANA CHULIVER: I said, OK, it's a tadpole. There is no doubt. But then, when I saw it under the binocular microscope, I said, this is the best tadpole ever because up to now, there wasn't any other fossil tadpole with the gill skeleton preserved.

CHANG: The best tadpole ever...

BARBER: I know.

CHANG: ...With a preserved gill skeleton.

BARBER: Yeah.

CHANG: OK, does this amazingly preserved specimen teach us anything about, you know, frogs or how they evolved?

BARBER: Yes, they think so. I mean, one of the interesting things about this specimen is its size. It's almost two times as big as the tadpoles we see today.

CHANG: Wow.

BARBER: And it is the oldest tadpole ever found by 20 million years.

KWONG: Yeah, this discovery proves that the tadpole phase goes way further back in evolutionary time than we knew. So, like, any kid who stared into a puddle knows how awesome tadpoles are.

CHANG: Yeah.

KWONG: It turns out they're even more awesome than we thought, if you ask evolution.

CHANG: Wow. I have an even more robust love for tadpoles now.

KWONG: Definitely. We share the Earth with so many other species but us, so I'm comforted by this.

CHANG: (Laughter) That is Emily Kwong and Regina Barber from NPR's science podcast Short Wave, which you can subscribe to for new discoveries, everyday mysteries and the science behind the headlines. Thank you to both of you.

BARBER: Thank you, Ailsa.

KWONG: Thank you, Ailsa.

(SOUNDBITE OF QUINCY JONES SONG, "TUXEDO JUNCTION") Transcript provided by NPR, Copyright NPR.

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