In Mobile Suit Gundam, protagonist Amuro Ray's father was an emotionally-distant Engineer who took his son into space. By contrast his mother is literallyCloser to Earth, having chosen to stay there and work in a refugee camp, and she's shown to be pretty irrational.
Tweeny Witches has the all-female witches living in a lush, Miyazaki-flavored valley-town fueled by magic while the in-name-only warlocks and their banished witch wives live under the desert in an underground fortress (basically the one in Neon Genesis Evangelion), surrounded by technology and artificial food. There are a few actual warlocks who can use magic, but they're very old and live outside the fortress.
Sailor Moon S: The Movie is a inversion; a female scientist and her emotional boyfriend who believes in myths.
In Naruto the only characters who can use Mokuton are male: Senju Harashima, Captain Yamato and Shimura Danzo. Later on, Uchiha Madara. However, the associated character traits are not present.
Princess Mononoke: Lady Eboshi is both of these in one; she provides food and shelter for the poor and sick, former prostitutes, and all other kinds of outcasts who don't have any other place to go, by running an industrial scale iron mine and expanding into advanced firearms development and production.
In the Batman universes, Poison Ivy and Catwoman fit the trope. Poison Ivy can control the growth of plants with her mind and is often depicted as being mothering to plants and so in harmony with the natural world to the point that she hates anything man-made. Catwoman is not so obvious, but she has an unexplained and very odd affinity with cats. In some continuities, even tigers will discard habitual ferociousness if she gives them the right look. In contrast, the logical/sciencey villains like Mr. Freeze or the Riddler tend to be male, although the Penguin does have an affinity with birds.
Even Penguin shows this when compared to Catwoman. Both have an affinity with an animal (Birds and Cats respectively), Penguin shows a higher preference for high tech gadgets (like his trick umbrellas) than Catwoman who relies on a plain whip, claws and acrobatics.
Then there's Harley, the mad psychiatrist. She may have started off as a psychiatrist, but she is driven by her insanely emotional devotion to The Joker.
In the Superman comic book story "Father Nature's Folly" a male alien arrives on Earth, and claims that he and his mate were the creators of life in many worlds. He claimed to be unhappy with the result of his mate's work on Earth, and would have mutated all life into bizarre forms had Superman not stopped him.
In From Hell, Sir William Gull gives a rather deranged, yet convincing Nietzschean speech about the Ancient Greek beliefs mentioned above, rationalising his actions as ensuring we would have a logical, Apollonian and masculine future of science and order instead of being dragged backwards into an emotional, Dionysian future of insanity and emotional female rule. It was well-argued enough that author Alan Moore talked himself into becoming a magician whilst writing it.
Zigzag inXenozoic Tales, featuring the very science-minded Hannah Dundee and the Earth father Jack Tenrec. Both of them have leanings for the opposite side. Jack, despite his undying devotion to the natural order, loves working on cars and other machines. Hannah, more subtly, believes in the mystic underpinnings of the world, but she considers they will be scientifically explicable, once they are better understood. There's also the indication that she's been chosen by the Grith.
ElfQuest is a genderflip. It has two major pairs of "sweet, mystical, peaceful boy" and "strong warrior woman" (Suntop and Ember, Redlance and Nightfall), and both are experienced as playing against type. An Animated Adaptation was proposed, but canceled when Executive Meddling demanded that the personalities be switched.
In Act I of Legends of Equestria, the two female Ancient Masters command the orders most in tune with nature. Terraria seeks a return to unity with the natural order, and Aquos wants to control the world with natural magic. The two males, by comparison, are far more rationalistic in their goals. Altas is a mathematician, and Seraph is an industrialist who seeks to rule nature.
Films — Animated
Inverted in Cloudy with a Chance of Meatballs: Flint Lockwood's mother was supportive of his scientific endeavors, while his father is mostly confused by anything more complicated than a fishing line.
Films — Live-Action
In Spider-Man 2, Doctor Octavius (later Octopus) and his wife Rosalie are both college professors, but whereas Otto specializes in nuclear physics, Rosalie teaches literature.
In The Incredible Hulk both Bruce Banner and Betty Ross were scientist working on the serum that lead to Bruce's transformation. Bruce is Marvel's resident Gamma radiation and physics expert whereas Betty is a professor of biology.
This is pretty exactly much how the Architect describes himself and the Oracle in The Matrix Reloaded. The Architect was a cold, logical perfectionist, while the Oracle was more focused on understanding human emotion and psychology.
Discworld is very complex and goes back and forth about this. Equal Rites brought these ideas to the fore.
Wizards are urban and associate with the Unseen University, thus are some variety of academia parody. They are often silly old duffers or giant nerds, but this does give the luster of hard science to their magic, and were more powerful once in Disc politics. The leading wizard, Ridcully, is pretty pompous but macho too (and ironically was thought to be Closer to Earth, but was actually an Egomaniac Hunter). In earlier stories they tended to assassinate each other a lot. They're also celibate because of the possibility of Sourcerors.
Witch stories focus around the trio of Nanny Ogg, Magrat, and Granny Weatherwax. Granny is a cynical, hardbitten, practical one who thinks wizards waste time with their 'jommetry' and 'supreme arch-whatever' just to look important. Nanny Ogg uses Obfuscating Stupidity and is a touch louche. Magrat is romantic and a little New Age and drippy. Overall, they're rural, more folk-magic, but closer to everyday concerns and problems than the wizards.
A few Witch characters have been seen to use wizard magic, which is a variety of Rule Magic and so there is really no reason why not. No wizard has been seen to use Borrowing or any other of the Witch specialties, but on the other hand there has never really been any suggestion that they couldn't if they wanted to. Granny once fought a magical duel with the then-current Archchancelor, and they fought to a standstill.
Diane Duane's Young Wizards series follows this. Nita's magic relates to nature and living things. Her male partner Kit tends to do better with technology and inanimate objects like rocks. However, later on Nita's sister subverts the whole thing by being a computer wiz with a magical affinity for technology and silicon-based lifeforms, and both Nita and Kit eventually grow out of their original specialties into others, which is apparently common for wizards. It's left open whether their initial foci came from awareness of the trope, but newcomers to magic in the books do tend to get it in a form which behaves as much the way they expect it to as is practical (without breaking Magic A Is Magic A).
In the Doctor Who New Adventures novels, the mythology of Gallifrey features a group of male scientists (led by Rassilon) and a group of female witch-priestesses (led by the Pythia) struggling for control. Rassilon won, and went on to found the Time Lord society. Different novels offer different opinions on whether this was good or bad.
In the novel Enduring Love, Clarissia is "mother nature" to Joe's "father science".
A Downplayed Trope in the The Belgariad prequels, Polgara notes that her mother encouraged her to learn by accepting, whereas her father taught her to question everything. The downplay is because, since her mother is literally a wolf, it's possible that species has at least as much to do with it as gender does.
In Courtship Rite, this is mostly averted; some of the top scientists in the Kaiel clan, for example, are women. Some clans believe this trope is true, though, like the o'Tghalie clan, professional mathematicians who forbid their daughters to study. Teenae, who is an o'Tghalie by birth and a Kaiel by marriage, is proof that the o'Tghalie are wrong about women; she is a mathematical whiz.
Jack and Annie from Magic Tree House, although given their ages, Jack simply has been in school longer than his sister.
Everything Dan Brown has ever written is a inversion of this trope. His hero is always an expert in some area of humanities, while his heroine is an expert in some mathematical field.
The Lord of the Rings: Despite the fact that they are a plant specices, they are a play on this trope. The Ents and Entwives in Treebeard explain that the Ents delighted in nature and the wilds, and would roam for long periods communing with plants and animals. Whereas:
[The Entwives] did not desire to speak with these things; but they wished them to hear and obey what was said to them. The Entwives ordered them to grow according to their wishes, and bear leaf and fruit to their liking; for the Entwives desired order, and plenty, and peace (by which they meant that things should remain where they had set them). So the Entwives made gardens to live in.
The Entwives then first taught humans agriculture, and how to farm the land. Their male counterparts remained wild, favouring a more intuitive connection with growing things.
Isaac Asimov's I, Robot: Averted by the coldly logical (and somewhat misanthropic) robopsychologist Susan Calvin. Calvin is misanthropic in the sense of the word that means she doesn't much care for anybody, regardless of sex. The most emotional she ever gets is in the story "Liar!," where she becomes absolutely vitriolic towards a robot that basically tricked her into revealing that she had feelings for another person.
The Doctor's first two human companions: Ian taught Science while Barbara taught History.
Most of the Doctor's female companions, by necessity of Cast Speciation. The stereotype goes - the Doctor, male, old, science, good but a bit morally alien, The Fettered, brave in the face of danger; the Companion, female, young, less knowledgeable/humanities, good but not able to moralise as objectively as the Doctor, the Doctor's Morality Chain, scared of the spooky monsters. Sliced even more roughly - the Doctor, a male Science Hero, and the Companion, a female The Heart. It should of course be noted that these are enormous generalisations and definitely do not always apply.
The Rani is meant to be a genius, and is usually shown doing evil science of some kind, but still falls partially within this trope in that her field seems to be biogenetics, as opposed to the engineering favoured by both the Doctor and the Master. Romana, who is canonically meant to be cleverer than the Doctor, is an inversion, especially when she makes her own (superior) sonic screwdriver that the Doctor tries to steal.
In "The Green Death" we get an interesting play on it. We get Mother Nature (the hippie commune) and Father Science (Global Chemicals) BUT the commune is made up of research scientists trying, among other things, to breed high protein fungus to act as a meat replacement.
In Dona Barbara, the title character (a wealthy landlady) represents the brutish nature while Santos Luzardo (a lawyer from the big city) is the civilization.
iCarly: Expect Carly and Sam to solve problems in the natural (or the brawn) way and Freddie to resort to geeky gadgets and tech stuff.
Played straight with iGo Nuclear. Carly's projects involve a crude compost pit and an organic pesticide, while Sam used her fingers to rip an orange apart. Contrast Freddie's high-tech modern composter, Spencer's electric-powered scooter, and Cal's illegal nuclear power generator.
3rd Rock from the Sun: Dick is a physicist and his love interest and co-worker Mary is an anthropologist. On the other hand, Dick is a Cloudcuckoolander alien while Mary is a cynical Grumpy Bear. Ironically, Dick's mission as an alien observer of humanity makes him an anthropologist as well, just on a much larger scale.
In the initial cast of Farscape, there is Crichton, a scientist (if one given to explosiveness under pressure), and Zhaan, a priestess. However, this might also count as an inversion, because Crichton is very emotional, and Zhaan at least tries to be calm and logical.
In the new Battlestar Galactica it seems that Head Six and Head Baltar represent spirituality and logic respectively — while both agree they represent a higher power, Head Six calls it God and believes it demands religious worship, while Head Baltar seems to have a more abstract view of this power/entity. And reminds her "He doesn't like that name."
The fourth season of Buffy the Vampire Slayer follows this theme, with the Slayers' magic vs. the Initiative's research in dealing with demonic forces, but with the leader of the intitative being the female Professor Walsh, and the expert of the Scoobies being the male Giles.
House is Father Science in contrast to pretty much everybody else as Mother Nature, but most especially Cameron, Masters, and Adams (and Cuddy, when she's actually involved in medical matters instead of being purely a bureaucrat). In a slight aversion, Wilson (male) is probably closer to the Mother Nature role than Thirteen (female, but bisexual, so there's that).
The primary female scientists in The Big Bang Theory work in the fields of neurobiology and microbiology while the males take to experimental physics, theoretical physics, astrophysics, and aeronautical engineering.
Bashir and Jadzia initially appear to be an inversion. Bashir is the medical officer and Jadzia is the science officer. However, Jadzia's scientific degrees are all in exo-biology, zoology and exo-archaeology. The only thing that gives her an apparent inversion over Bashir is that she also has a degree in astrophysics. This is later negated by the revelation that Bashir is a genetically engineered genius who can grasp science and maths as the plot demands, making him innately better at grasping, theorising, forecasting and calculating astrophysics and engineering principles than Jadzia and O'Brien combined.
Later played more obviously straight with Bashir and Ezri. They're both in medicine whereas he's set up to be 'hard-core' medical and she's the 'softer' psychologist.
In Stargate SG-1, we have a genderflip. Daniel Jackson is a linguist, archaeologist and anthropologist whereas Samantha Carter is a genius astrophysicist. She's also amazing at math and engineering in general.
Agent Fox Mulder and Agent Dana Scully are classic inversions. Mulder is a psychologist, a believer in the paranormal, and relies heavily on intuition in his investigations. Scully is a forensic pathologist with an undergrad degree in physics, a total skeptic about paranormal phenomena, and works from logic and hard evidence. Furthermore, Mulder is usually the one who's unafraid to show his feelings, while Scully is The Stoic. Mulder gets to be right more often, at least about the existence of the paranormal, but the show suggests very strongly that he'd be a failure without Scully there to keep him grounded. This was all done very deliberately by the writers.
Booth and Brennan in Bones. A complete inversion. Brennan disapproves of anything that isn't discovered through logical analysis (usually while poking around a corpse), and dislikes psychology, calling it a "soft science." Booth, on the other hand, is perfectly willing to go out on a limb without facts to support him, and crafts plausible scenarios, the potential for personal bias be damned. Booth isn't on the side of Nature, but he's a far cry from the logic of the squints.
Farscape is also a genderflip: D'Argo, the Proud Warrior Race Guy of deep feeling, and Aeryn, stone-coldBad Ass soldier. Over time, both become less and less like this, Aeryn's emotional growth (while not losing her self-control) a key part of the story, while D'Argo becomes more and more self-aware and almost meta in his thinking: "John, I'm going to tell you something I've never put into words. I really like shooting stuff. And I'm very good at it."
Star Trek: Voyager: Chakotay and Seven of Nine Chakotay is a Magical Native American who likes going on vision quests. Seven is an Emotionless Girl who was raised by the Borg who refuses to go back to her human name. Her emotional growth is explored throughout the series. The romance happens in the final season.
Buffy the Vampire Slayer: The first season episode "I Robot, You Jane" has a sort of inversion. Giles is books and eye of newt, Jenny is computers and techomagic.
Series/Eureka has Alison as the logical scientist and Carter as the emotional one with a stronger grasp of the human element.
In Agents Of Shield the teams scientific team are Fitz, a man who specializes in physics andelectronics and Simmons, a woman, who specializes in biology and chemistry. However the teams hacker and computer scientist Skye, is also a woman.
Inuit mythology has two "nature" deities: Sedna, ruler of the creatures of the seas, and Torngarsoak, master of animals of the land.
Averted in Norse Mythology, in which gender was used to represent different facets of both nature and logic/wisdom, rather than to distinguish them. Nature was represented by a plethora of gods, giants and spirits, most prominently by the siblings Frey and Freya, who represent male and female fertility, respectively, while both Odin and his wife Frigg were associated with the wisdom deemed appropriate for each gender, specifically in the roles as patriarch and matriarch. (Still gender-normative, yes, but Fair for Its Day.)
Inverted by the Dagda or the Green Man, a Celtic nature god. He appears today in a lot of leafy-carved garden ornaments.
Often inverted in Classical Mythology, as deities of nature and science can come from both genders. For example, the two great rivals, the sea god Poseidon and the wisdom goddess Athena.
Played straight in Eberron. In the Sovereign Host, Aureon the god of Lore and Onatar the god of Craftsmen are both males. Arawai is the goddess of Life, and is female.
The Brothers' War arc of Magic: The Gathering gives us the eventual contrast of warring brothers Urza and Mishra, two male masters of artifice, and Gaea and Titania of Argoth, two female masters of nature. A third option is eventually presented in the mana of the land (which can be technically "nature", but is unknown to both parties), which Urza takes as he activates the Weapon of Mass Destruction to end the war. This choice activates his spark, turning him into a planeswalker.
In contrast to the trope title, 'Father Nature' figures do occasionally crop up. Dungeons & Dragons third edition featured two nature deities; the all encompassing Obad-Hai, a male 'Father Nature' figure, and Ehlonna, a female deity specifically of the woodlands. Obad-Hai remained staunchly neutral, encompassing all of nature's aspects, while Ehlonna was good-aligned, and usually portrayed as subordinate to Obad-Hai. In the Forgotten Realms setting, the deities are similar. Nature as a whole is covered by Silvanus; so much a 'Father Nature' that his title is the Oakfather. Mielikki plays the same role as Ehlonna; she serves him, and while accepting that there's a natural cycle, out of tender-heartedness tends to intervene benevolently. There is a 'Mother Nature' figure, Chauntea, but she is described as specifically the deity of how humans interact with nature. Nature itself comes under Silvanus. It's still played straight with the science half of things. Of the Greyhawk deities, Boccob is the coldly intellectual deity of magic and learning, and male, while Wee Jas is the female goddess of magic and death-but called a Witch Goddess of mysticism rather than enlightenment. Of the Forgotten Realms? All four of the deities of knowledge, invention, and learning are male (Oghma, Deneir, Gond, and Milil), Azuth, the god of wizards and academic magical learning is male. The only female deities who come remotely close are Mystra, goddess of magic, and Selune, goddess of the moon, and both have an extremely mystical bent rather than academic. The story is similar for all the non-human pantheons. Averted, however, by the 4th edition pantheon, in which Nature and Magical Study are the domains of goddesses Melora and Ioun, respectively.
The Magic: The Gathering card Stronghold Biologist is male, while his counterpart Stronghold Machinist is female.
In Sid Meierís Alpha Centauri, the hippie environmentalist faction is led by Deirdre Skye, a woman, and the scientific technological faction is led by Prokhor Zakharov, a man. Alien Crossfire then inverts this by introducing Aki Zeta-5, an Emotionless Girl leader of an entire faction of Spocks, and Cha'Dawn, a young man who is supposedly a Messianic Archetype, head of the Cult Of Planet. The expansion also played it straight with the two alien factions: the Caretakers, led by a female sworn to preserve the planet, and the Usurpers, led by a male and hellbent on exploiting its power for their own gain. As an inversion, the expert hackers (Data Angels) and the ultra-militaristic faction (Spartans) are led by women, while the humanitarian Peacekeepers are led by a man.
In the Myst series, Atrus is an avid scientist and total rationalist, while his wife, Catherine, is more emotional and spiritual, and their Writing reflects their differing views. Their children, Sirrus, Achenar, and Yeesha also seem to follow this trope.
Final Fantasy VII has Dr. Hojo, who tends to initially dismiss supernatural theories about The Promised Land, and tends to see everything and everyone in terms of facts or varibles. He is contrasted by Dr. Lucrecia Cresent who dedicated her career to ancient, magical occurrences within the planet. Significant in that Sephiroth is their child; the combination of polemical forces to essentially create the game's version of the anti-Christ. Though the addition of a Third Wheel known as Jenova, an Eldritch Abomination that eats a Planet's Lifestream also probably had something to do with it.
In Ōkami the Goddess Amaterasu is the Sun God and is in charge of restoring nature while her archnemesis is Yami, God of Darkness and creator of Technology.
The siblings Animebona and Animenkhna, the spirits of Albion and Earth, also represent Magic and respectively science. They don't get along very well.
Sword of the Stars: In Zuul mythology the species that genetically engineered them is "father" and the universe is "mother". Note that Zuul females are non-sapient and often are eaten by their own larvae, they use this myth as an excuse for strip-mining their colonies and pillaging other races in their search for their missing gods.
Averted in Portal, where the science-loving GLaDOS is clearly female.
Inverted in the Mass Effect series, the female Tali is an engineering genius and Wrench Wench, while the male Dr. Mordin Solus specializes in biology.
Xenoblade Chronicles takes place on two giants, each controlled by a god: the natural Bionis and the mechanical Mechonis. The gender roles are reversed though, as Lady Meyneth is Mechonis while Lord Zanza is Bionis. They do keep their gender's personality traits, as Meyneth cares for the people on both giants, while Zanza only cares about himself.
In Gunnerkrigg Court, Surma Carver could speak withthe Guides, and she served as the mediator between the Court and the magical Gillitie Wood. Her husband, Anthony, was a surgeon and, according to Jones:
Antimony: I had no idea [Surma] worked here. She never mentioned it. Jones: Oh? That was your father's influence, I suspect. Yes, he never had patience for matters that didn't fall into a scientific category.
Anthony's views on magic aside, Gunnerkrigg subverts the whole thing pretty soundly by treating magic as another form of science. It's explicitly referred to as the "etheric sciences". Kat's dad was able to cast that one shield spell because he's a sub-user on his wife's etheric computer.
Kat, and her mother, both fall on the side of science.
Subtly inverted in Homestuck, where John is an amateur magician while Jade is a big science geek, though you'd be forgiven for not noticing the trope before they have an argument about whether magic or science is better in Act 6.
In Gargoyles, Fox's parents are a male scientist/robotics engineer and Titania. Yes, that Titania. Queen of Faerie Titania. And yet it works perfectly, in part because Titania appreciates science as a kind of "magic".
In one episode of The Simpsons, Bart and Lisa's school was split into Boys' and Girls' sections. The Boys learned everything pretty much the same way, but the Girls reverted to some absolutely bizarre New Age teaching methods. While the boys' teaching methods worked better, outside of class their side of the school looked like a scene from Lord of the Flies.
Teacher: How do numbers make you feel...
The Secret Saturdays lives this trope. Doc Saturday is a scientist through and through, while his wife Drew is more a believer in the paranormal. Faced with any problem Doc will always seek a logical solution while Drew will explore more mystical alternatives. They're still Happily Married though so that's cool.
In Captain Planet, the Planeteers are led by Gaia, the spirit of the Earth. The main villains are almost all male, except for one —Dr. Babs Blight, a rare femaleMad Scientist. The male villains tend to be in business, though Duke Nukem used to be a scientist as well.
Paleolithic sites of Europe and the Middle East are filled with figures and drawings of either obese or pregnant women that are generally assumed to be fertility goddesses. From the Neolithic on, these goddesses are joined by increasing depictions of bulls or horned male figures that are rendered as personifications of agriculture.
In Myers-Briggs, the "Thinking" function is seen as masculine and the "Feeling" function is seen as feminine. It may or may not be a coincidence that there are more male Thinkers and female Feelers in Real Life.
In the Seduction Community it is widely believed that that men think logically whereas women think using irrational, emotional "chick logic".
If Truth in Television can be an inversion: the view of nature as feminine is questioned by some modern Neopagan groups, where a Mother Nature figure, if present, is often complemented by male nature deities such as the Horned God, or the cycle of Oak King and Holly King. Nature as a whole is not completely the domain of either gender.
Interestingly, in both Greek and Latin 'scientia' (knowledge), and 'sophia' (wisdom), are female. Additionally, philosophy is one of the few humanities that remains male-dominated, especially in terms of faculty. Although philosophy heavily involves logic, it's generally classified as one of the humanities.
Ecofeminism and "difference feminism" generally play this trope straight, arguing that Western society has traditionally privileged "masculine" sources of knowledge and ways of approaching nature over "feminine" values like intuition, nurturing and respect for the natural world. Note that neither of these are really widely accepted by mainstream feminists these days, although they're still significant side factions.