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"Quod Erat Demonstrandum" note 
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Kana Mizuhara is an Ordinary High-School Student who is at an arcade one night with a friend when she comes to the rescue of a fellow classmate. The classmate, she comes to learn, is Sou Touma: a MIT-graduate Teen Genius who came to Japan to attend high school like a normal student. Of course his lack of social skills and his encyclopedia knowledge on a variety of advance subjects make him far normal.

When her friend receives news her father has died, Kana drags Sou along to console her only to learn her father (a police detective) is on the scene...and Kana's friend's father was murdered.

Realizing that Sou has noticed something about the murder, Kana forces him to help to find information and clues to the killer's identity. In doing so the two form a genuine friendship and the series follows them as they repeatedly stumble into crimes or are ask to investigate mysteries.

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Q.E.D. Shōmei Shūryō, usual shortened to Q.E.D., is a manga series written by Motohiro Katou and first began serialization in July 1997 and still going strong to this day. Initially published in Magazine Plus, the series is now featured in Magazine R under the title Q.E.D. iff following the Magazine Plus publication's cancellation.note 

One of the most notable aspects about the series is its taking advantage of Sou's status as a Teen Genius; every chapter has him explaining in (accurate) detail one of number of advance subjects revolving around mathematics, cosmology, engineering and a whole host of other subjects as related the current case. This makes for a double edge sword as translating the manga proves difficult leading to slow releases in English and other languages.

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Since the manga's launch, two more series by the author has been released and are on-going: C.M.B. and Rocket Man. The first of the two, C.M.B., follows a young man who is revealed to be Sou's cousin and his friend, revolving around history and archeology as opposed to science. Rocket Man is a revolves a teenager with the skills of a trained doctor and his friend, as he investigates the mystery of his missing memories focusing as action-adventure with elements of Spy Fiction. Needless to say the author loves this dynamic. note 

In need of a character page and some Wiki Love Magic.


"We have supplied tropes for the following case in the manner which you asked us to:"

  • A.I. Is a Crapshoot: Subverted. The AI crashing Tokyo's traffic is only a simple life simulation program without any evil intentions.
  • Absent-Minded Professor: Deconstructed in one case. The case show you how bad the impact of Absent-Minded Professor can have toward people around him. It was so bad that to salvage the situation, Sou had to take the blame. See False Confession.
  • Action Girl: Kana. who with Nanase can thrash the whole squad of desert raiders empty-handedly.
    • And now they fight gun-toting diamond-smuggling mafia led by tyrants. In a church. And its rooftop. With only two wooden stick.
  • Agent Mulder: For parody purposes, there is one character of a recurring detective trio who has a habit of making deduction of linking everything to aliens or mystical/mythical things, thus people call him Mulder. To enforce said parody, he's said to have a book with "X" alphabet largely printed and attached on the front cover.
  • Alien Geometries: One case involves murder in a recreation of M. C. Escher Ascending and Descending.
  • All Love Is Unrequited: A case involves 4 people who like someone while being liked by another person within the circle. One of them intentionally creates a situation so that a person they harbor a grudge on like them while they admit to like another person to make them seem like a good person.
  • Always Murder: Averted. There are great deal of cases like burglary, vandalism, thieving, fraud, even mistaken for two timer misunderstanding case.
  • Asshole Victim: A detective series is bound to have these, even though it's often subverted.
  • Attention Deficit... Ooh, Shiny!: Sou's little sister, Yuu, has tendencies to be distracted by things surrounding her. However, it's Definitely not played for laughs during her introductory chapter. She unknowingly let her family dog outside to go to the bathroom but forgot to take it back inside which ended up with the dog getting run over. Sou who already knew this decided to not tell her anything, causing a bit of an estrange in their relationship.
  • April Fools' Day: A case revolved on helping a small country from corrupt investors, an international April Fools' Day contest involving high-profile officials, and Sou's effort to relieve his Champion title from said contest.
  • Batman Gambit: Toma employs this at the climax of the first chapter. He bluffs the suspect by pouring liquid that he says could trace the culprit's name. The liquid is just water, but the suspect scrambles it out of fear, proving himself as the culprit. The bluff will falter if the suspect maintains his cool just a little bit longer, but as Toma says in the conclusion, only machines are completely controlled by logic.
  • Berserk Button: At least in the first books, insinuating that Sou is Kana's boyfriend can get you KO'ed by an iron fist.
  • Bookworm: Sou, to the point Yuu prefers to sleeps in a hotel rather than their family's apartment in Tokyo because she knows it's going to be full of his books. And his library and collection is actually big enough, he (or his family) has to rent a warehouse at the docks.
    • In Q.E.D.iff has Sou moving into a new house which Kana discovers is to be more or less doubles as a massive library.
  • Brains and Brawn: Sou and Kana.
  • Brand X: In "Calamity Man's Wedding", Alan imagined that "Alan & Ellie Foundation", their wedding gift, would be the talk of every news outlet with an image of "Taimu" magazine and "World Times" nwespaper as background, no doubt a parody of Time Magazine and China's "Global Times".
  • Catch Phrase: End of Demonstration. It's the translation of Quod Erat Demonstrandum.
  • Character Check: Sou was portrayed as an aloof boy at first, usually got dragged by Kana/Loki to solve a case. Character Development saw that he took initiatives on several cases without being asked. First chapter of iff had him revert to the "if-I'm-not-interested-don't-bother-me" mindset.
  • The Chessmaster: "Dog Bowl" is a story of how Sou demonstrate this ability of his to help a bunch of elderies in shogi community catch a serial con artist.
  • Child Prodigy:
    • Sou has a BS in Mathematics before the others even started high school. He's also quite famous at MIT, seen as one of two Aces of his year's batch with Loki.
    • A case involves an even younger child prodigy whose parents are about to divorce because they don't agree in how to educate the kid. She's the one who, at one time, invites couples on a brink of divorce along with her own parents so that they sort out their differences using Fermat's Last Theorem as theme.
    • Another example which serves as a twist. there's a case in iff which involves a betting website under server attack by a notorious underworld hacker called "Crash." Crash however upped the ante by attempting to take the company net security specialist's life because white hat named "Wizard" breached Crash's IP address. It turns out Wizard's current identity is a little girl named Chloe Rodriguez who got the handle name from Sou, who was implied to have used it at least back in his MIT years.
  • Church of Happyology: During one of Sou's flashbacks, District Attorney Annie Craner was assigned to prosecute a widower who is accused of murdering her husband so she can inherit his fortune to continue paying for the self-help cult like group called "The Path to Arcadia", an organization she is a part of. As the trial continues, the group sends death threats to Annie, protest against her and accuse the prosecution of a Witch Hunt. Then one of the widow's friend, an old lady, shoots her when the case is about to be finished. She seemingly was killed. Well, not. It got stranger from there, with her father involved.
  • Circling Birdies: Played for laughs with Kana: when Sou is tutoring Kana for her mathematics test, she doesn't understand it to the point there's some festival dancer circling over her head. And Sou can see them too.
  • Cloudcuckoolander
    • The Touma Family is really out there. Sou in one instance do his thinking at the bottom of a swimming pool. Yuu can think of Town Musicians of Bremen just by looking at a shrine gate and ema. And their father is thrilled to see a thunderstorm.
  • No Celebrities Were Harmed: Alan Blade, the richest man and the owner of the biggest software company? Are you sure you're not Bill Gates?
  • Common Tongue: Due to his past education at MIT, Sou gets to know a lot of friends and acquaintances from different parts of the world. However, they seem to know how to speak Japanese. While it's debatable whether it's a case of this or Translation Convention, Kana being Book Dumb is an argument agains the favor of the latter.
  • Cool Bike: Appears at least once as Kana's transportation method.
  • Crossover: Twice with C.M.B.. Shinra is Sou's cousin from his mother's side, cementing the fact that the mangas are in one universe.
  • Disproportionate Retribution:
    • Quite a few of the crimes' motivations, even the more serious crimes, are a result of seemingly minor offences blown far out of proportion by the perpetrators.
    • Sou himself can be utterly merciless when people he cares about are hurt.
      • An upperclassman's scheme to get a girl by engineering a conflict with her boyfriend who is also said upperclassman's friend - extremely petty considering Sou has faced actual murders - still had Sou coldly and ruthlessly humiliating said upperclassman at the end in front of the girl he was pining for and her boyfriend. All because his scheme had inadvertently hurt Kana's arm.
      • Sou had a good yet overconfident talent manager stripped off of the latest talent he was managing and then eventually fired from the industry using said manager's own personality because he talked down to Kana twice during a contract negotiation.
  • The Drag-Along: Sou is sometimes framed as one, as he's only doing the brainworks if someone (usually Kana, but not always) dragged him into the thick of the current Mystery of the Week.
  • Eagleland: Discussed. At least Eva believes that "if they dropped bombs all over the world, the USA would be the enemy of every nation in the world."
    Researcher 1: Do you think America should bomb every conflict?
    Researcher 2: Of course! That's America's duty as the world police!
  • Encyclopaedic Knowledge: For someone who took his major in Maths, Sou sure knows a lot about almost every other subjects, up to and including quantum physics, history, art, etc.
  • Everybody Hates Math: Or at least Kana, to the point of catatonia after hearing advanced math explanation. Kinda ironic that Sou got a Math Degree from MIT.
  • Faking the Dead: A case involves someone gathering people who hated him in his private cruise and faked his own stabbing so that those who hated him would be afraid to kill him later on. However, he didn't predict that one of them would stab him equal to the amount of potential suspect, thus killing him for good.
  • False Confession: In "Dedekind Cut", Sou did this so that Professor Hilbert would forget about John who supposedly stalks him. The reason he did it is because the professor has a persecution complex due to feeling inferior with John after Hilbert accidentally deleted John's papers which delays John from becoming an assistant. Due to that, Hilbert would makes a scene and assume that it was John who did it, creating a memory disorder and forget of him doing it. Before he confessed, Sou did try to tell him several times on why he refuse to go to court to accused John but Hilbert keeps forgetting, rejecting his answer. With no other choice and also partials to be blame for making him remember back note , he decides to 'confess' so that he would forget the whole incident with John. It works.
  • Foil:
    • Sou is one to his cousin, Shinra Sakaki. While both has similar approach to solve a problem, and similar high, if fair, esteem in their skills, Shinra is a happy-go-lucky boy that have no problem openly expressing his views, while Sou is more level-headed and prefers the subtle, yet pointed approach when communicating his thoughts (when he decides to do so anyway).
    • Conversely, Kana is one to Nanase. While both is Action Girls in their own rights, Kana prefers fighting with weapon as her school's Kendo Club Ace, while Nanase is adept in barehanded fighting as the local Aikido Dojo Ace. Besides that, Kana is a daughter of a middle-class household that often feels amazed with the upper class treatment given by Sou's friends and acquiantances, while Nanase is a granddaughter of a local upper-class family whose parents decided to live as a middle-class family by operating a public bathroom.
  • The Ghost: Sou and Yu's parents are mentioned sparsely and when they are their faces are never seen. A flashback in Q.E.D.iff finally subverts this.
  • Good Is Not Nice: In one case, Sou Touma mercilessly humiliates the culprit in front of his friends for accidentally hurting Kana's arm in his roundabout trick, erasing any chance of redemption for the said culprit. See Disproportionate Retribution trope above.
  • He Is Not My Boyfriend: But recent development has shown otherwise....
    • That is, until they played it straight again. Or it seems to be. Kana is made to believe that Sou believe this is the case while actually he said that their relationship is whatever Kana said.
    • Happens more often in the live-action adaptation, with more characters actually outright asking if Sou is Kana's boyfriend.
  • Hollywood Tone-Deaf: Singing is not Sou's forte at all. His singing ability is so bad people are stunned how anyone could be that horrible in singing.
  • Inspector Lestrade: Kana's father is a Police Inspector that occasionally get some help from Sou and his daughter.
  • It Runs in the Family: His sister is a linguist Cloudcuckoolander, his parents are renowned archaeologists. His teenage cousin is also the holder of the CMB Rings, and a curator in a museum.
  • Intelligence = Isolation: Loki was very lonely until Sou showed up. Similarly, Sou is bullied in his first year in uni because he is a Grade Skipper Teen Genius.
  • Improbable Age: Sou, the 14 years old MIT graduate.
  • Improbable Aiming Skills: Kana once threw a roof tile to a sniper located far away, and she deliberately missed only several centimeters away from the said sniper. Heck, the throw was only a distraction!
  • Instant A.I.: Just Add Water!: Averted, the cause of traffic crashes in Tokyo in Jacob's Ladders case is actually only a simple life-simulation program designed by Eva's team in MIT, looking for a large enough memory space as programmed.
    Loki: Poor guys, they only wanna live.
    Sou: No, they're only programmed that way. They are not alive.
  • Incorruptible Pure Pureness: Sou Touma. Good Is Not Nice indeed, but he can be extremely forgiving at times.
    • When Touma discovered that Eva was the one who destroyed his thesis back then in MIT, he did not make any attempt of revenge and went as far as asking Loki to forgive her.
    • Touma had enough motive (and brain capability) to kill everyone who had made Annie Cranernote  suffered in the past, but he did not do it because he simply is not a murderer, as acknowledged by his friends.
  • Karmic Death: A story in iff called "The Three Murderers" tells about three people who devise three separated murder plan on a money-hunger swindler. He evaded all those attempts by pure luck, but then suffocated himself when he tried to take his assets in the form of gold bars he hid under his swimming pool's drainage system.
  • Kendo Team Captain: Kana, despite being a girl, really counts.
  • Kid Detective: Sou is a bit of Sherlock Holmes-esqe type with an expansive knowledge on a variety of subjects that have nothing to do with detective work combining it with simple deductive reasoning. Though the way he and Kana stumble upon cases most times kind of makes him more like Jessica Fletcher.
  • Last-Name Basis: It causes some confusion in the Indonesian translation, where Yuu call his brother Touma, a.k.a. their family name.
  • Locked Room Mystery: Some of the cases available are this. Some of the solutions are usually simple. One locked room murder example is in "Black Nightshade" chapter.
  • Masculine Girl, Feminine Boy: The Action Girl Kana with calmer, academic Sou.
  • Mind Screw: In Chapter 38 where the bosses of Shanghai mafia kill each other. According to the witness, the last boss killed is murdered by the first boss killed. The truth is, Toma's friend, Hu Jia Hui, has feigned the death of the first boss in order to incite a Cycle of Revenge that destroys the mafia. Then who kills Hu in the end?
  • Mistaken for Murderer: Second case. Which is completely Played for Laughs since every person involved thought that their loved ones was the one who kill the Jerkass debitor, and as result, involved in Zany Scheme to protect the "suspect", while in reality, it was completely an accident.Spoiler 
  • Never My Fault:
    • During "In the Corner of the Galaxy", despite being proven that it's the professor who stole the alien picture, the professor still believes that he didn't do anything wrong based on the Jonbar Hinge theory. Cue Mizuhara Kana slapping his face for trying to cover it for his own benefit and accused for being the thief.
    • In "Red File", after the killer was captured, Director Uchiwa does this since he nearly lead his investment company into bankruptcy due to him selecting the riskiest program from one of Sou's friend, Chris Flyer. Unfortunately, Kana snaps him out of it since he should admit his own mistakes as he had a choice to choose safer options.
    • In "Venus", after the killer was arrested, it was revealed that his motive was due to witnessing the victim's misdeeds online and decide to kill him out of heroic justice (ala Social Justice Warrior). He even goes as far as to frame innocent suspects just because they are friends with the victim. However he was corrected by the police upon their investigations that the suspects have their own personal issues and the victim himself has financial issues, which also cause some haters to fake his misdeeds online. Unfortunately, the killer refuse to accept it; he argues that it has nothing to do with him, even going as far as to demand the police to apologize and release him. It is unknown if the victim's misdeeds are true but the killer deluded himself that he has nothing to do with it when the innocent suspects has not harm him at all or even know him.
  • No "Arc" in "Archery": Averted. Sou solved a case where a man is shot with an arrow using a bow in the end of a low corridor, and one of the facts he quickly notes is that the shot is almost impossible to do.
  • Non-Action Guy: Sou, so much. But that doesn't mean he's a complete wimp, though.
  • No Social Skills: As a result, Sou often incidentally angers other people, but that's because he just doesn't know any better. Kana helps him get over it, though.
  • Not-So-Fake Prop Weapon: This happens in one case where a male lead in a movie was accidentally stabbed by an actress during filming with a lot of press covering the scene. Investigation then said that the knife used to stab the male lead could only be switched in public. It's not unintentional on the actress' behalf. She switched the knife herself using her daughter who starred in the same film as distraction.
  • Omnidisciplinary Scientist: If there's a science-thingy need explaining, be it history, advanced mathematics, or even quantum physics, Sou will be there to explain it. And Loki will be there to dumb it down.
  • Onsen Episode: Subverted in the fact that it while the lands had an onsen, there was a murder and they went there to translate documents. They never got a chance to get into the onsen itself.
  • Parental Abandonment: Downplayed. The Sou siblings doesn't seems to be very close with their parents. But they understand their parent's motivation and independent enough to be living by themselves.
  • Platonic Life-Partners: This seems to be the default for Kana and Sou's relationship, with Kana saying that their relationship doesn't have a name yet.
  • Renaissance Man: Sou is one. Let's see... BS in Mathematics from MIT before enrolling in a Japanese High School, knowledgeable in (at least) Computer Science, Physics, Biology (including Botany), History, Geography, International Law; fluent in at least English, Japanese, German, Spain; hold some patents too...
  • Title Drop: Always shown before Sou's deduction in one way or another, usually related to the case itself (as a command prompt in a case related to computers, and cards in a case related to games). Also, since the full original title is Q.E.D. - Shoumei Shuuryou and Sou's habit of ending his explanation using "Shoumei Shuuryou" (translated into "End of demonstration") can be considered act of one.
  • Ship Tease: Happens once in a while with Sou and Kana in the manga. In fact, the manga has this going until "The Rainbow Mirror" case and beyond, after which the tease is non-subtly phased out for clear affection from both sides (and still able to make it platonic).
    • The live action series is even more blatant, with a love song playing over the pair as the ending theme. The penultimate episode even ends with Kana taking an imaginary picture of Sou and holding it to her heart, and the finale is a Maybe Ever After that all but outright states they're a couple now.
    • There's also some between Alan Blade and Ellie. Despite his often spoiled and rude characteristics, he seems to hold her and her loyalty in special regard and confidence. There's also hints that despite Ellie's exasperation with him sometimes, she sticks with him out of more than just being a loyal secretary. Confirmed in chapter 43 where Alan proposes and she gladly accepts.
  • Shipper on Deck: Annie was glad that Sou was finally more open to other people, she went as far as supporting him to be with Kana and saying that she "would not be so mean" to appear in Sou's life again and risking Sou's "relationship" with Kana.
  • Shown Their Work: Its notable that everything Sou, or someone else, explains is often correct and accurate though unfortunately scientific develops make have since debunks some of these theories such as the chapter revolving around "dark matter." note 
  • Shut Up, Hannibal!: Sou delivers one in the "John Doe Serial".
    Sou: I never wants to be a god. I only want to be a human.
  • They Fight Crime!: Though mostly by Kana's insistence.
  • The Unreveal: The culprit's name in the "John Doe Serial" case is never revealed. It's in line with the theme of the case, though.
  • Viewers Are Geniuses: This is probably why it took so long to get scanlated, since many of the terms are just too... advanced for someone who didn't take university or understand the subject matter.
    • For example, Sou can have a casual conversation on Quantum Mechanics. You know, the thing Stephen Hawking was working on.
  • Villainous Breakdown: A calm and composed seasoned scammer who has been able to get away with his crime deliver this when Sou uses his scamming tricks against him and erases any chance for him to evade compensating his victims and escape fraud charges, which ultimately ends with his arrest because he expresses his anger by hitting the one he intially recruited to be his scapegoat in public.
  • Voice with an Internet Connection: If he really has to, Sou prefer to be this to Kana's fieldwork. Of course, he'd rather instruct Kana what to do and wait for the result without any supervision whatsoever, but if he feels like it, he'll give Kana everything she'll need to finish the mission, and maybe chat with her.
  • The Watson: Kana plays this role, but rare for the genre, Kana is shown to be able to pretty easily follow Sou's train of thought and often helps solve the case just as much as Sou does.
    • Even then, that's because Sou takes time to explain things to Kana (he figured out she will be more helpful if she gets what she was doing) and even then, sometimes if the explanation involved advanced science (like mathematic, for example)... yeah.
  • The Wonka: Alan Blade from Alansoft is a very... problematic man to say the least. He's also the CEO of Alansoft, whose OS penetrated 90% of the world's computer.
    Alan (while fishing in his own swimming pool): Ellie, do you know about my worries? First, it's these tax deductions. Second, the quality of our recent employee has goes down. Third, I am getting bored of my hobby of Trout Fishing!


Sou: End of Demonstration.


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