Can a butterfly flapping its wings across the globe cause a hurricane?  “No one can predict a hurricane,” states Arthur Seldom, a mathematics professor emeritus who plays logic against the odds.  When an American student named Martin crosses the globe to get near Seldom in a grad program, his mentorship mixed with universal questions, unrequited love, wrath, and destiny test the theorems of Seldom.  Seldom states, “No truth exists outside of mathematics.  Philosophy is dead so there is no refutable truth to answer the questions of mankind.”  But when a symbolic structure of a mathematical paradigm and the Fibonacci sequence intersect with a series of murders, the riddle combines the wits of the seasoned professor played by John Hurt and the student played by Elijah Wood.
The butterfly effect is Elijah Wood, the Oxford grad student, who rents from the home of Julia Eagleton, widower of the inventor of factual dimensions who helped decipher German codes with an Enigma machine in WWII.  He chose the residence because Ms. Eagleton is connected to Arthur Seldom through a tragic car accident that killed both their spouses.  Without intending to, Julia’s daughter Beth falls for Elijah and asks him how to feel free.  She feels trapped caring for her mother, who has outlived cancer five years.  Martin says, “I’d rather make mistakes than do nothing.  I’d rather mess up than miss out completely.”  
The next scene portrays Seldom in a rare public lecture where Martin challenges the professor.  “I believe in the number Pi. The source of nature is organized by a numerical basis that follows a model in which the secret meaning of numbers will result in the secret meaning of reality.”  Martin is basing his postulate on the belief that following a sequence will reveal a deeper meaning to life and causation.  Pythagoras reality is essentially mathematical in nature, a system of principles existing through numbers.
This scene sets the stage for a series of murders that take place in which the murderer leaves a Pythagoras symbol at each crime.  The first to die is Julia Eagleton. A circle symbol is left and also the word “kreis,” which means circle in German, arranged on her Scrabble ledger.  The first to arrive at the scene of the crime, at the same time, are Martin and Arthur.  Martin, doubting his choice to stay at Oxford after his mentor ridicules him in public, was coming home to impulsively gather his belongings.
When the police arrive, Arthur reveals to them that the circle is the parent shape that allows all the other shapes to exist from the center of the circle, based on Pythagoras.  He doesn’t reveal the exact theory but a foreshadowing hunch that it is the handiwork of someone to get his attention as a scholar.  He assures the police that another symbol will most likely be present at the next serial death.  
A short time later, a man dying in a hospital bed next to Arthur’s friend Kalman is given a deadly intravenous needle accompanied by a fish symbol, or two intersecting circles.  The symbol that is created from two intersecting circles is called a dyad, which represents duality or otherness.  The center created by two circles intersecting is the idea of expansion from the core.  The ancient mathematicians paralleled symbols to symmetry and patterns in the universe. The Greeks said the dyad is audacious because of the boldness of separation from the one circle and because of the anguish at the tension to return to one.  
Needless to say, the symbolism of the next crime heightens Martin and Arthur’s trail of complexity as they try to assist the police in anticipating the third murder.  Martin stumbles upon Arthur at Guy Fawkes Night, a traditional celebration to honor King James I, who survived a gunpowder plot.  During the performance, one of Martin’s classmates attempts to hang a malicious banner, which draws the police off the trail of an orchestra member who falls to his death while playing the triangle.  The triangle or tetrad symbol, which reaches into the corners of the circle, is supposed to produce harmony, stability, and synthesis after war.  A circle drawn along a line that connects the two centers from the lines of the triangle creates a perfect square shape that conveys four seasons, four ages of man, and four directions of the earth.  Four becomes the perfect number in the decad, the number 10, as well. 1 + 2 + 3 + 4 = 10, and is associated with wholeness.  Four is the last number to complete the equation.  The power of the number 10 lies in the number four, the tetrad, for if one exceeds the tetrad, one will exceed the number 10 (Aetius).  
The significance of an orchestra player who dies with a triangle symbol on his music stand is not given credence until Arthur tells Martin of a murder where a man plotted 14 ways to kill his wife in a diary.  She discovered the diary and murdered him instead, but was acquitted by the jury because of the atrocity of the diary.  Years later, it was discovered that the wife’s lover planted the diary to make it look like he intended to kill.  Arthur Seldom states, “The perfect crime is not one which is solved, but solved incorrectly.”  
The last number sequence is a decad, a symbolic combination of triangles that will reveal the intent of the serial killer.  Martin speculates that the killer this time may be interested in killing more than just one person.  While he is in the bookstore with his girlfriend Lorna, they discover the pattern of the Pythagorean Theorem and realize the last incident may be crucial.  Martin’s girlfriend picks up a book in the bookstore that states that serial killers may use weaker victims in society to do experiments.  Martin has a flashback and remembers a man holding the same book on surgery, the same man he saw next to the man who died in the hospital.  Frank, the man with the book, was visiting his daughter who was dying of lung disease and needed a transplant.  
Martin tips the police off that the man is a bus driver for developmentally disabled students and that he may try to kill one or some of the students to transplant an organ to save his daughter’s life.  The police stop the wrong bus, and Arthur Seldom is interrogated but is still unaware that Frank has hijacked the bus of kids and intends to kill them.  Eventually the police find the location of Frank and the kids, but as soon as they do, the bus blows up, killing everyone.  Frank was going to jump out of the bus with the intent to kill the students and use one of their organs to save his daughter.  
Only Martin solves the full riddle.  Julia was killed intentionally by her daughter because she wanted to live free, and Arthur covered it up.  He put a needle in a dying man’s arm that was not lethal but included a dyad symbol.  The police are duped and rely on Arthur for a third possibility of death.  The man who died at the concert was just a coincidence.  But the man who killed the disabled children intended to, because he was inspired by Arthur’s pursuit of symbols in all the deaths.  He fulfilled the symbol of the decad by killing ten children.  
At the end of the movie, Martin poses the butterfly theory to Arthur, who states that none of his actions caused real-life consequences.  Yet, his false presentation of symbolized death motivated a father to kill.  Martin states, “In the real world, any decision has irreversible consequences.  Truth is not numbers.  Truth is absurd, random, and deeply unpredictable” implying humans are not part of an orchestrated continuum.   Arthur’s earlier words in the film: “Numbers are not pre-existing concepts… man is incapable of reconciling mind and matter or can confer an entity on ideas.  Or can bear the notion that the purely abstract exists in our brain.”   When abstract thinking provokes blood, consequences prevail.
Martin moves beyond those cerebral transfixions when he discovers love in the movie, saying, “You are the unshaken heart of a well-rounded truth.”  The circular thinking sways and causes fluctuations.  Oppositionally, the realization of lying and wrongdoing transcends numerical definition.  Man’s deception can outweigh fate, destiny, and consequence.  Grade A-