The DC Comics Universe is filled with mystical powers, super-powered beings, and scientifically advanced alien species. Even with these myriad wonders, one of the most elusive, sought-after, powerful, and mysterious elements remains the all-powerful Anti-Life Equation. Introduced by the legendary comics creator Jack Kirby in 1971, as part of his multi-title spanning Fourth World series, the Anti-Life Equation has been sought after by some of the DC Universe's most powerful and diabolical villains, most notably the notorious New God and master of the war world Apokolips, Darkseid.
The Anti-Life Equation was first postulated by Darkseid himself some 300 years in the past; after making contact with the Martians, Darkseid learned that their entire philosophy revolved around the "Life Equation", which is synonymous with free will. If a Life Equation exists, so goes Darkseid's logic, then the opposite must also exist. The Anti-Life Equation saps its sentient targets of free will, dominating them, and also imparts reality-distorting power, as well as dominion over life and death. Within the pages of Forever People #5, the name is derived as such, "if someone possesses absolute control over you—you're not really alive."
Darkseid's obsession over the Equation has brought his attention to Earth on more than one occasion, each time in search of bits and pieces of the Equation, which had been scattered throughout the totality of human subconsciousness. One such possessor of the Anti-Life Equation was "Billion Dollar" Bates, a rotund, obscenely wealthy businessman who had used the Equation to subvert the will of his competitors and become remarkably rich and powerful. He was thwarted by the Forever People and was subsequently killed by his own militia during a ritual meant to transmit his will across the planet. Darkseid, who had been following Bate's movements, then attempted to reacquire the Equation by cloning Bates.
While Bates was born with full knowledge of the Equation, he was ill-equipped to exploit it, using it to gain wealth rather than cosmic power, shortsightedness that didn't sit well with Darkseid, who would continue attacking Earth in search of the Equation. Several Earth-bound heroes know some, if not all, of the Equation, including the New God Mister Miracle, who has the will not to yield to it (and is one of the few people able to not be tempted by it); Teen Titan Empress also knows part of the Equation, which allows her limited control of the minds of some enemies. Such unsuspecting users included the Flash enemy, Pied Piper, who uses it unknowingly to control his victims
The total Equation has been utilized a few times throughout the history of the DC Universe. During the Death Of The New Gods storyline, Mister Miracle --- driven increasingly insane by Big Barda's death --- uses the Equation, eventually becoming obsessed with finding the killer of the New Gods. Though he himself perishes, he discovers that the Equation is the dark half of the all-powerful entity, the Source, from which all energy and life in the universe derives. The next most prominent use of the Equation was during Final Crisis: Darkseid, having finally acquired the full Equation, uses it to attack Earth, enslave billions (including several superheroes), and attempt to remake Earth as a New Apokolips. Most recently, the crossover storyline DCeased was set in a reality where the Anti-Life Equation transformed most of the DC Universe into zombies.
The Equation itself is represented thus: loneliness + alienation + fear + despair + self-worth ÷ mockery ÷ condemnation ÷ misunderstanding x guilt x shame x failure x judgment n=y where y=hope and n=folly, love=lies, life=death, self=dark side. The formula is usually depicted as a series of fiery, floating glyphs in an alien language, although speaking the Equation out loud allows Darkseid to assert his will and control on others, although several heroes (such as the aforementioned Mister Miracle; younger superhero Static; and the Flash, utilizing the Speed Force) can negate or overcome the effects of the Equation. What once began as a theorized concept has since grown into one of the most powerful formulas in DC Comics, and, when wielded, provides the ultra-powerful Darkseid near-omnipotent power, and the DC Universe some of its most classic stories.