Paul Adrien Maurice Dirac, OM, FRS (8 August 1902 – 20 October 1984) was a British theoretical physicist. Dirac made fundamental contributions to the early development of both quantum mechanics and quantum electrodynamics. He held the Lucasian Chair of Mathematics at the University of Cambridge and spent the last fourteen years of his life at Florida State University. Among other discoveries, he formulated the Dirac equation, which describes the behaviour of fermions and which led to the prediction of the existence of antimatter. Dirac shared the Nobel Prize in physics for 1933 with Erwin Schrödinger, "for the discovery of new productive forms of atomic theory."

Paul Dirac was born in Bristol, England, and grew up in the Bishopston area of the city. His father, Charles Dirac, was an immigrant from Saint-Maurice in the Canton of Valais, Switzerland. His mother was originally from Cornwall and the daughter of a mariner. Paul had an elder brother, Félix, who committed suicide in March 1925, and a younger sister, Béatrice. His early family life appears to have been unhappy due to his father's unusually strict and authoritarian nature. He was educated first at Bishop Road Primary School and then at Merchant Venturers' Technical College (later Cotham School), where his father was a French teacher. The school was an institution attached to the University of Bristol, which emphasized scientific subjects and modern languages. This was an unusual arrangement at a time when secondary education in Britain was still dedicated largely to the classics, and something for which Dirac would later express gratitude.

Dirac studied electrical engineering at the University of Bristol, completing his degree in 1921. He then decided that his true calling lay in the mathematical sciences and, after completing a BA in applied mathematics at Bristol in 1923, he received a grant to conduct research at St John's College, Cambridge, where he would remain for most of his career. At Cambridge, Dirac pursued his interests in the theory of general relativity (an interest he gained earlier as a student in Bristol) and in the nascent field of quantum physics, under the supervision of Ralph Fowler. Dirac noticed an analogy between the Poisson brackets of classical mechanics and the recently proposed quantization rules in Werner Heisenberg's matrix formulation of quantum mechanics. This observation allowed Dirac to obtain the quantization rules in a novel and more illuminating manner. For this work, published in 1926, he received a Ph.D. from Cambridge.

In 1928, building on 2x2 spin matrices which he discovered independently (A Pais quoted Dirac as saying "I believe I got these (matrices) independently of Pauli and possibly Pauli got these independently of me") of Wolfgang Pauli's work on non-relativistic spin systems, he proposed the Dirac equation as a relativistic equation of motion for the wave function of the electron. This work led Dirac to predict the existence of the positron, the electron's antiparticle, which he interpreted in terms of what came to be called the Dirac sea. The positron was observed by Carl Anderson in 1932. Dirac's equation also contributed to explaining the origin of quantum spin as a relativistic phenomenon.

The necessity of fermions, i.e., matter being created and destroyed in Enrico Fermi's 1934 theory of beta decay, however, led to a reinterpretation of Dirac's equation as a "classical" field equation for any point particle of spin ħ/2, itself subject to quantization conditions involving anti-commutators. Thus reinterpreted as a (quantum) field equation accurately describing quarks and leptons, i.e., all elementary matter particles, this Dirac field equation is as central to theoretical physics as the Maxwell, Yang-Mills and Einstein field equations. Dirac is regarded as the founder of quantum electrodynamics, being the first to use that term. He also introduced the idea of vacuum polarization in the early 1930s. This work was key to the development of quantum mechanics by the next generation of theorists, and in particular Schwinger, Feynman, Sin-Itiro Tomonaga and Dyson in their formulation of quantum electrodynamics.

Dirac's Principles of Quantum Mechanics, published in 1930, is a landmark in the history of science. It quickly became one of the standard textbooks on the subject and is still used today. In that book, Dirac incorporated the previous work of Werner Heisenberg on matrix mechanics and of Erwin Schrödinger on wave mechanics into a single mathematical formalism that associates measurable quantities to operators acting on the Hilbert space of vectors that describe the state of a physical system. The book also introduced the delta function. Following his 1939 article, he also included the bra-ket notation in the third edition of his book, thereby contributing to its universal use nowadays.

In 1933, following his 1931 paper on magnetic monopoles, Dirac showed that the existence of a single magnetic monopole in the universe would suffice to explain the observed quantization of electrical charge. In 1975, 1982, and 2009 intriguing results suggested the possible detection of magnetic monopoles, but there is, to date, no direct evidence for their existence.

Dirac was the Lucasian Professor of Mathematics at Cambridge from 1932 to 1969. In 1937, he proposed a speculative cosmological model based on the so-called large numbers hypothesis. During World War II, he conducted important theoretical and experimental research on uranium enrichment by gas centrifuge.

Dirac's quantum electrodynamics made predictions that were - more often than not - infinite and therefore unacceptable. A workaround known as renormalization was developed, but Dirac never accepted this. "I must say that I am very dissatisfied with the situation," he said in 1975, "because this so-called 'good theory' does involve neglecting infinities which appear in its equations, neglecting them in an arbitrary way. This is just not sensible mathematics. Sensible mathematics involves neglecting a quantity when it is small — not neglecting it just because it is infinitely great and you do not want it!" His refusal to accept renormalization, resulted in his work on the subject moving increasingly out of the mainstream. However, from his once rejected notes he managed to work on putting QED on "logical foundations" based on Hamiltonian formalism that he formulated. He found a rather novel way of deriving the anomalous magnetic moment "Schwinger term" and also the Lamb shift, afresh, using the Heisenberg picture and without using the joining method used by Weisskopf and French and the two pioneers of modern QED, Schwinger and Feynman, in 1963. That was two years before the Tomonaga-Schwinger-Feynman QED was given formal recognition by an award of the Nobel Prize for physics! Weisskopf and French (FW) were the first to obtain the correct result for the Lamb shift and the anomalous magnetic moment of the electron. At first FW results did not agree with the incorrect but independent results of Feynman and Schwinger. The 1963-1964 lectures Dirac gave on quantum field theory at Yeshiva University were published in 1966 as the Belfer Graduate School of Science, Monograph Series Number, 3. After having relocated to Florida in order to be near his elder daughter, Mary, Dirac spent his last fourteen years (of both life and physics research) at the University of Miami in Coral Gables, Florida, and Florida State University in Tallahassee, Florida.

Amongst his many students was John Polkinghorne, who recalls that Dirac "was once asked what was his fundamental belief. He strode to a blackboard and wrote that the laws of nature should be expressed in beautiful equations."

Dirac married Eugene Wigner's sister, Margit, in 1937. He adopted Margit's two children, Judith and Gabriel. Paul and Margit Dirac had two children together, both daughters, Mary Elizabeth and Florence Monica. Margit, known as Manci, visited her brother in 1934 in Princeton from her native Hungary and, while at dinner at the Annex Restaurant (1930s–2006), met the "lonely-looking man at the next table." This account came from a physicist from Korea who met and was influenced by Dirac, Y.S. Kim, who has also written: "It is quite fortunate for the physics community that Manci took good care of our respected Paul A.M. Dirac. Dirac published eleven papers during the period 1939-46.... Dirac was able to maintain his normal research productivity only because Manci was in charge of everything else."

A reviewer of the 2009 biography writes: "Dirac blamed his [emotional] frailties on his father, a Swiss immigrant who bullied his wife, chivvied his children and insisted Paul spoke only French at home, even though the Diracs lived in Bristol. 'I never knew love or affection when I was a child,' Dirac once said." She also writes that "[t]he problem lay with his genes. Both father and son had autism, to differing degrees. Hence the Nobel winner's reticence, literal-mindedness, rigid patterns of behaviour and self-centredness. [Quoting the biography:] 'Dirac's traits as a person with autism were crucial to his success as a theoretical physicist: his ability to order information about mathematics and physics in a systematic way, his visual imagination, his self-centredness, his concentration and determination.'" Dirac was known among his colleagues for his precise and taciturn nature. His colleagues in Cambridge jokingly defined a unit of a dirac which was one word per hour. Niels Bohr complained that he did not know how to finish a sentence in a scientific article he was writing, Dirac replied, "I was taught at school never to start a sentence without knowing the end of it." He criticized the physicist J. Robert Oppenheimer's interest in poetry: "The aim of science is to make difficult things understandable in a simpler way; the aim of poetry is to state simple things in an incomprehensible way. The two are incompatible." Dirac himself wrote in his diary during his postgraduate years that he concentrated solely on his research, and only stopped on Sunday, when he took long strolls alone. An anecdote recounted in a review of the 2009 biography tells of Werner Heisenberg and Dirac sailing on a cruise ship to a conference in Japan in August 1929. "Both still in their twenties, and unmarried, they made an odd couple. Heisenberg was a ladies' man who constantly flirted and danced, while Dirac — 'an Edwardian geek', as [biographer] Graham Farmelo puts it — suffered agonies if forced into any kind of socialising or small talk. 'Why do you dance?' Dirac asked his companion. 'When there are nice girls, it is a pleasure,' Heisenberg replied. Dirac pondered this notion, then blurted out: 'But, Heisenberg, how do you know beforehand that the girls are nice?'" According to a story told in different versions, a friend or student visited Dirac, not knowing of his marriage. Noticing the visitor's surprise at seeing an attractive woman in the house, Dirac said, "This is... this is Wigner's sister". Margit Dirac told both George Gamow and Anton Z. Capri in the 1960s that her husband had actually said, "Allow me to present Wigner's sister, who is now my wife."

Dirac was also noted for his personal modesty. He called the equation for the time evolution of a quantum-mechanical operator, which he was the first to write down, the "Heisenberg equation of motion". Most physicists speak of Fermi-Dirac statistics for half-integer-spin particles and Bose-Einstein statistics for integer-spin particles. While lecturing later in life, Dirac always insisted on calling the former "Fermi statistics". He referred to the latter as "Einstein statistics" for reasons, he explained, of "symmetry".

Dirac once said: "God used beautiful mathematics in creating the world." Heisenberg recollects a friendly conversation among young participants at the 1927 Solvay Conference about Einstein and Planck's views on religion. Wolfgang Pauli, Heisenberg and Dirac took part in it. Dirac's contribution was a poignant and clear criticism of the political purpose of religion, which was much appreciated for its lucidity by Bohr when Heisenberg reported it to him later. Among other things, Dirac said:

Heisenberg's view was tolerant. Pauli, raised as a Catholic but soon to leave that church had kept silent after some initial remarks, but when finally he was asked for his opinion, jokingly he said: "Well, I'd say that also our friend Dirac has got a religion and the first commandment of this religion is 'God does not exist and Paul Dirac is his prophet.'" Everybody burst into laughter, including Dirac.

In 1984, Dirac died in Tallahassee, Florida where he is buried.

The Dirac-Hellmann Award at FSU was endowed by Dr Bruce P. Hellmann (Dirac's last doctoral student) in 1997 to reward outstanding work in theoretical physics by FSU researchers. The Paul A.M. Dirac Science Library at FSU is named in his honour. In 1995, a plaque in his honour bearing the Dirac equation was unveiled at Westminster Abbey in London with a speech from Stephen Hawking. His childhood home in Bristol is commemorated with a blue plaque and the nearby Dirac Road is named in recognition of his links with the city. A commemorative garden has been established opposite the railway station in Saint-Maurice, Switzerland, the town of origin of his father's family.