One day, the Russian physicist Piotr Kapitsa asked Paul Dirac for his opinion on the book *Crime and Punishment* . The latter’s laconic response: “Very well, but the author was mistaken, because he described two sunrises on the same day.” Dirac spoke little, very little and never to say nothing. It is said that his physicist colleagues and students had invented a unit to measure the rate of speech, the “Dirac”, equivalent to “one word per day.” Preliminary and minimalist, Dirac’s words therefore have a specific weight: neither long tirade nor trivial remark. However, this singular but phlegmatic man was more than a researcher with a fertile and proliferative imagination. Dirac’s silence masked his very talkative dialogues, using a new language, with mathematical objects that live in abstract spaces and reveal the harmony and “Beauty” of the equations of physics.

**A life of passion for mathematics**

Dirac was born in Bristol on 8 August 1902. He attended primary school, then the technical college where his father taught French. Very early at school, he was described as a quiet student, except to correct the teacher. At the age of 13, a teacher gave him, in order to keep him occupied, a book on Riemannian geometry, which generalises the traditional geometry of Euclid in curved spaces, a discipline normally taught in the 3rd ^{cycle} of mathematics at the University. He devoured the book, the premise of a vocation.

However, at the age of 16, and at his father’s express request, he studied electrical engineering at the University of Bristol. Dirac became an engineer in 1921, but this degree would not serve him: he preferred to change direction. It was mathematics and physics that found favor in his eyes. Dirac was not yet 20, but he had already studied Einstein’s general relativity as an autodidact, which fascinated him. He found it surprisingly “beautiful” even if certain mathematical subtleties prevented him from accessing a deep understanding of the subject. He applied for and received a scholarship to study mathematics at the University of Bristol, allowing him to acquire advanced training in mathematics, which would be very useful to him.

In 1923, Dirac enrolled in a PhD program at Cambridge’s Department of Scientific and Industrial Research, which was at the heart of the ongoing quantum revolution. He was fascinated by the beauty contained in the equations of general relativity, but to his dismay, his supervisor Ralph Fowler invited him to study quantum physics instead.

Although he initially seemed to lack enthusiasm for this new vision of the atomic world, he would very quickly develop an attraction to this theory after encountering the work of Niels Bohr , Erwin Schrödinger and Werner Heisenberg . Concerning the formalism developed by the latter, Dirac would also have these words: “Nature cannot be so complicated”.

**The search for “beauty” and “truth”**

This is how Paul Dirac set out, guided by his characteristic sense of the “beautiful”. In May 1926, he defended his thesis under the most succinct title, *Quantum Mechanics* , in which he developed a new mathematical formulation of quantum mechanics, known as Dirac algebra. This avant-garde work elegantly demonstrates that the two formalisms of quantum physics, formulated respectively by Heisenberg and Schrödinger, are equivalent and therefore describe the same physical reality.

After this work, he continued his almost mystical quest for the “beautiful” and the “true” of physics, he took up the famous Schrödinger equation which describes the movement of particles on a quantum scale. The equation is certainly “beautiful”, but, and this is its big flaw, it is not relativistic: it cannot describe quantum particles moving at speeds close to those of light.

It was on this problem that Dirac was seized by a happy *eureka moment* . By reformulating Schrödinger’s equation, his calculations revealed two new notions. On the one hand, electrons seem to have a mysterious property: spin . On the other hand, this equation, now called the “Dirac equation”, has two solutions: one with a negative electric charge, which describes an electron, and the other with a positive charge! Everything happens as if each particle in the universe was associated with its double, an antiparticle, which would have exactly the same mass, but an opposite charge.

This mathematical consequence of Dirac’s equation was subject to much criticism and was rejected by all physicists of the time. After years of debate and hard work, Dirac gave in to the “beauty” and “truth” of his equation and named the hypothetical particle of negative energy an “antielectron”.

In 1932, the American physicist Carl David Anderson, while studying cosmic radiation, observed, using a cloud chamber, a particle with a charge opposite to that of the electron but with a mass much lower than that of the proton, the only positively charged particle known at the time. This particle marked the discovery of antimatter. On this subject, Dirac would later say: “My equation was smarter than me.”

**Dirac’s Legacy**

Dirac leaves behind a considerable legacy. He is frequently cited as one of the most influential scientists in English history. His name is displayed on a commemorative plaque in Westminster Abbey, alongside Isaac Newton, Charles Darwin and Stephen Hawking.

He remains one of the founding fathers of quantum physics, perhaps the theory that has best withstood the test of time and scientific challenges. The applications related to his equation number in the hundreds.

His contributions have been invaluable to many fields of physics. We detect antiparticles created by phenomena such as cosmic radiation, lightning or natural radioactivity on a daily basis . His proposals for the formalism of quantum physics are still widely used in signal processing.

**Antimatter: from theoretical physics to medicine**

Today we know how to create and store positrons and antiprotons. In medicine, positron detection is used to scan the human body, this is the technique of positron emission tomography, or PET-scan. By injecting tracers into the patient’s bloodstream, weakly radioactive biological substances that bind to glucose, it is possible to detect cancerous tissues, which consume large amounts of glucose. During their radioactive decay, these tracers emit positrons that provide valuable information to identify the position of the tumor.

The PET scan thus makes it possible to produce a functional image of the organism by targeting the activity of a specific organ. The applications are numerous: detection of small cancerous tumors, degenerative brain diseases such as Alzheimer’s or possible necrosis of cardiac tissue after a heart attack.

Starting from a research halfway between mathematics and aesthetics, Paul Dirac produced fundamental results that current physics continues to exploit. Through his quest for mathematical beauty, he opened a new field of understanding of our reality. On the occasion of a conference he gave when he received the James Scott Prize , he declared on this subject: “It is becoming increasingly evident that the formalisms that mathematicians find most interesting are also those that Nature has chosen for itself.”

**Author Bio:** Waleed Mouhali is a Teacher-Researcher in Physics at ECE Paris