Alexander Friedmann was born to the composer and ballet dancer Alexander Friedmann (who was a son of baptized Jewish cantonist) and the pianist Ludmila Voyachek. He lived much of his life in Saint Petersburg. He fought in World War I (on behalf of Imperial Russia) as a bomber and later lived through the Russian Revolution of 1917.

Friedmann obtained his degree in St. Petersburg State University (1910), became a lecturer in St.-Petersburg State College of Mines, and a professor in Perm State University in 1918.

In June 1925 he was given the job of the director of Main Geophysical Observatory in Leningrad. In July 1925 he participated in a record setting balloon flight, reaching the elevation of 7,400 m (24,300 ft).

Friedmann died on September 16, 1925, at the age of 37, from typhoid fever that he contracted during a vacation in Crimea.

The moon crater Friedman is named after him.

Friedmann discovered the expanding - universe solution to the general relativity field equations in 1922, which was corroborated by Edwin Hubble's observations in 1929. Friedmann's 1924 papers, including "Über die Möglichkeit einer Welt mit konstanter negativer Krümmung des Raumes" (On the possibility of a world with constant negative curvature of space) published by the German physics journal Zeitschrift für Physik (Vol. 21, pp. 326 – 332), demonstrated that he had command of all three Friedmann models describing positive, zero and negative curvature, respectively, a decade before Robertson and Walker published their analysis.

This dynamic cosmological model of general relativity would come to form the standard for the Big Bang and steady state theories. Friedmann's work supports both theories equally, so it was not until the detection of the cosmic microwave background radiation that the steady state theory was abandoned in favor of the current favorite Big Bang paradigm.

The classic solution of the Einstein field equations that describes a homogeneous and isotropic universe is called the Friedmann – Lemaître – Robertson – Walker metric, or FLRW, after Friedmann, and Howard Percy Robertson and Arthur Geoffrey Walker, and Georges Lemaître who worked on the problem in 1920's and 30's independently of Friedmann.

In addition to general relativity, Friedmann's interests included hydrodynamics and meteorology.

George Gamow and Vladimir Fock were among his students.

After a classical education at a Jesuit secondary school (Collège du Sacré - Coeur, Charleroi), Lemaître began studying civil engineering at the Catholic University of Louvain at the age of 17. In 1914, he interrupted his studies to serve as an artillery officer in the Belgian army for the duration of World War I. At the end of hostilities, he received the Belgian Croix de Guerre with palms.

After the war, he studied physics and mathematics, and began to prepare for priesthood. He obtained his doctorate in 1920 with a thesis entitled l'Approximation des fonctions de plusieurs variables réelles (Approximation of functions of several real variables), written under the direction of Charles de la Vallée - Poussin. He was ordained a priest in 1923.

In 1923, he became a graduate student in astronomy at the University of Cambridge, spending a year at St Edmund's House (now St Edmund's College, Cambridge). He worked with Arthur Eddington who initiated him into modern cosmology, stellar astronomy, and numerical analysis. He spent the following year at Harvard College Observatory in Cambridge, Massachusetts, with Harlow Shapley, who had just gained a name for his work on nebulae, and at the Massachusetts Institute of Technology, where he registered for the doctorate in sciences.

In 1925, on his return to Belgium, he became a part time lecturer at the Catholic University of Louvain. He then began the report which would bring him international fame, published in 1927 in the Annales de la Société Scientifique de Bruxelles (Annals of the Scientific Society of Brussels), under the title "Un Univers homogène de masse constante et de rayon croissant rendant compte de la vitesse radiale des nébuleuses extragalactiques" ("A homogeneous Universe of constant mass and growing radius accounting for the radial velocity of extragalactic nebulae"). In this report, he presented his new idea of an expanding Universe (he also derived Hubble's law and provided the first observational estimation of the Hubble constant) but not yet that of the primeval atom. Instead, the initial state was taken as Einstein's own finite - size static universe model. Unfortunately, the paper had little impact because the journal in which it was published was not widely read by astronomers outside of Belgium.

At this time, Einstein, while not taking exception to the mathematics of Lemaître's theory, refused to accept the idea of an expanding universe; Lemaître recalled him commenting "Vos calculs sont corrects, mais votre physique est abominable" ("Your math is correct, but your physics is abominable.") The same year, Lemaître returned to MIT to present his doctoral thesis on The gravitational field in a fluid sphere of uniform invariant density according to the theory of relativity. Upon obtaining the PhD, he was named Ordinary Professor at the Catholic University of Louvain.

In 1930, Eddington published in the Monthly Notices of the Royal Astronomical Society a long commentary on Lemaître's 1927 article, in which he described the latter as a "brilliant solution" to the outstanding problems of cosmology. The original paper was published in an abbreviated English translation in 1931, along with a sequel by Lemaître responding to Eddington's comments. Lemaître was then invited to London in order to take part in a meeting of the British Association on the relation between the physical Universe and spirituality. There he proposed that the Universe expanded from an initial point, which he called the "Primeval Atom" and developed in a report published in Nature. Lemaître himself also described his theory as "the Cosmic Egg exploding at the moment of the creation"; it became better known as the "Big Bang theory," a term coined by Fred Hoyle.

This proposal met skepticism from his fellow scientists at the time. Eddington found Lemaître's notion unpleasant. Einstein found it suspect because he deemed it unjustifiable from a physical point of view. On the other hand, Einstein encouraged Lemaître to look into the possibility of models of non - isotropic expansion, so it's clear he was not altogether dismissive of the concept. He also appreciated Lemaître's argument that a static - Einstein model of the universe could not be sustained indefinitely into the past.

In January 1933, Lemaître and Einstein, who had met on several occasions - in 1927 in Brussels, at the time of a Solvay Conference, in 1932 in Belgium, at the time of a cycle of conferences in Brussels and lastly in 1935 at Princeton - traveled together to California for a series of seminars. After the Belgian detailed his theory, Einstein stood up, applauded, and is supposed to have said, "This is the most beautiful and satisfactory explanation of creation to which I have ever listened." However there is disagreement over the reporting of this quote in the newspapers of the time, and it may be that Einstein was not actually referring to the theory as a whole but to Lemaître's proposal that cosmic rays may in fact be the left over artifacts of the initial "explosion." Later research on cosmic rays by Robert Millikan would undercut this proposal, however.

In 1933, when he resumed his theory of the expanding Universe and published a more detailed version in the Annals of the Scientific Society of Brussels, Lemaître would achieve his greatest glory. Newspapers around the world called him a famous Belgian scientist and described him as the leader of the new cosmological physics.

On 17 March 1934, Lemaître received the Francqui Prize, the highest Belgian scientific distinction, from King Léopold III. His proposers were Albert Einstein, Charles de la Vallée - Poussin and Alexandre de Hemptinne. The members of the international jury were Eddington, Langevin and Théophile de Donder. Another distinction that the Belgian government reserves for exceptional scientists was allotted to him in 1950: the decennial prize for applied sciences for the period 1933 - 1942.

In 1936, he was elected member of the Pontifical Academy of Sciences. He took an active role there, becoming its president in March 1960 and remaining so until his death. During Vatican II he was asked to serve on the first special commission to examine the question of contraception. However, as he could not travel to Rome because of his health (he had suffered a heart attack in December 1964), Lemaître demurred, expressing his surprise that he was even chosen, at the time telling a Dominican colleague, P. Henri de Riedmatten, that he thought it was dangerous for a mathematician to venture outside of his specialty. He was also named prelate (Monsignor) in 1960 by Pope John XXIII.

In 1941, he was elected member of the Royal Academy of Sciences and Arts of Belgium.

In 1946, he published his book on L'Hypothèse de l'Atome Primitif (The Primeval Atom Hypothesis). It would be translated into Spanish in the same year and into English in 1950.

In 1953, he was given the very first Eddington Medal awarded by the Royal Astronomical Society.

During the 1950s, he gradually gave up part of his teaching workload, ending it completely with his éméritat in 1964.

At the end of his life, he was devoted more and more to numerical calculation. He was in fact a remarkable algebraist and arithmetical calculator. Since 1930, he used the most powerful calculating machines of the time, the Mercedes. In 1958 he was introduced to the University's Burroughs E 101, its first electronic computer. Lemaître maintained a strong interest in the development of computers and, even more, in the problems of language and programming. Throughout his latter years these were abiding interests until they absorbed him almost completely.

He died on 20 June 1966, shortly after having learned of the discovery of cosmic microwave background radiation, which provided further evidence for his intuitions about the birth of the Universe.

In 2005, Lemaître was voted to the 61st place of De Grootste Belg (Dutch for "The Greatest Belgian"), a Flemish television program on the VRT. In the same year he was voted to the 78th place by the audience of the Le plus grand belge (French for "The Greatest Belgian"), a television show of the RTBF.

Lemaître was a pioneer in applying Albert Einstein's theory of general relativity to cosmology. In a 1927 article, which preceded Edwin Hubble's landmark article by two years, Lemaître derived what became known as Hubble's law and proposed it as a generic phenomenon in relativistic cosmology. Lemaître also estimated the numerical value of the Hubble constant. However, the data used by Lemaître did not allow him to prove that there was an actual linear relation, which Hubble did two years later.

Einstein was skeptical of this paper. When Lemaître approached Einstein at the 1927 Solvay Conference, the latter pointed out that Alexander Friedmann had proposed a similar solution to Einstein's equations in 1922, implying that the radius of the universe increased over time. (Einstein had also criticized Friedmann's calculations, but withdrew his comments.) In 1931, Lemaître published an article in Nature setting out his theory of the "primeval atom."

Friedmann was handicapped by living and working in the USSR, and died in 1925, soon after inventing the Friedmann - Lemaître - Robertson - Walker metric. Because Lemaître spent his entire career in Europe, his scientific work is not as well known in the United States as that of Hubble or Einstein, both well known in the U.S. by virtue of residing there. Nevertheless, Lemaître's theory changed the course of cosmology. This was because Lemaître:

• Was well acquainted with the work of astronomers, and designed his theory to have testable implications and to be in accord with observations of the time, in particular, to explain the observed redshift of galaxies and the linear relation between distances and velocities;
• Proposed his theory at an opportune time, since Edwin Hubble would soon publish his velocity - distance relation that strongly supported an expanding universe and, consequently, the Big Bang theory;
• Had studied under Arthur Eddington, who made sure that Lemaître got a hearing in the scientific community.

Both Friedmann and Lemaître proposed relativistic cosmologies featuring an expanding universe. However, Lemaître was the first to propose that the expansion explains the redshift of galaxies. He further concluded that an initial "creation - like" event must have occurred. In the 1980s, Alan Guth and Andrei Linde modified this theory by adding to it a period of inflation.

Einstein at first dismissed Friedmann, and then (privately) Lemaître, out of hand, saying that not all mathematics lead to correct theories. After Hubble's discovery was published, Einstein quickly and publicly endorsed Lemaître's theory, helping both the theory and its proposer get fast recognition.

Lemaître was also an early adopter of computers for cosmological calculations. He introduced the first computer to his university (aBurroughs E101) in 1958 and was one of the inventors of the Fast Fourier Transform algorithm.

In 1933, Lemaître found an important inhomogeneous solution of Einstein's field equations describing a spherical dust cloud, the Lemaître – Tolman metric.

In 1948 Lemaître published a polished mathematical essay "Quaternions et espace elliptique" which clarified an obscure space. William Kingdon Clifford had cryptically described elliptic space in 1873 at a time when versors were too common to mention. Lemaître developed the theory of quaternions from first principles so that his essay can stand on its own, but he recalled the Erlangen program in geometry while developing the metric geometry of elliptic space. H.S.M. Coxeter, another contributor to elliptic geometry, summarized Lemaître's work for Mathematical Reviews.