Alexander Friedmann

Friedmann was born in Saint Petersburg and studied mathematics and physics at Saint Petersburg University, where he developed interests extending from pure mathematics to physical theory.¹ During the First World War he worked in military aviation and meteorology, experiences that connected his theoretical interests with atmospheric and ballistic problems. After the war, he held academic and research positions, including a professorship at the University of Perm, before returning to Petrograd and contributing to Soviet scientific institutions.² His broader research included hydrodynamics, meteorology, and the mathematics of relativity. This range mattered because Friedmann approached cosmology not as philosophical speculation but as a problem in differential equations and mathematical physics.

Friedmann’s central achievement was to demonstrate that Einstein’s field equations permit homogeneous and isotropic universes whose scale changes over time.¹ In his 1922 paper, he studied cosmological models with positive spatial curvature; a 1924 paper extended the analysis to spaces of constant negative curvature.² The modern Friedmann equations describe how the expansion rate depends on energy density, pressure, spatial curvature, and the cosmological constant. They underpin the standard mathematical treatment of the expanding universe, including models that expand forever, recollapse, or pass through different eras dominated by radiation, matter, or dark energy.³ Friedmann’s solutions did not by themselves establish which model describes nature; observations were needed to determine the parameters.

Friedmann’s first cosmological paper drew a published objection from Albert Einstein, who initially argued that the calculations contained an error. Friedmann replied by defending the derivation, and Einstein later acknowledged that the objection had been mistaken.¹ The episode illustrates how unfamiliar the idea of a changing cosmos was even within early relativistic physics. Friedmann’s work appeared before observational evidence for cosmic expansion had become widely accepted, and it was initially less influential than later treatments by Georges Lemaître and others. Once observations and theory converged on an evolving universe, Friedmann’s mathematical results became recognized as a foundational part of relativistic cosmology.⁴ The models are also associated with the broader Friedmann–Lemaître–Robertson–Walker framework, although that name reflects later synthesis rather than a single paper by Friedmann.

Friedmann’s scientific career was unusually broad for a theorist identified today mainly with cosmology. He contributed to meteorology and atmospheric modeling, and his wartime work included practical aviation research.² He also helped popularize modern physical ideas in Russian scientific culture through teaching and exposition. His life was brief: he died in 1925 after contracting typhoid fever, only a few years after publishing the work that established dynamic relativistic models.¹ A subtle point in his legacy is that “Friedmann universe” can refer to idealized models with no preferred location or direction, whereas actual cosmological modeling may add radiation, dark matter, dark energy, perturbations, and observational constraints. The name therefore covers both a historical discovery and a continuing family of mathematical models.

General relativity

Albert Einstein’s theory of gravitation in which matter and energy determine the curvature of spacetime.

Cosmological principle

The simplifying assumption that the universe is homogeneous and isotropic on sufficiently large scales.

Spatial curvature

The geometric curvature of three-dimensional space, commonly represented in cosmological models as positive, zero, or negative.

Cosmological constant

A term in Einstein’s field equations associated with the energy density of empty space and, in modern cosmology, dark-energy behavior.