Person: Haret, Spiru
Spiru Haret was a Romanian mathematician, astronomer and politician. He made a fundamental contribution to the n-body problem in celestial mechanics.
Mathematical Profile (Excerpt):
- The country sought independence from the Ottoman Empire and Russia, and the first major steps occurred at around the time Haret was born.
- Already while he was a high school student, Spiru Haret published two mathematics texts, one on algebra and one on trigonometry.
- Haret won the competition which provided funds for him to study in Paris.
- Haret studied mathematics and physics at the Sorbonne.
- Even if not decisive, Haret's results helped and determined Poincaré to search for, to find, and to offer new fundamental methods, primarily intended to tackle this problem, but revolutionary and useful for most domains of science.
- Haret's and Poincaré's achievements marked, respectively, the end of a old era and the beginning of a new era in celestial mechanics and, in general, in mathematics.
- Which is the link between Haret's and Poincaré's achievements from the narrow standpoint of the concrete problem they studied?
- Haret proved instability of the model of the nnn-body problem, but considering frequencies (mean motions) to be incommensurable.
- Taking also into account commensurabilities, and using generalized Fourier series (which generate quasiperiodic solutions), Poincaré proved the divergence of these series, which means instability, confirming in this way Haret's result.
- Haret's and Poincaré's results show that the question of the Solar system's stability remains still unsolved.
- Haret's work marked the beginning of the end of an era, that of exclusively quantitative endeavours in mathematics.
- "Spiru Haret's theorem" is to be naturally added to the logical succession of theorems with respect to this problem known as "Laplace-Lagrange theorem" and "Poisson's theorem".
- Using his own method to explain mathematically the phenomenon of secular acceleration of Moon's "mean motion", Spiru Haret gives a criterion for separating the higher order gravitational perturbations from every non-gravitational perturbation in the motion of natural or artificial celestial bodies ...
- After defending his thesis in 1878, Haret returned to Romania.
- Haret attempted to set up a system of mechanics that would describe the forces that govern social and economic phenomena.
Born 15 February 1851, Iasi, Romania. Died 17 December 1912, Bucharest, Romania.
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Origin Romania
Thank you to the contributors under CC BY-SA 4.0! 
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- @J-J-O'Connor
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References
Adapted from other CC BY-SA 4.0 Sources:
- O’Connor, John J; Robertson, Edmund F: MacTutor History of Mathematics Archive
