30 November] 1784) was a Finnish-Swedish astronomer, mathematician, and physicist who spent most of his life in Imperial Russia, where he was known as Andrei Ivanovich Leksel (Андрей Иванович Лексель).

Lexell made important discoveries in polygonometry and celestial mechanics; the latter led to a comet named in his honour.

La Grande Encyclopédie states that he was the prominent mathematician of his time who contributed to spherical trigonometry with new and interesting solutions, which he took as a basis for his research of comet and planet motion.

Lexell was one of the most prolific members of the Russian Academy of Sciences at that time, having published 66 papers in 16 years of his work there.

At the age of fourteen he enrolled at the Royal Academy of Åbo and in 1760 received his Doctor of Philosophy degree with a dissertation Aphorismi mathematico-physici (academic advisor Jakob Gadolin).

She was aware of the importance of science and ordered to offer Leonhard Euler to "state his conditions, as soon as he moves to St. Petersburg without delay".

[3] Soon after his return to Russia, Euler suggested that the director of the Russian Academy of Science should invite Lexell to study mathematics and its application to astronomy, especially spherical geometry.

To be admitted to the Russian Academy of Sciences, Lexell in 1768 wrote a paper on integral calculus called "Methodus integrandi nonnulis aequationum exemplis illustrata".

He participated in observing the 1769 transit at St. Petersburg together with Christian Mayer, who was hired by the Academy to work at the observatory while the Russian astronomers went to other locations.

Lexell made a large contribution to Lunar theory and especially to determining the parallax of the Sun from the results of observations of the transit of Venus.

Hence, in 1780, Lexell was supposed to leave St. Petersburg and return to Sweden, which would have been a great loss for the Russian Academy of Sciences.

Therefore, Director Domashnev proposed that Lexell travel to Germany, England, and France and then to return to St. Petersburg via Sweden.

Sending academicians abroad was quite rare at that time (as opposed to the early years of the Russian Academy of Sciences), so Lexell willingly agreed to make the trip.

The aims were as follows: since Lexell would visit major observatories on his way, he should learn how they were built, note the number and types of scientific instruments used, and if he found something new and interesting he should buy the plans and design drawings.

[4] Lexell departed St. Petersburg in late July 1780 on a sailing ship and via Swinemünde arrived in Berlin, where he stayed for a month and travelled to Potsdam, seeking in vain for an audience with King Frederick II.

In Sweden he spent time in his native city Åbo, and also visited Stockholm, Uppsala, and Åland.

However, unofficial letters to Johann Euler often contain detailed descriptions of places and people whom Lexell had met, and his impressions.

On 18 September 1783, after a lunch with his family, during a conversation with Lexell about the newly discovered Uranus and its orbit, Euler felt sick.

Lexell became a corresponding member of the Turin Royal Academy, and the London Board of Longitude put him on the list of scientists receiving its proceedings.

[5] When applying for a position at the Russian Academy of Sciences, Lexell submitted a paper called "Method of analysing some differential equations, illustrated with examples",[6] which was highly praised by Leonhard Euler in 1768.

[9] Concurrently with Euler, Lexell worked on expanding the integrating factor method to higher order differential equations.

He stated that his method could be expanded for the case of four variables: "The formulas will be more complicated, while the problems leading to such equations are rare in analysis".

Lexell's first work at the Russian Academy of Sciences was to analyse data collected from the observation of the 1769 transit of Venus.

Lexell then found the record of a star observed in 1759 by Christian Mayer in Pisces that was neither in the Flamsteed catalogues nor in the sky by the time Bode sought it.

He then stated that, based on his data on various comets, the size of the Solar System can be 100 AU or even more, and that it could be other planets there that perturb the orbit of Uranus (although the position of the eventual Neptune was not calculated until much later by Urbain Le Verrier).