London Learned Societies
British Association for the Advancement Of Science
Institute of Actuaries
London Mathematical Society
Royal Astronomical Society
Royal Society of Arts
The Spitalfields Mathematical Society
Institute of Actuaries
London Mathematical Society
Royal Astronomical Society
Royal Society of Arts
The Spitalfields Mathematical Society
British Association for the Advancement Of ScienceThe British Association for the Advancement Of Science (BAAS) was founded in 1831 and is presently at Fortress House, 23 Savile Row, London, W1X 1AB. Its Section A is mathematics, though this has rarely been a major feature of the Association. Nonetheless a number of its presidents have been of mathematical interest: Airy (1851), Hopkins (1853), Stokes (1869), Thomson (Lord Kelvin) (1871), Spottiswoode (1878), J. J. Thomson (1909), Rutherford (1923), W. H. Bragg (1928), Jeans (1934), D. Hodgkin (1977).
Institute of ActuariesThe Institute of Actuaries was founded in 1848 and is located in Staple Inn Hall, High Holborn.
London Mathematical SocietyThe London Mathematical Society (LMS) had for a long time its office in the Royal Astronomical Society (see below) but has now moved to De Morgan House, Russell Square. It was founded in 1865 by G. C. De Morgan, A. C. Ranyard and friends. Augustus De Morgan was the first President and T. A. Hirst was first Vice-President. Almost all notable British mathematicians since then have been officers and/or have received prizes of the LMS. The premier prize is the triennial De Morgan Medal, first given to Cayley in 1884. This has now been supplemented with a new Polya Medal, to be given in the years that the De Morgan Medal is not given. The first recipient was John Conway, in 1987.
Royal Astronomical SocietyThe Royal Astronomical Society, in Burlington House, Piccadilly, has numerous portraits and busts of mathematical interest. It even has a piece of Newton's apple tree!! This is apparently as authentic as it is possible to be. It also has De Morgan's scrapbooks. Babbage, F. Baily, Colebrooke, O. Gregory, J. Herschel, J. South were among the founders. W. Herschel was first president, with Babbage, Bailey and J. Herschel among the first secretaries. John Louis Emil Dreyer, the cataloguer of nebulae and clusters and historian of astronomy (particularly of Tycho Brahe), was President in 1923-1925.
In Jan 1935, Subrahmanyan Chandrasekhar presented his ideas on the collapse of stars to the Society. Eddington and others were incredulous. The ideas were the foundation of red giants, neutron stars, quasars and black holes. It was 33 years before the discovery of pulsars and the recognition that they were neutron stars verified his predictions, leading to the Nobel Prize in Physics in 1983. 
Royal InstitutionThe Royal Institution is in its original building at 21 Albemarle Street. It was founded in 1799 by the American Benjamin Thomson, later Count Rumford. It has a most distinguished history in the physical sciences. Its directors have included Davy, Faraday, Tyndall, Dewar, Rayleigh, J. J. Thomson, Rutherford, both Braggs, Andrade and George Porter! Thomas Young was also here, and there is some connection with Henry Cavendish. Maxwell demonstrated the first colour photograph here on 17 May 1861 (see in Section 3 for details). The Ambulatory, under the famous Lecture Theatre, has exhibits and memorabilia relating to notable persons connected with the Institution. The Institution possesses one of two examples of a wave demonstration model made by Wheatstone, c1840 . Rayleigh was Professor in 1887-1905 when he discovered argon - Nobel Prize in Physics, 1904. J. J. Thomson described his discovery of the electron here on 29 Apr 1897. He was Professor here in 1905-1920 - Nobel Prize in Physics, 1906.
Royal SocietyThe Royal Society is now at 6 Carlton House Terrace, an elegant Regency building overlooking The Mall, designed by John Nash in 1827-1829. (Not in Pall Mall, as given in .
The Royal Society is a outgrowth of groups which started meeting in London and in Oxford in 1645. At the Restoration, many of these people had moved to London. The group generally met at Gresham College at the time of the Society's founding in 1660 and for some time after its first Charter of 15 Jul 1662. On 28 Nov 1660, a group gathered to hear a lecture by Wren and decided to meet weekly. There were 12 in this group: Ball, Boyle, Brouncker, Bruce, Goddard, Hill, Moray, Neile, Petty, Rooke, Wilkins, Wren. Wilkins was appointed chairman, Ball Treasurer and Croone, though absent, Registrar (= Secretary). They resolved to meet at Rooke's room in Gresham College during term time and at Ball's room in the Temple in vacation. They made a list of 41 others who might be interested in joining, nearly all of whom later joined. On 5 Dec, Sir Robert Moray reported that the King was encouraging and an expanded list of names was prepared, consisting of almost all those on the previous list and 73 others. The poet Abraham Cowley was one of the 41 and was elected on 6 Mar 1661. Later in 1661, he published A Proposition for the Advancement of Experimental Philosophy which advocated a College of twenty professors. However, he moved away from London and was not one of the Charter members. The Society was originally open to all interested, but since 1848 elections are limited to distinguished scientists, at most 40 per year, with at most 6 Foreign Members.
Prior to the first charter, the President or Director was a monthly post and rotated among Moray, Wilkins, Brouncker, Boyle and possibly George Ent. The first Charter was granted on 15 Jul 1662, naming 21 persons as the Council: Balle, Boyle, Brereton, Brouncker (President), Timothy Clarke, Digby, Ent, Erskine, Evelyn, Goddard, Henshawe, Moray, Neile, Oldenburg (Secretary), Dudley Palmer, Petty, Slingesby, Wallis, Wilkins, C. Wren, M. Wren. The Society was considerably reorganized by a second charter on 22 Apr 1663 with the fuller name "the Royal Society of London for promoting Natural Knowledge", with Brouncker still as President and Wilkins and Oldenburg as Secretaries. (There was a third charter in 1669, but it was basically a grant of land and made few changes.) In May and Jun 1663, 119 original fellows were named. Ashmole, Aubrey, Barrow, Boyle, Brouncker, Colwall, Croone, Digby, Ent, Evelyn, Glisson, Goddard, Graunt, Hooke, Huygens, Moray, Neile, Oldenburg, Pell, Pett (father & son), Petty, Walter Pope, Vermuyden, Wallis, Ward, Wilkins, F. Willoughby, Wren were among these, along with the poets Denham, Dryden and Waller. The Philosophical Transactions was started by Oldenburg in 1665 and is the oldest continuing scientific journal. (The Journal des sçavans also started in 1665, but I don't know whether it was before or after this.)
The RS continued to meet at Gresham College until 1710, except when displaced as a result of the Great Fire to Arundel House, on the south side of the Strand at Arundel St, from 1666 to 1673. In 1710, it bought a house in Crane Court, on the north side of Fleet St, a site now(?) occupied by the Scottish Corporation. In 1780, it moved to Somerset House; in 1857, it moved to Burlington House, Piccadilly; in 1968, it moved to the present site.
Mathematical PRSs have been: Brouncker (1662-1677), Wren (1680-1682), Newton (1703-1727), Davies (Giddy) Gilbert (1827-1830 - he wrote on negative numbers), William Parsons, third Earl of Rosse (1848-1854), Airy (1871-1873), Spottiswoode (1878-1883), Stokes (1885-1890), Thomson (Lord Kelvin) (1890-1895), Rayleigh (1905-1908), J. J. Thomson (1915-1920), Rutherford (1925-1930), W. H. Bragg (1935-40), Blackett (1965-70), Atiyah (1990-1995).
The Society's premier medal is the Copley Medal, begun in 1731, which has occasionally been awarded to mathematicians and others of interest: Bradley (1748), J. Harrison (1749), B. Franklin (1753), Charles Hutton (1778), Waring (1784), Ramsden (1795), Hellins (1798), Troughton (1809), Ivory (1814), Brewster (1815), J. Herschel (1821), Arago (1825), Peter Barlow (1825), Airy (1831), Faraday (1832), Poisson (1832), G. Plana (1834), Gauss (1838), Faraday (1838), Robert Brown (1839), Sturm (1840), Ohm (1841), MacCullagh (1842), LeVerrier (1846), J. Herschel (1847), J. C. Adams (1848), Foucault (1855), Weber (1859), Chasles (1865), Plücker (1866), Wheatstone (1868), Joule (1870), Sylvester (1880), Cayley (1882), Thomson (Lord Kelvin) (1883), George Salmon (1889), Simon Newcomb (1890), Stokes (1893), Weierstrass (1895), Rayleigh (1899), Gibbs (1901), Mendeleeff (1905), Michelson (1907), G. W. Hill (1909), F. Galton (1910), G. H. Darwin (1911), F. Klein (1912), Thomson (1914), Lorentz (1918), Larmor (1921), Rutherford (1922), H. Lamb (1923), Einstein (1925), Planck (1929), W. H. Bragg (1930), C. T. R. Wilson (1935), Bohr (1938), Langevin (1940), G. I. Taylor (1944), Hardy (1947 - he died on the day it was to be presented), Chadwick (1950), Dirac (1952), Whittaker (1954), R. A. Fisher (1955), Blackett (1955), Littlewood (1958), H. Jeffreys (1960), S. Chapman (1964), W. L. Bragg (1966), Mott (1972), Hodge (1974), D. Hodgkin (1976), Chandrasekhar (1984), Atiyah (1988).
The first Royal Medals were awarded to John Dalton and James Ivory. The first Royal Medal to be awarded in mathematics was given to George Boole in 1844. (This is stated in , but Ivory, Hamilton and Fox Talbot preceded Boole - but perhaps their work was considered 'applied'.)
The Society has established a triennial Sylvester Medal for mathematics which was first awarded to Poincaré in 1901, followed by Cantor, Wirtinger, Baker, Glaisher, Darboux, MacMahon, Levi-Civita, Whitehead, W. H. Young, Whittaker, Russell, Love, Hardy, Littlewood, G. N. Watson, Mordell, Besicovitch, Titchmarsh, M. H. A. Newman, Philip Hall, Cartwright, Davenport, Temple, Cassels, D. G. Kendall, Higman, J. F. Adams, J. G. Thompson, C. T. C. Wall (1988), P. Whittle (1994).
The Michael Faraday Award for the furtherance of the public understanding of science was started in 1986. E. C. Zeeman received the 1988 award and Ian Stewart received the 1995 award.
The Society's premier lectureship in physical sciences is the Bakerian Lecture, begun in 1775, but very few have been mathematical, the only really mathematical ones being W. G. Adams (1875), G. H. Darwin (1891) and Atiyah (1975).
Henry Oldenburg was one of the first Secretaries in 1663-1677, with Wilkins in 1663-1668. Evelyn, Hooke, Halley, Brook Taylor, John Machin, J. Herschel, Roget, Stokes, Rayleigh, Larmor, Jeans, Hodge and Lighthill have also been Secretaries. Charles Hutton, Thomas Young and Rayleigh have been Foreign Secretaries. Spottiswoode and Kempe have been Treasurers. b was an editor of the Phil. Trans.
Robert Hooke (1635-1703) was appointed Curator in Nov 1662, on Boyle's recommendation. He was expected to produce new experiments and devices on a regular basis. This was poorly paid, but gave him apartments at Gresham College. In 1664, John Cutler, a City merchant, founded the Cutlerian Lectures for Hooke. Six of these were given, starting in 1670, and were published in 1674-1678. In the first lecture of 1670, An Attempt to Prove the Motion of the Earth from Observations, Hooke stated the law of universal gravitation, but without the inverse square term - though he later added this. He was later incensed with Newton for failure to acknowledge this, but Newton probably felt that the bare statement was not sufficient to warrant acknowledgement. In other lectures, Hooke described his invention of the balance watch, the clock driven telescope, the universal joint, and his discovery of Hooke's Law. Cutler apparently never paid the funds promised. In 1665, Hooke's Micrographia was the first work on microscopy and the source of the concept and term 'cell', and also suggested that light was a wave. In 1674, Hooke made the first Gregorian telescope and presented it to the Society. Hauksbee and Desaguliers were later Curators.
John Robertson, teacher of mathematics and the first to produce a slide rule with a runner attached, in 1775, was later Librarian of the Royal Society .
Pringle was forced out for supporting Franklin's pointed lightning rods in opposition to George III's belief that rounded or knobbed rods were better, and more patriotic. Banks's accession to PRS marked a long period of dominance by biologists, accentuated by Banks forcing Hutton out of the Foreign Secretaryship and the consequent withdrawal of many physical scientists from participation in RS activities .
The Royal Society is filled with portraits, busts, manuscripts and other memorabilia of these and many other persons too numerous to mention. (See , though much of the material described there was transferred to national museums during the 1968 move.) Newton presented his second telescope in 1671 and the Society was apparently unaware that he had made an earlier example in 1668 and it is not known what happened to the 1668 example. The example in the Society has a brass plate inscribed: The first reflecting telescope invented bi Sr Isaac Newton and made with his own hands in the year 1671. But recent study shows that the 1671 example perished - a 1731 inventory lists only its two mirrors, and these vanished sometime between 1765 and 1827. The telescope now in the Society was first mentioned in 1758 and was presented to the Society in 1766. It appears to contain some parts of his third telescope, made under his supervision in 1671-1672, see elsewhere in this gazetteer. It is probably the oldest surviving reflecting telescope, though its mirror is badly tarnished. It has a focal length of over 8" with the eyepiece corresponding placed. Newton's mirrors had focal length of 6-", and there is a plugged eyepiece hole at this distance. This third example was still with Newton in 1694 when David Gregory saw it and noted that the mirror had been damaged by Newton in trying to clean it. Even the first example magnified about 40 times, making it about as good as the best instrument that Galileo ever had.  In 1993, Heritage Instruments, with the Society's permission, began producing replicas of the telescope with focal length 6-" and magnification of 38, which can be obtained for £3995 (as of 1995) - the first example is in the Society's Library. The Society also has: a purported watch of Newton's and his death mask; several lenses made and signed by Christianus Huygens (1629-1695); Wren's dividers (but  says they are gone); a Tompion clock. They have the earliest, 1687, manuscript of Newton's Principia. The leaflet for their 1993 exhibition on timekeeping says the RS also has: Kater's invertible pendulum, used to measure gravity at various places in the early 19C; a Tompion clock; a chronometer used by Cook on his 2nd and 3rd voyages and another used on the 2nd voyage; the sundial carved into the wall of Woolsthorpe Manor by Newton as a boy. A catalogue of 1681 mentions: Boyle's airpump; Wilkins' airgun; Wren's raingauge; and a calculator of Hooke.  says they have a lock of Newton's hair. A copy of the bust of Ramanujan was presented in 1994 by S. Chandrasekhar. In 1769, the Society requested funds from George III to send an expedition to Tahiti to observe the Transit of Venus. This was Cook's first voyage. There was a surplus and the Society had a bust of George III made by Nollekens and this stands in the entrance hall.
The result of the expedition to measure the curvature of light was presented at a joint meeting of the Royal Society and the Royal Astronomical Society on 6 Nov 1919 - presumably in Burlington House. Whitehead and Lodge were present .