Gresham College: Over four centuries of adult education Raymond Flood ALM-23, Maynooth Wednesday 6th July 2016 Sir Thomas Gresham (1519-79) Sir Thomas Gresham, 1544 Sir Thomas Gresham, 1565-70 (aged 26) (aged 46-50) Career • Employed on Business abroad; trading in gunpowder for Henry VIII • Royal agent for Edward VI, then Mary I • Raising loans and negotiating interest for the Crown; saved Crown from bankruptcy by application of ‘Gresham’s Law’ • Continued under Elizabeth I (1558). Knighted in 1559 • Built Royal Exchange 1565 • Died in 1579 and left his estate for benefit of the City of London The Will: the Corporation I Will and Dispose that one Moiety.. shall be unto the Mayor and Commonalty and Citizens of London … and the other to the Mercers … and from thence, so long as they and their Successors shall by any means or title have hold or enjoy the same , they and their successors, shall give and distribute, to and for the sustenation, maintenance and Finding Four persons, from Tyme to Tyme to be chosen, nominated and appointed …. And their successors to read the Lectures of Divinity, Astronomy, Musick and Geometry… The Will: the Corporation I Will and Dispose that one Moiety.. shall be unto the Mayor and Commonalty and Citizens of London … and the other to the Mercers … and from thence, so long as they and their Successors shall by any means or title have hold or enjoy the same , they and their successors, shall give and distribute, to and for the sustenation, maintenance and Finding Four persons, from Tyme to Tyme to be chosen, nominated and appointed …. And their successors to read the Lectures of Divinity, Astronomy, Musick and Geometry… The Mercers were responsible for the appointment of the other three original professorships in Law, Physic (Medicine) and Rhetoric. … an important fact for the history of science in England is that the Chairs for Astronomy and Geometry at Gresham were the first Chairs in those subjects at any English university. In choosing these subjects, Thomas Gresham appeared to have clearly understood and recognised their importance as separate disciplines in scholarship, many years earlier than either Oxford or Cambridge, where they continued to be studied only as part of a broader classical curriculum. Gresham recognised the importance of applying in practice the knowledge gained from theoretical study. In astronomy for example, the emphasis was on its use for mariners in navigation and geography generally. Dr. Valerie Shrimplin, Academic Registrar of Gresham College 10 Andrew Tooke 1704 Gresham Professors of Geometry 11 Thomas Tomlinson 1729 1 Henry Briggs 1596 12 George Newland 1731 2 Peter Turner 1620 13 William Roman 1749 3 John Greaves 1631 14 Wilfred Clarke 1759 4 Ralph Button 1643 15 S Kittleby 1765 5 Daniel Whistler 1648 16 Samuel Birch 1808 6 Laurence Rooke 1657 7 Isaac Barrow 1662 17 Robert Pitt Edkins 1848 8 Arthur Dacres 1664 18 Benjamin Morgan Cowie 1854 9 Robert Hooke 1665 19 Karl Pearson 1890 20 William Henry Wagstaff 1894 1939–45 Lectures in abeyance 21 Louis Melville Milne-Thomson 1946 22 Thomas A A Broadbent 1956 23 Sir Bryan Thwaites 1969 24 Clive W. Kilmister 1972 25 Sir Christopher Zeeman 1988 26 Ian Stewart 1994 27 Sir Roger Penrose FRS 1998 28 Harold Thimbleby 2001 29 Robin Wilson 2004 30 John D. Barrow 2008 31 Raymond Flood 2012 Henry Briggs Logarithms log10 1 = 0 and log10 10 = 1. Then to multiply two numbers one simply added their logarithms. log10 ab = log10 a + log10 b Karl Pearson Charles Darwin 1857 - 1936 1809 - 1882 10 Andrew Tooke 1704 Gresham Professors of Geometry 11 Thomas Tomlinson 1729 1 Henry Briggs 15967 12 George Newland 1731 2 Peter Turner 1620 13 William Roman 1749 3 John Greaves 1631 14 Wilfred Clarke 1759 4 Ralph Button 1643 15 S Kittleby 1765 5 Daniel Whistler 1648 16 Samuel Birch 1808 6 Laurence Rooke 1657 7 Isaac Barrow 1662 17 Robert Pitt Edkins 1848 8 Arthur Dacres 1664 18 Benjamin Morgan Cowie 1854 9 Robert Hooke 1665 19 Karl Pearson 1890 20 William Henry Wagstaff 1894 1939–45 Lectures in abeyance 21 Louis Melville Milne-Thomson 1946 22 Thomas A A Broadbent 1956 23 Sir Bryan Thwaites 1969 24 Clive W. Kilmister 1972 25 Sir Christopher Zeeman 1988 26 Ian Stewart 1994 27 Sir Roger Penrose FRS 1998 28 Harold Thimbleby 2001 29 Robin Wilson 2004 30 John D. Barrow 2008 31 Raymond Flood 2012 Sir Christopher Zeeman Ian Stewart Harold Thimbleby Sir Roger Penrose Robin Wilson John Barrow Current Gresham Professors www.gresham.ac.uk • Background of the audience • Expectations of – The audience – Me! • Accessibility – Assume little technical familiarity – Assume little notational familiarity – Use History – Take a visual approach where possible Accessibility • Selection of lecture topic • Visual aids • Computer simulations • Modelling the world • Proof or framework Shaping Modern Mathematics Applying Modern Mathematics Great Mathematicians, Great Mathematics Great Mathematicians, Great Mathematics Accessibility • Selection of lecture topic • Visual aids • Computer simulations • Modelling the world • Proof or framework Isaac Newton’s memorial in Westminster Abbey From Newton’s A Treatise of the System of the World Leibniz notation d (or dy/dx) notation for differentiation: ∫ notation for integration: Gottfried Leibniz First appearance of the Integral sign, ∫ 1646 - 1716 on October 29th 1675 Memorials Accessibility • Selection of lecture topic • Visual aids • Computer simulations • Modelling the world • Proof or framework Symmetric random walk At each step you move one unit up with probability ½ or move one unit down with probability ½. 1/2 An example is given by tossing a coin where if you get heads 1/2 move up and if you get tails move down and where heads and tails have equal probability Coin Tossing Law of long leads or arcsine law • In one case out of five the path stays for about 97.6% of the time on the same side of the axis. Law of long leads or arcsine law • In one case out of five the path stays for about 97.6% of the time on the same side of the axis. • In one case out of ten the path stays for about 99.4% on the same side of the axis. • A coin is tossed once per second for a year. – In one in twenty cases the more fortunate player is in the lead for 364 days 10 hours. – In one in a hundred cases the more fortunate player is in the lead for all but 30 minutes. Accessibility • Selection of lecture topic • Visual aids • Computer simulations • Modelling the world • Proof or framework The tide predictor William Thomson (1824–1907), soon after graduating at Cambridge in 1845. He became Lord Kelvin in 1892. Weekly record of the tide in the River Clyde, at the entrance to the Queen’s www.ams.org/featurecolumn/archive/tidesIII2.html Dock, Glasgow Accessibility • Selection of lecture topic • Visual aids • Computer simulations • Modelling the world • Proof or framework Leonhard Euler, 1707–1783 Read Euler, read Euler, he is the master of us all! Portrait by Jakob Emanuel Handmann, 1756 Polyhedra Comes from the Greek roots, poly meaning many and hedra meaning seat. Convex polyhedron has the property that the line joining any 2 points in the object is contained in the polyhedron, or it can rest A polyhedron has many on any of its faces. seats – faces - on which it can be set down Polyhedra Convex Non convex Icosidodecahedron Hexagonal torus Euler’s formula for convex polyhedra, V – E + F = 2 V = number of vertices E = number of edges F = number of faces Tetrahedron V – E + F = 2 Vertices, V = 4 Edges, E = 6 Faces, F = 4 V – E + F = 4 – 6 + 4 = 2 Cube or Hexahedron V – E + F = 2 Vertices, V = 8 Edges, E = 12 Faces, F = 6 V – E + F = 8 – 12 + 6 = 2 Octahedron V – E + F = 2 Vertices, V = 6 Edges, E = 12 Faces, F = 8 V – E + F = 6 – 12 + 8 = 2 Dodecahedron V – E + F = 2 Vertices, V = 20 Edges, E = 30 Faces, F = 12 V – E + F = 20 – 30 + 12 = 2 Icosahedron V – E + F = 2 Vertices, V = 12 Edges, E = 30 Faces, F = 20 V – E + F = 20 – 30 + 12 = 2 V – E + F • If we remove an edge and a face at the same time then number of vertices – number of edges + number of faces stays the same. Because you are taking away one less edge but adding on one less face • Similarly we remove an edge and a vertex at the same time then number of vertices – number of edges + number of faces stays the same. Because you are taking away one less edge but adding on one less vertex. 1: Deform the convex polyhedron into a sphere V – E + F left unchanged 2: Remove an edge so as to merge two faces. Leaves V – E + F unchanged Remove this edge, so merging the two adjacent faces into one 3: End up with only 1 face and the edges and vertices forming a graph with no loops – a tree Remove this edge, so merging the two adjacent faces into one 4: remove a terminating vertex and edge from the tree. Leaves V – E + F unchanged Remove this edge, so Remove this merging the terminating edge two adjacent and vertex from faces into one the tree 5: As F = 1, E = 0 and V = 1 V – E + F = 2 Remove this edge, so Remove this merging the terminating edge two adjacent and vertex from faces into one the tree Picture Source: 17 Equations that Changed the World, Ian Stewart, Profile Books, 2012 In a regular polyhedron all the faces are the same and the arrangement of faces at each vertex is the same.