Talk:Math Museum
From TheTangentSpace
Here are the sections of a museum being devised by Glen Whitney ( http://mathfactory.org/tiki-index.php?page=Exhibit%20Plans )for comparison:
• Mathematics of Shape Collection — focusing on two-dimensional geometry, polygons, tesselations, etc.
• Polyhedron Collection
• Goudreau Collection — focusing on mathematical puzzles and other exhibits included in the former Goudreau Museum, or exhibits in a similar spirit.
• Mathematics of Music Collection
• Mathematics in Art Collection
• Mathematics of Physical Sciences Collection
• Mathematics of Life Sciences Collection
• Mathematics of Social Dynamics
• Mathematics and Computers — algorithms, information processing, communications, etc.
• Mathematics of Chance — probability theory, statistics as well.
• Mathematics of Numbers — although we want to dispel the myth that math is just about numbers, there are plenty of exciting topics there, too, that we don't want to ignore • Knot Theory Collection
• Origami Mathematics Collection
• Curves Collection — focusing on curves and curved surfaces, like conic sections, cycloids, hyperboloids, etc.
• Function Room
• Movie theater - for showing math films
• Outdoor Exhibits
• Mathematics Library - a place to relax while perusing some great math books
• Miscellaneous Exhibits — for items that don't (yet) fit into an organized collection.
Here is my (D Williams) first attempt at organising some mathematical displays:
1. What is Mathematics?
Portray its spirit, scope and connectedness. Give overview, introduce later themes. Pose questions: Is the Solar System stable? How do computers play chess? What is randomness? How many shuffles do you need to mix a deck of cards? Is space inifinte? Could a super large computer solve all mathematical problems? How long is the coast of Tasmania? How accurate are polls? Are month long weather predictions possible? How many twists do you need to unscramble a Rubik’s cube? Does a new temperature record imply climate change? How are statistics used to lie? Objective: whet appetites
2. Pattern
• In space (tessellations, platonic solids) • With numbers (fibonacci numbers, diophantine equations,Kaprekar’s process, etc) • In nature (self-similarity, Mandelbrot set)
3. Numbers
• Early history (Sumerians, Greeks, Pythagorean mythlogy, Romans, Hindu, Middle East) • Natural numbers (primes, congruences,,etc) • Real numbers (pi,e,phi, Bernoulli numbers) • Others types of artihmetic (Russian multiplication, shortcuts, etc) • Other number systems (algebraic numbers, complex, vectors, etc)
4. Geometries
• Euclidean • Non-Euclidean (esp: Riemann) • Projective • Multidimensional • Topology (map colouring, mobius strip, Mordell’s 1922 conjecture) • Fractal dimensions (Hausdorff, Sierpinksi, Koch curve) • Noncommutative geometries
5. Chance
• Gambling, polls • Common mistakes (gambler’s fallacy, cancer clusters) • Bell Curve (Central Limit Theorem, etc) • Stochastic Systems (random walks, markov chains) • Poisson Processes (customer arrivals, passing cars, static on telephones) • Paradoxes (Simpson’s, Parrando’s, etc) • What is randomness? (psuedo-random number generators, Noise (white, 1/f), entropy)
6. Groups
• Solvability of equations • 17 2D and 230 3D symmetry groups • Classification of finite simple groups (26 sporadics) • 5-fold semi-symmetry, quasicrystals and non-periodic tiles • Rubik’s cube • Orthogonal Latin Squares
7. Analysis
• Zeno’s paradoxes and Archimedes, Hindu and Middle East anticipations • Let there be Newton! (and Liebniz) • Modelling the Universe (predicted discovery of Neptune, etc) • Euler,Gauss, Jacobi, Hardy-Ramanujan • 3 body problem (recent wild non-standard orbits – horseshoes, figure 8’s, etc) • Principle of Least Action, fixed point theorems • Complex plane, conformal mapping, etc • Reimann’s zeta function and hypothesis • Fourier series, Wavelet theory • PDEs (wave equation, Navier-Stokes equation) • Hilbert Space and Quantum Mechanics • Multiplicative calculi
8. Chaos
• Turbulence: Lucretian physics, the clinamen and Laplace’s God • Intimations by Poincare, May • Lorenz (strange attractors) • Feigenbaum (cascading bifurcations) • Mandelbrot (fractals) • KAM theory (Is the Solar Syastem stable?)
9. Infinity
• Problems of: Aristotle, Galileo • Cantor’s paradise • Continuum Hypothesis (Cantor, Cohen) • Surreal numbers
10. Mathematics and Art
• Middle Eastern tilings, Penrose tiles • Escher • Golden mean • Perspective • Computer simulation of shading/reflection • Mathematical sculpture • Fractal mountains, leaves, etc (special effects) • Maths in Movies (Jurassic Park, A Beautiful Mind, Good Will Hunting)
11. Logic
• Axiomatic systems (Euclid’s postulates, Peano, etc) • Boolean algebra • False proofs within Euclidean geometry • Set theory • Russell, Hilbert’s program • Fasle dreams of consistency/completeness (Godel, Turing) • Unprovable propositions • Axiom of choice plus Banach-Tarski paradox • Formalism, Logicism, Intuitionism
12. Computation
• Early computers (slide rules,Babbage’s Analytical Engine, valve computers, Enigma decoder) • Calculator tricks (and errors (truncation, etc)) • Turing machines, decision problems (busy beaver, the word problem, Turing test) • Case study: Hilbert’s 10th problem • Enumerable sets and Diophantine equations • Cellular automata (game of life) • Chess programs (min-max theorem) • Game theory (prisoner’s dilemma, tit-for-tat) • Hard problems (travelling salesman, hamiltonian circuits, factoring) • Randomness of Arithmetic (Chaitin) • Demos of mathematical software • Computer discoveries and assisted proofs (4 color problem, Feigenbaum conjectures, BBP algorithm, 111 order latin squares, counterexamples ( Merten’s conjecture))
13. Applications
• CAT scans and Radon Transforms • “Interplanetary Highway” (low energy transfers) • Communications (public key cryptography, error-correcting codes, concept of entropy, Information theory (Shannon)) • Biomathematics (gene sequencing, evolutionary trees, ecosystem simulation,etc) • Business (decision theory, queueing theory, optimization, logistics, etc) • Simulations/Modelling (airflows, ecosystems, galaxies, climate (Courant’s condition, Lewis Richardson), bushfires, epidemics)
14. The Future
• Unsolved Problems (twin primes, Goldbach’s conjecture, Riemann’s Hypothesis, 3x+1 problem, etc) • Exploratory maths (computer exploration and discovery) • Lack of women mathematicians (not a feminist rant). Need for more mathematicians, public awareness and appreciation • Areas deserving attention • Quantum computing • The Unreasonable Effectiveness of Mathematics • In Praise of Amateurs (Fermat, Ramanujan, Margorie Rice, Mandelbrot, Wikipedia) • Modus Operandi (mathematicians telling how they work)
15. Resources
• Contacts/material • Merchandise (books, clothes, puzzles, software,CDs, DVDs, calculators, computers) • In-house mathematician • Thank you to sponsors, comments book
