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Modelling, creativity and knots

Potsdam Universität May 25 2016
by

Christian Mercat

on 16 October 2017

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Transcript of Modelling, creativity and knots

Creativity


1. Posing the right questions
2. Real world → math formulation
3. Computation
4. Back to reality, verification
Christian Mercat
IREM de Lyon
Pedro Lealdino F.
nstitut
de
echerche
sur l'
nseignement
des
athématiques
Université Claude Bernard
Institut Camille Jordan
Modelling and Mathematics
Lady of Shalott
Cédric Villani
© Yann Pineill & Nicolas Lefaucheux
© Cédric Villani
≈≈
≈≈
≈≈
≈≈
≈≈
≈≈
≈≈
≈≈
mc
Squared
Idea
Business
Business
model
What are you dealing with?

What is the universe?

What are the relationships?
Identify
Define
Connect
Alfred Lord Tennyson
by William Maw Egley
Vito Volterra
Validate
X
X
Albert Einstein
Werner Heisenberg
Uncertainty of the individual replaced by certainty of probabilities
Albert
Bernard
Cheryl
knows the month
knows the day
I don't know when
Cheryl's birthday is,
but I know that Bernard
does not know too.
At first I don't know
when Cheryl's birthday
is, but I know now!
Then I
also
know!
Occam's razor
Horst.Burkhardt - Waldir - wikimedia CC BY SA
mc
Squared
What is math?
http://www.ted.com/talks/conrad_wolfram_teaching_kids_real_math_with_computers
math >> computation
> ≠ =
>
Lateral Thinking
*
parasitic vs symbiotic relationships
birth rate
environment
ecology
Iterate
Tip!
If you don't use it, please don't mention it...
make genuine choices that matter
Nobody likes to be wrong. There is not a unique model for a situation.
Abstraction is not the problem, reality is messy, simplifying it means making choices.
Create a world for your situation, give names to your creation.
What are the rules in your game? How do we get around your world?
vs. creativity
Originality
Flexibility
Fluency
Elaboration
infrequent , more than correct, impredictible, unique, surprising
different points of view, receptivity, tolerance, versatility, capacity to change
many alternatives, analogies, relations
Henri Poincaré
La science et l'hypothèse
Jacques Hadamard
Essai sur la psychologie de l'invention dans le domaine mathématique
Théorème vivant
Cédric Villani
Guilford, Lowenfeld, Torrance
careful, full of details, following a path of thought
+
Analysis
Synthesis
Communication
Mind openness
Marín, de la Torre
preparation
incubation
illumination
translation
verification
preparation
incubation
illumination
translation
verification
preparation
incubation
illumination
translation
verification
Divergent
Convergent
Henri de Toulouse-Lautrec, Au lit (huile sur carton, 1892, Musée d'Orsay, Paris)
publication
Individual
Product
Process
Context
reflection
what is the source of creativity?
Maths week 2017, Dublin
Knots
draw nice
Modelling to
_
_
_
.
_
.
© Trinity college
© Luckyfish http://www.art-tattoo.com/
Andreas F. Borchert CC-BY-SA-3.0-2.5-2.0-1.0, via Wikimedia Commons
http://www.hypatiasoft.fr
http://www.nctm.org/Publications/Mathematics-Teacher/2016/Vol110/Issue5/Mathematical-Modeling-in-the-High-School-Curriculum/
Maths of XXI: graph, algorithmic, fuzzy logic, information
complexity, control
mining, game theory
probability, decisions
logistic, optimisation
certainty is the instrument of demonstration
intuition is the instrument of invention
Full transcript