Can Mathematics Drive Creativity?
Exploring Constructive Mathematics
As an Opportunity
Mark LeeJanuary 2017
Fields Medalists Connect Disparate Mathematics Fields (connecting ideas = creativity)
The ability to detect hidden connections between
different areas of mathematicsCedric Villani
2010 Fields Medalist 1‘
a fundamental structural connection between
elliptic curves & modular formsAndrew Wiles
2016 Abel Prize Winner 2
“Monstrous Moonshine”: (a) & (b) (a) Group Theory (monster group)
1 + 196,883 (b) Number theory (j-function)
196,884Richard Borcherds
1998 Fields Medalist
“Math is … building bridges where on one side you see more clearly than on the other,” Duncan said. “
... this bridge was so unexpectedly powerful
that before you see the proof it’s kind of crazy.” 3
1 Birth of a Theorem: A Mathematical Adventure – Cedric Villani2 https://www.myscience.org/wire/fermat_s_last_theorem_proof_secures_mathematics_top_prize_for_sir_andrew_wiles-2016-oxford3 Https://www.quantamagazine.org/20150312-mathematicians-chase-moonshines-shadow/
Fields Winners(Math Genius)
BorcherdsVillaniWiles
Creativity Mathematics
Drives
Drives?
Creativity Drives Mathematics Can Mathematics Drive Creativity?
SG Challenge Identify
How Mathematics
Drives Creativity
“It is by logic that we prove, but by intuition that we discover”
Henri Poincare
Univalent Foundations Enable Correctness & (?) Creativity
Proof Assistant
Properties Connections
Formal System & Structure(for the next 1,000 years)
Enable
Math Objects(sub-set of ideas)
forMathematicians
forHumankind
Symbiotic Genius
.LT. 100K ~1.3 Billion Working Adults
Exploration of Creativity
Checking of Correctness
UnderDevelopment
To BeDeveloped
a mental construct that satisfies a collection of
explicit formal rules on which
mathematical reasoning can be carried out.
Committee on the Mathematical Sciences in 2025;
Board on Mathematical Sciences and Their Applications
Math Structure
IDEA a mental construct that satisfies a collection of
explicit formal rules on which
mathematical reasoning can be carried out.
A Math Structure is an Idea
Transforming an Idea (Polynomial Equation) into a Structure
https://www.quantamagazine.org/20170103-fractal-dynamics-from-3d-julia-sets/
Symbiotic Genius Transforms Creativity
Solo Group Symbiotic Genius
Within 1 Human Between Humanse.g.
Watson & Crick
Future: 2017 Growth of Genius
Between Human & Machine
HumanImagination
MachineIntelligence
Math withWatson
Crick
AI Drives A Creativity Revolution: Symbiotic Genius
HumanImagination
MachineIntelligence
UF Math Revolution bProvides Medium
b Under Development
Mathematics of Ideas aEnables Message
a To Be Developed UF: Univalent Foundations
4 Drivers of A Creativity Revolution: Symbiotic Genius
1. Human Imagination
4. MachineIntelligence
2. Math as Message a
3. Math as Medium b
Supplemental Slides
Applying Mathematics to Economics: Nobel Prize
Adam Smith1776 Publication
Paul Samuelson 1947 Publication
1970 Nobel Laureate
171 Years
Economics Mathematics of Economics
mathematics … essential
to an understanding of … economics
Identifying Technology Progress as Primary Driver of Growth 1987 Nobel Prize
Robert Solow1987 Nobel Laureate
Solow calculated that about four-fifths of the growth in US output per worker was attributable to technical progress.
Classical Mathematics and Constructive Mathematics
AOCLEM
ClassicalWell
Developed
ConstructiveUnder
Development
Mathematics of Ideas (Worthy of a Nobel Prize in Economics?)
Mathematics of Economics
Technical Progress (Solow Residual)
Mathematics of Ideas
Paul Samuelson 1970 Nobelist
Robert Solow1987 Nobelist
Ideas drive
TBD Future LaureateIdea Production Function
“I think you just blew my mind”Professor Vollrath
Dimensional Analysis for a Nobel Prize In Economics
Mathematics ofEconomics
Paul Samuelson 1970 Nobelist
Economics of Ideas
Paul RomerPossible Nobelist
XMathematics ofEconomics
Economics of Ideas
Mathematics ofIdeas