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