The (Nonperfect) Mathematics of Trust
@vaidehijoshi
@vaidehijoshi
1735
Professor Roman Sznajder
but seemed to me worthy of attention
This question is so banal,
in that [neither] geometry,
nor algebra,
nor even the art of counting
was sufficient to solve it.
"
sufficient
—Leonard Euler
MAA Euler Archive
Vaidehi's Super Fast And Exceedingly Friendly Guide to Graph Theory
™
(no PhD required!)
nodes or vertices
edges
undirected
directed
ordered pairs
(x, y)
(V, E)
(x, y)
G = (V, E)
G = (V, E)
a set of vertices
a set of edges
G = (V, E)
a
b
c
V = { a, b, c }
E = { {a, b}, {b, c}, {c, a} }
G = (V, E)
a
b
c
V = { a, b, c }
E = { (a, b), (b, c), (c, a) }
degree
how many vertices are adjacent to this one?
a
b
c
d
e
d = 2
e = 1
a = 4
path
getting from an origin to a destination
simple
without
without repeating vertices
a
b
c
simple path
Eulerian path
All of the vertices with a nonzero degree must be connected
Two vertices must have an odd degree
All of the vertices in the connected graph must be of an even degree
OR
2.
1.
2.
Euler proved something impossible by proving what was possible.
was
"Geometry of Position"
Graph theory
Euler's problem
graph theory is all over computer science
The Knight's Tour
Wikimedia Foundation
Cayley Graphs
Jaap's Puzzle Page
Google's PageRank Algorithm
Wikimedia Foundation
graph theory
is all over the web
literally is the web
is all over the web
website a
website b
website c
website d
website e
website f
Euler's problem
Euler's problem
computer
science
bioinformatics
sequencing the
human genome
2001
de Bruijn graph
Cold Spring Harbor Laboratory Press
Euler's problem
computer
science
genome sequencing
Euler's problem
computer
science
genome sequencing
Euler's problem
computer
science
2001
Nicholas Christakis
We’re all embedded in massive social networks that have massive influences on our wellbeing.
"
Harvard University
Harvard University
our connections can influence each other in positive or negative ways
humans are connected by edges
genome sequencing
Euler's problem
computer
science
genome sequencing
Euler's problem
computer
science
sociology
6 degrees
of Kevin Bacon
genome sequencing
Euler's problem
computer
science
sociology
genome sequencing
Euler's problem
computer
science
Kevin Bacon?
sociology
But it's not just Kevin Bacon!
directed graphs
undirected graphs
genome sequencing
Euler's problem
computer
science
Kevin Bacon?
sociology
sharing
economy
genome sequencing
Euler's problem
computer
science
Kevin Bacon?
sociology
sharing
economy
economy
genome sequencing
Euler's problem
computer
science
Kevin Bacon?
sociology
trust
sharing
economy
the sharing economy leverages our interconnectedness
how we relate to one another
how we navigate our careers

People are more likely to be referred for jobs by their 2nd and 3rd degree connections.

Connections matter most in technologyrelated industries.

Men typically have larger professional networks than women, but women’s connections appear to be higher quality when it comes to jobhopping.
how we choose our government
how we choose our government
Fake accounts based in Russia purchased more than $100,000 worth of ads on divisive issues in the runup to the 2016 presidential election.
$10 and 15 minutes
20,658 employees
2 billion monthly users
1 employee for every 97,000 users
It can be very easy to trust the algorithms that automate our world.
But the mathematics behind them can't be trusted blindly.
Trust is a (very) hard math problem.
to pick up where the math ends,
We need humans to intervene,
to innovate better approaches to the really hard problems.
to evaluate whether the math is fair to everyone,
That's exactly what Euler did.
Whatever happened to Königsberg?
Thank you!
@vaidehijoshi
The (NonPerfect) Mathematics of Trust
By Vaidehi Joshi