Thinking like a Mathematician


El Farol on Canyon Road in Santa Fe, New Mexico

Game Theory

“Oh that place. It’s so crowded nobody goes there anymore.” — Yogi Berra

Definition


“Allegations that the online retailer uses data from its own third-party sellers to create competing products”


Open Problems

There are infinitely many twin primes
(3,5), (5,7), (11,13), (17,19), (29,31), (41,43), (59,61), (71,73), (101, 103), (107, 109), (137, 139), ...

Origins


Resistance map of E.coli bacteria to 3rd Generation Cephalosporin antibiotics around the world (CDDEP, 2020)

Lessons from H1N1


Left: Richard Feynman at 41 years old, from his Cornell Lectures in 1959. Right: Richard Feynman 27 years later at his office at the California Institute of Technology in 1986, aged 68 (Photos: Wikimedia Commons)

The Feynman Essays

“We have a different kind of awareness about what might happen than we have of what probably has happened”

It is obvious to everyone that the phenomena of the world are evidently irreversible. I mean, things happen that do not happen the other way. You drop a cup and it breaks, and you sit there a long time waiting for the pieces to come together…


Left: Claude Shannon (1916–2001). Right: Shannon’s notable 1949 paper “Communication Theory of Secrecy Systems” in Bell System Technical Journal 28(4) pp. 656–715.

CRYPTOGRAPHY

Example (Boneh & Shoup, 2020)
Suppose Claude and Marvin want to use a ciper such that Claude can send an encrypted message that only Marvin can read.
Then, Claude and Marvin must in advance agree on a key k ∈ K. Assuming they do, then when Claude wants to…


The Feynman Essays

“I would like to make a number of remarks on the relation of mathematics and physics”

Differences in Epistemology

“Mathematicians prepare abstract reasoning that’s ready ‘to be used’ even though they don’t know what it’s being used for”

Mathematicians are only dealing with…


The Feynman Essays

Audience Question

Do you think there will ever be a machine that will think like human beings and be more intelligent than human beings?

Richard Feynman’s Answer

First of all, do they think…


Thinking Like a Mathematician

The Envy-Free Cake-Cutting procedure states that if two people are to share a cake in way in which each person feels that their share is at least as good as any other person, one person ("the cutter") cuts the cake into…

Jørgen Veisdal

Writer of Privatdozent. Editor-in-Chief at Cantor’s Paradise. Associate professor.

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