QED 19: Dependency Tracking
The number of degrees of freedom in a system is equal to its number of unknowns minus its number of equations. That is also equal to the number of ind...
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Explore the intersection between software and mathematics. Michael L Perry takes you on a journey through the history of computing, information theory, cryptography, distributed systems, and everywhere else that math has influenced technology. Not only will you dive into math papers, but you'll also learn valuable programming techniques that you can apply in any language. Code Erat Demonstrandum
Q.E.D. 18: Paxos
Leslie Lamport wrote a paper describing the Paxos algorithm in plain English. This is an algorithm that guarantees that a distributed system reaches c...
QED 17: Pythagoras
The Pythagoreans were a cult of Greek mathematicians that believed that all things were composed of large enough integers. Their leader, Pythagoras, i...
QED 16: Elements
Euclid's Elements takes a disciplined, formal approach to proving assertions based only on simple axiomatic statements. While most of these axioms are...
QED 15: The Y Combinator
The Lambda Calculus uses simple replacement to compute expressions. However, it does not define a way to replace a parameter of a function with the fu...
QED 14: Equivocation
Claude Shannon followed up one incredibly important paper with a second of even greater significance. In Communication Theory of Secrecy Systems, he a...
QED 13: The First Program
in a translation of a paper on the Analytical Engine, Ada Lovelace improved upon L. F. Menambrea's work by applying rigor to the calculations that he ...
QED 12: Difference Engine
The Difference Engine was a mechanical computer that could calculate tables of numbers based on polynomials. The amazing thing is, though, that it cou...
QED 11: The Lambda Calculus
Alonzo Church invented The Lambda Calculus as a simple set of rules that, when applied correctly, could compute anything that you could do with a penc...
QED 10: The Two Generals Problem
Listener Richard Allen writes to ask about proving enough of a program correct to constrain the number of tests that must be written. I respond that y...