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Category Archives: open problems
Book review: Fermat’s Enigma
Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical ProblemSimon Singh After having it recommended to me several times, I finally picked up this book when I happened to see it at our favorite local used bookstore. I … Continue reading
Book Review: The Enigma of the Spiral Waves
The Enigma of the Spiral Waves (Secrets of Creation Volume 2)words by Matthew Watkins, pictures by Matt Tweed Matthew Watkins and Matt Tweed have done it again! I previously wrote a (very positive) review of Volume I—this book is just … Continue reading
Book review: In Pursuit of the Traveling Salesman
As mathematical problems go, the “traveling salesman problem” (TSP) is a rare gem: it is simultaneously of great theoretical, historical, and practical interest. On the theoretical front, it is a wellknown example of the class of “NPcomplete” problems, which lie … Continue reading
Posted in books, computation, geometry, open problems, review
Tagged book review, salesman, TSP. traveling
6 Comments
17×17 4coloring with no monochromatic rectangles
Quick, what’s special about the following picture? As just announced by Bill Gasarch, this is a grid which has been fourcolored (that is, each point in the grid has been assigned one of four colors) in such a way that … Continue reading
Posted in open problems, pattern, people, pictures
Tagged 17x17, fourcoloring, graph, grid, monochromatic, rectangles
5 Comments
The Collatz conjecture is safe (for now)
A few days ago John Cook reported a draft paper claiming to solve the Collatz conjecture. Of course, since the Collatz conjecture is so simple to state, it constantly attracts tons of wouldbe solvers, and most of the purported “proofs” … Continue reading
Posted in open problems, proof
43 Comments
P vs NP: What’s the problem?
As promised (better late than never), I’m going to begin explaining the (in)famous P vs NP question (see the previous post for a bit more context). As a start, here’s a superconcise, 30,000foot version of the question: Are there problems … Continue reading
Posted in computation, open problems
Tagged binary, decision, Kalamazoo, P vs NP, problem
9 Comments
P ≠ NP?
A few days ago, Vinay Deolalikar, a Principal Research Scientist at HP Labs, began circulating a draft of a paper entitled “P ≠ NP”. The mathematics and computer science communities immediately erupted in a frenzy of excitement and activity. The … Continue reading
Posted in computation, links, open problems, people, proof
Tagged Deolalikar, Millenium, P vs NP, prize
7 Comments
A gentle introduction to the 5th Polymath project
I highly recommend reading Jason Dyer’s description of the Erdős discrepancy problem, the subject of the most recent Polymath project (the Polymath projects are an experiment in massively collaborative mathematics, where anyone at all can contribute something towards a solution). … Continue reading
Posted in arithmetic, counting, links, number theory, open problems
Tagged discrepancy, Erdős, polymath
Comments Off on A gentle introduction to the 5th Polymath project
Perfect numbers, part III
This is the last in a series of posts about perfect numbers. A quick recap of the series so far: in part I, I defined perfect numbers as positive integers n for which , where denotes the sum of the … Continue reading
Posted in algebra, number theory, open problems, primes, solutions
11 Comments