Math Trek

Probing Wikipedia editors’ hive mind for rules on cooperative behavior
Wikipedia acts a bit like one big brain. Similar to how independently firing neurons somehow in aggregate produce thought, independently operating editors together produce the vast online encyclopedia, which, it has been argued, has an accuracy approaching that of the carefully curated Encyclopedia Brittanica. Taken as a whole, the system performs a sort of enormous […]

Math
Flatland and its sequel bring the math of higher dimensions to the silver screen
In 1884, Edwin Abbott wrote a strange and enchanting novella called Flatland, in which a square who lives in a twodimensional world comes to comprehend the existence of a third dimension but is unable to persuade his compatriots of his discovery. Through the book, Abbott skewered hierarchical Victorian values while simultaneously giving a glimpse of […]

Math
A field where breakthroughs are hard to come by produces two big advances on a single day
Problems in number theory often have a certain exasperating charm: They are extraordinarily simple to state, but so difficult to prove that centuries of effort haven’t sufficed to crack them. So it’s pretty remarkable that on one day this May, mathematicians announced results on two of these mathematical conundrums. Both proofs address one of the […]

Math
One of the most abstract fields in math finds application in the ‘real’ world
Every pure mathematician has experienced that awkward moment when asked, “So what’s your research good for?” There are standard responses: a proud “Nothing!”; an explanation that mathematical research is an art form like, say, Olympic gymnastics (with a much smaller audience); or a stammered response that so much of pure math has ended up finding […]

A theorem in limbo shows that QED is not the last word in a mathematical proof
When a toptier mathematician announced in August that he had proved one of the greatest problems in mathematics, the claim was trumpeted in the New York Times, Nature, Science and the Boston Globe. But that didn’t make the abc conjecture proven. People often think of mathematics as a solitary pursuit, with a written proof as […]

Math
A mathematician puts Fermat’s Last Theorem on an axiomatic diet
Fermat’s Last Theorem is so simple to state, but so hard to prove. Though the 350yearold claim is a straightforward one about integers, the proof that University of Oxford mathematician Andrew Wiles finally created for it nearly two decades ago required almost unimaginably complex theoretical machinery. The proof was a dazzling demonstration of that machinery’s […]

Grocers stacking oranges demonstrate intuitive grasp of spherepacking math
They may not know it, but grocers face some of the most difficult questions in mathematics when stacking produce each day. Four centuries ago, the astronomer and mathematician Johannes Kepler guessed that the standard grocers’ method of piling oranges packs the most fruit into the least space. Confirming he was right had to wait until […]

Turning numbers into shapes offers potential medical benefits
Until recently, topology was seen as being among the most abstract fields of mathematics, one that bore out Henry John Stephen Smith’s 19th century toast: “Pure mathematics — may it never be of use to anyone!” But now the field, which deals with the shape of manydimensional objects, has unexpectedly proved its usefulness in, of all places, […]