tingilinde

an easy to state problem that involves huge numbers

I've know about tetration and the Ackermann function - here's a practical sounding problem that gets into the really big numbers.

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It’s not often that 5-year-olds can grasp questions at the frontiers of computer science, but it can happen. Suppose, for instance, that a kindergartner named Alice has two apples, but she prefers oranges. Fortunately, her classmates have developed a healthy fruit-trading system with strictly enforced exchange rates: Give up an apple, say, and you can get a banana. Can Alice execute a series of trades, by picking up and offloading bananas or cantaloupes, that gets her to her favorite fruit?

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a high school student and fermat

A high school student and Carmichael numbers  - a nice piece in Quanta.

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[...] These became known as Carmichael numbers, named after the American mathematician Robert Carmichael. After they were discovered, new questions popped up: Are there other ways to identify Carmichael numbers? Do they have any other special properties? Are there infinitely many of them? If so, how frequently do they occur?

It was this last question that ultimately caught the attention of Daniel Larsen. Mathematicians had proved that there were indeed infinitely many Carmichael numbers, but to show this they had to construct Carmichael numbers that were very far apart. This left open the question of how these infinitely many Carmichael numbers are distributed along the number line. Are they always far apart by their nature, or might they occur with more frequency and regularity than this initial proof showed?

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on walking through walls

Greg updates his video..  fine work!

new ways to tie ties

Not something I worry about = at least not sartorially, but hey...  Someone has to do it.

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Soon, Mocka found an online community devoted to tie knots. He discovered knots like the Merovingian, which was named for a character in the 2003 film “The Matrix Reloaded”; it’s unusual because the tail is knotted in front of the blade, as though the tie is wearing a smaller tie. On YouTube, he started following tievangelists like Patrick Novotny, a Canadian realtor who wears uncommon tie knots to stand out while networking. Mocka ultimately created more than a thousand videos of his own. He established or articulated dozens of basic techniques: twisting, swirling, spiralling, tunnelling, snaking, flaring. He’d sometimes wake up in the middle of the night with a new idea, and rouse his sleeping wife by crying, “I got it!”

In the small world of tie-tying, Mocka became a minor celebrity. One prolific knot designer, a South African court interpreter named Mabu Letsoalo, called him a genius and a major influence on him. Novotny, whose tie-themed YouTube videos have more than twenty million views, told me, “I think everybody in the tie community could probably look toward Boris for inventing the most knots.” This is a surprisingly difficult thing to adjudicate, however. Mocka said that he reached out to Guinness World Records, but the organization said that a record would be too hard to establish; all of its records must be measurable, breakable, standardizable, and verifiable. Ties raise questions. Is any knot in a tie a tie knot, or are there rules? Can you turn an old knot into a new knot simply by adding a twist or a loop? When you combine two knots, do they become one? These are not just aesthetic questions—they’re math problems, too.

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othello is solved

Another game is solved..  a few of you will find this fascinating. 

a tip of the hat to Greg

 

something very cool from greg blonder

turning a sphere inside out

Greg notes this very clear and beautiful video on turning a sphere inside out.  My hat is off to the illustrator

p vs np and on to meta-complexity

Believe it or not, a well-written non-specialist piece on meta-complexity.

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t seems that proving that computational problems are hard to solve is itself a hard task. But why is it so hard? And just how hard is it? Carmosino and other researchers in the subfield of meta-complexity reformulate questions like this as computational problems, propelling the field forward by turning the lens of complexity theory back on itself.

“You might think, ‘OK, that’s kind of cool. Maybe the complexity theorists have gone crazy,’” said Rahul Ilango, a graduate student at MIT who has produced some of the most exciting recent results in the field.

By studying these inward-looking questions, researchers have learned that the hardness of proving computational hardness is intimately tied to fundamental questions that may at first seem unrelated. How hard is it to spot hidden patterns in apparently random data? And if truly hard problems do exist, how often are they hard?

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why is x used in algebra

Something I've never thought about - here's some speculation.

 

 

mathematical traditions

From one of Feynman's public lectures