Essence of linear algebra - "[Grant Sanderson of 3Blue1Brown (now at Khan Academy) animates] the geometric intuitions underlying linear algebra, making the many matrix and vector operations feel less arbitrary." [more inside]
Logic hacking - "Writing shorter and shorter computer programs for which it's unknowable whether these programs run forever, or stop... the winner of the Busy Beaver Game for N-state Turing machines becomes unknowable using ordinary math - somewhere between N = 5 and N = 1919." [more inside]
Univalent Foundations Redefines Mathematics - "When a legendary mathematician found a mistake in his own work, he embarked on a computer-aided quest to eliminate human error. To succeed, he has to rewrite the century-old rules underlying all of mathematics." (previously) [more inside]
Understanding e to the pi i - "An intuitive explanation as to why e to the pi i equals -1 without a hint of calculus. This is not your usual Taylor series nonsense." (via via; reddit; previously) [more inside]
Alcazar is a neat little path-finding logic game. There are also printable puzzles, strategy tips and metapuzzles to be had. [more inside]
Get 10 is a new browser game from veewo, creators of 1024.
Computers are providing solutions to math problems that we can't check - "A computer has solved the longstanding Erdős discrepancy problem! Trouble is, we have no idea what it's talking about — because the solution, which is as long as all of Wikipedia's pages combined, is far too voluminous for us puny humans to confirm." (via; previously ;)
Using computer systems for doing mathematical proofs - "With the proliferation of computer-assisted proofs that are all but impossible to check by hand, Hales thinks computers must become the judge." [more inside]
Is your elementary school youngster struggling with math? Are they a visual person? Would math games and videos help them learn? Enter Math Playground, to assist with problem solving and real world math. Try the enticing logic game Sugar, Sugar or beef up your math word problem skills. There are plenty of games to help educate while entertaining.
Entertaining, collected bon mots and surprisingly interesting, collected poems by various authors. From a likable math brainiac's site, Dr T.E. Forster, a Cambridge University lecturer. He also knits and writes about Buddhist logic [pdf]. Bonus, there's a fun gif.
"Perhaps twenty or thirty people in England may be expected to read this book." G.H. Hardy's review of Whitehead and Russell's Principia Mathematica, published in the Times Literary Supplement 100 years ago last week. "The time has passed when a philosopher can afford to be ignorant of mathematics, and a little perseverance will be well rewarded. It will be something to learn how many of the spectres that have haunted philosophers modern mathematics has finally laid to rest."
Bret Victor on WorryDream The power to understand and predict the quantities of the world should not be restricted to those with a freakish knack for manipulating abstract symbols. When most people speak of Math, what they have in mind is more its mechanism than its essence. This "Math" consists of assigning meaning to a set of symbols, blindly shuffling around these symbols according to arcane rules, and then interpreting a meaning from the shuffled result. The process is not unlike casting lots.
Interested in teaching yourself some statistics? Here is an excellent online and interactive statistics textbook developed at UC Berkeley, and also used at CUNY, UCSC, SJSU, and Bard. Here is the syllabus for the course at Berkeley. And here are some insightful reflections from the professor on developing Berkeley's first fully approved online course.
The Sexaholics of Truthteller Planet - yes, it's one of those rotten logic problems, one of many that can be found at Tanya Khovanova’s Math Guide to the MIT Mystery Hunt.
Douglas Hofstadter's Gödel, Escher, Bach: An Eternal Golden Braid has been recorded as a series of video lectures for MIT's Open Courseware project.
The Mathemagician and Pied Puzzler (PDF, rough table of contents here) is a collection of puzzles created by members of the Gathering 4 Gardner Foundation, in tribute to the man himself (previously). Also freely available at the G4G site is Puzzle Craft (PDF), by Stewart Coffin. (The Puzzling World of Polyhedral Dissections, also by Coffin, is available here.)
Geek Logik is Garth Sundem's book & blog about equations for every day living, including how many cups of coffee you require to be functional, who to vote for, and others.
Who has the fish? Einstein logic puzzle. If I can do it, you guys can.
Gödel and the Nature of Mathematical Truth : A Talk with Verena Huber-Dyson
Godel's theorems have been used to extrapolate a great many "truths" about the world. Torkel Franzen sets the record straight in his new book Godel's Theorem: An Incomplete Guide to Its Use and Abuse. Read the introduction (PDF). If you want, check out his explanation of the theorems.
The Logic of Diversity "A new book, The Wisdom of Crowds [..:] by The New Yorker columnist James Surowiecki, has recently popularized the idea that groups can, in some ways, be smarter than their members, which is superficially similar to Page's results. While Surowiecki gives many examples of what one might call collective cognition, where groups out-perform isolated individuals, he really has only one explanation for this phenomenon, based on one of his examples: jelly beans [...] averaging together many independent, unbiased guesses gives a result that is probably closer to the truth than any one guess. While true — it's the central limit theorem of statistics — it's far from being the only way in which diversity can be beneficial in problem solving." (Three-Toed Sloth)
"WARNING!!! The puzzles on this site are very difficult, and most require the use of a good spreadsheet program in order to solve them. It will take many hours, perhaps days, to solve each puzzle..."
What Color is My Hat? I [heart] these mathematical conundrums -- simple, easy-to-state, seemingly obvious logic problems that have solutions that completely defy common sense. Here's another you can spring on a friend: "You want to fry up three pieces of french toast. You have a frying pan that is just large enough to accomodate two pieces of bread at a time. If it takes you 30 seconds to fry one side of bread, and each piece of must be fried on both sides, how long will it take you to cook up three pieces (assuming that the act of flipping a piece or adding/ removing it to or from the pan takes no time). Think about it. Answer inside.