An anonymous Quora commenter has written an exhaustive and fascinating response to the question, "What is it like to understand advanced mathematics?" (more…)

]]>An anonymous Quora commenter has written an exhaustive and fascinating response to the question, "What is it like to understand advanced mathematics?" (more…)

]]>On the BBC's More or Less podcast (previously), Tim Harford and his team carefully unpick the numerical claims made by both sides in the UK/EU referendum debate. (more…)

]]>On the BBC's More or Less podcast (previously), Tim Harford and his team carefully unpick the numerical claims made by both sides in the UK/EU referendum debate. (more…)

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Britain faces a major maths challenge. The challenge involves a **stock** of people and a **flow** of learners.
(more…)

Britain faces a major maths challenge. The challenge involves a **stock** of people and a **flow** of learners.
(more…)

Meet Danica McKellar who as an undergraduate in college co-published a paper titled "Percolation and Gibbs states multiplicity for ferromagnetic Ashkin-Teller models on Z2," research that resulted in the Chayes–McKellar–Winn theorem. Oh yeah, before that, McKellar was Winnie on The Wonder Years.

(And just to confirm, Josh Saviano who played Paul Pfeiffer did not grow up to become Marilyn Manson.)

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Meet Danica McKellar who as an undergraduate in college co-published a paper titled "Percolation and Gibbs states multiplicity for ferromagnetic Ashkin-Teller models on Z2," research that resulted in the Chayes–McKellar–Winn theorem. Oh yeah, before that, McKellar was Winnie on The Wonder Years.

(And just to confirm, Josh Saviano who played Paul Pfeiffer did not grow up to become Marilyn Manson.)

]]>

Since its inception as a 2012 Kickstarter, the Reading With Pictures project has gone from strength to strength, culminating in a gorgeous, attractively produced hardcover graphic anthology of delightful comic stories that slot right into standard curriculum in science, math, social studies and language arts. (more…)

]]>Since its inception as a 2012 Kickstarter, the Reading With Pictures project has gone from strength to strength, culminating in a gorgeous, attractively produced hardcover graphic anthology of delightful comic stories that slot right into standard curriculum in science, math, social studies and language arts. (more…)

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Exotic polyhedron purveyor Dice Lab's crowning randomizer is its monstrous, $12 120-sided die. (more…)

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Exotic polyhedron purveyor Dice Lab's crowning randomizer is its monstrous, $12 120-sided die. (more…)

]]>Statistician Patrick Ball runs an NGO called the Human Rights Data Analysis Group, which uses extremely rigorous, well-documented statistical techniques to provide evidence of war crimes and genocides; HRDAG's work has been used in the official investigations of atrocities in Kosovo, Guatemala, Peru, Colombia, Syria and elsewhere. (more…)

]]>Statistician Patrick Ball runs an NGO called the Human Rights Data Analysis Group, which uses extremely rigorous, well-documented statistical techniques to provide evidence of war crimes and genocides; HRDAG's work has been used in the official investigations of atrocities in Kosovo, Guatemala, Peru, Colombia, Syria and elsewhere. (more…)

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I have vague memories of my older scientist brother Mark wearing a slide rule in a leather case on his belt. It was really one of the first wearable computers, albeit a mechanical, analog one. Then in 1974, he was able to purchase a Texas Instruments SR-50, the first mass-market commercial electronic calculator. The slide rule was buried in Mark's desk drawer, where the SR-50, and later his Sharp Wizard, Palm Pilot, and their descendants would ultimately end up as well. (Mark died wearing a calculator wristwatch!)

In this episode of Numberphile, Alex Bellos explains the seduction of the slide rule and also the Halden Calculex, a device he calls the "iPhone of Slide Rules."

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I have vague memories of my older scientist brother Mark wearing a slide rule in a leather case on his belt. It was really one of the first wearable computers, albeit a mechanical, analog one. Then in 1974, he was able to purchase a Texas Instruments SR-50, the first mass-market commercial electronic calculator. The slide rule was buried in Mark's desk drawer, where the SR-50, and later his Sharp Wizard, Palm Pilot, and their descendants would ultimately end up as well. (Mark died wearing a calculator wristwatch!)

In this episode of Numberphile, Alex Bellos explains the seduction of the slide rule and also the Halden Calculex, a device he calls the "iPhone of Slide Rules."

]]>

Pythagoras' Theorem, x^{2}+y^{2}=z^{2}, is true when x=3, y=4, and z=5. In fact, there are an infinite number of whole number solutions for Pythagoras' Theorem.

But there are no known solutions for x^{n}+y^{n}=z^{n}, when n equals any whole number other than 1 or 2. In 1637 mathematician Pierre de Fermat wrote in the margin of a book that he had devised a proof that there are no whole number solutions. The note was found 30 year later, and ever since then, no one has been able to prove it, though people have been trying for centuries.

This BBC documentary is about Oxford professor Andrew Wiles' lifelong obsession with Fermat's Last Theorem, which he read about when he was 10 years old. Wiles proved Fermat's Last Theorem in 1995. The proof is 150 pages long. If Fermat really did prove it, one can only guess how long his proof was.]]>

Pythagoras' Theorem, x^{2}+y^{2}=z^{2}, is true when x=3, y=4, and z=5. In fact, there are an infinite number of whole number solutions for Pythagoras' Theorem.

But there are no known solutions for x^{n}+y^{n}=z^{n}, when n equals any whole number other than 1 or 2. In 1637 mathematician Pierre de Fermat wrote in the margin of a book that he had devised a proof that there are no whole number solutions. The note was found 30 year later, and ever since then, no one has been able to prove it, though people have been trying for centuries.

This BBC documentary is about Oxford professor Andrew Wiles' lifelong obsession with Fermat's Last Theorem, which he read about when he was 10 years old. Wiles proved Fermat's Last Theorem in 1995. The proof is 150 pages long. If Fermat really did prove it, one can only guess how long his proof was.]]>

Mark says:

What would happen if you mixed a math education tutoring site with a late night 900 number?

Well, someone did, and it might end up being one of the strangest new startups out of Cambridge. It's called SolveX4U.com.

While this might look like a silly idea it's been gaining a lot of traction in the past week and the tech behind it is actually pretty advanced and useful for students who are looking for help with math, statistics and other subjects.

Anyone can submit any math problem and they will get help solving it (the first one is free too).

A New Tutoring Startup Is Branding Itself as an Adult Hotline]]>

Mark says:

What would happen if you mixed a math education tutoring site with a late night 900 number?

Well, someone did, and it might end up being one of the strangest new startups out of Cambridge. It's called SolveX4U.com.

While this might look like a silly idea it's been gaining a lot of traction in the past week and the tech behind it is actually pretty advanced and useful for students who are looking for help with math, statistics and other subjects.

Anyone can submit any math problem and they will get help solving it (the first one is free too).

A New Tutoring Startup Is Branding Itself as an Adult Hotline]]>

Derek Bruff teaches a first-year college writing seminar in mathematics, an unusual kind of course that covers a lot of ground, and uses a novel as some of its instructional material -- specifically, my novel Little Brother. (more…)

]]>Derek Bruff teaches a first-year college writing seminar in mathematics, an unusual kind of course that covers a lot of ground, and uses a novel as some of its instructional material -- specifically, my novel Little Brother. (more…)

]]>Ben Kraft teaches a unit on gerrymandering -- rigging electoral districts to ensure that one party always wins -- to high school kids in his open MIT Educational Studies Program course. As he describes the problem and his teaching methodology, I learned that district-boundaries have a lot more subtlety and complexity than I'd imagined at first, and that there are some really chewy math and computer science problems lurking in there. (more…)

]]>Ben Kraft teaches a unit on gerrymandering -- rigging electoral districts to ensure that one party always wins -- to high school kids in his open MIT Educational Studies Program course. As he describes the problem and his teaching methodology, I learned that district-boundaries have a lot more subtlety and complexity than I'd imagined at first, and that there are some really chewy math and computer science problems lurking in there. (more…)

]]>Michael from Muckrock sez, "A Hungarian born in the early 20th century, Paul Erdős, mathematician, was well-known and well-liked, the sort of eccentric scientist from the Soviet sphere that made Feds' ears perk up in mid-century America." (more…)]]>

Michael from Muckrock sez, "A Hungarian born in the early 20th century, Paul Erdős, mathematician, was well-known and well-liked, the sort of eccentric scientist from the Soviet sphere that made Feds' ears perk up in mid-century America." (more…)]]>

Noah writes, "Fabienne Serriere, a hacker and machine knitting enthusiast, is running a Kickstarter currently for provably unique mathematical scarves modeled off of cellular automaton and made of Merino wool. ]]>

Noah writes, "Fabienne Serriere, a hacker and machine knitting enthusiast, is running a Kickstarter currently for provably unique mathematical scarves modeled off of cellular automaton and made of Merino wool. ]]>

“Enjoy the parabolic envelopes that form while those bright, sparkling, parabolic curves are etched into the sky tonight.” —Visualizing Math.
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“Enjoy the parabolic envelopes that form while those bright, sparkling, parabolic curves are etched into the sky tonight.” —Visualizing Math.
]]>

Rudy Rucker -- mathematician, cyberpunk, computer scientist, gonzo hoopy frood happy mutant -- has released an 828 page volume of his journals! (more…)

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Rudy Rucker -- mathematician, cyberpunk, computer scientist, gonzo hoopy frood happy mutant -- has released an 828 page volume of his journals! (more…)

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Mathematician and origami expert Tom Hull created this pleated multi-sliced cone from paper, never before accomplished since Robert Lang designed it via computer. (more…)

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Mathematician and origami expert Tom Hull created this pleated multi-sliced cone from paper, never before accomplished since Robert Lang designed it via computer. (more…)

]]>Seb writes, "Citizen Maths is a new CC-BY licensed open online maths course produced in the UK for adults and college students who want to improve their grasp of maths at what in the UK is known as Level 2 (the level that 16 year old school leavers are expected to reach, though many do not)." (more…)]]>

Seb writes, "Citizen Maths is a new CC-BY licensed open online maths course produced in the UK for adults and college students who want to improve their grasp of maths at what in the UK is known as Level 2 (the level that 16 year old school leavers are expected to reach, though many do not)." (more…)]]>

Regular BB readers know one of my favorite head trips is the idea that we're living in a simulation or control system of some kind. Decades before The Matrix, folks like Jacques Vallee, John Keel, Stephen Wolfram, Rudy Rucker, Hans Moravec, and Ed Fredkin explored this notion. And of course it's also been the subject of countless science fiction novels. In recent years, Oxford philosopher Nick Bostrom developed a mathematical argument to support the mind-bending theory. A week ago, UC Berkeley mathematician Edward Frankel, author of Love and Math: The Heart of Hidden Reality, summed up the Simulation Argument in the New York Times Sunday Review and asked whether we can test the hypothesis.

Is the Universe a Simulation? *(Thanks, Marina Gorbis!)*]]>

Regular BB readers know one of my favorite head trips is the idea that we're living in a simulation or control system of some kind. Decades before The Matrix, folks like Jacques Vallee, John Keel, Stephen Wolfram, Rudy Rucker, Hans Moravec, and Ed Fredkin explored this notion. And of course it's also been the subject of countless science fiction novels. In recent years, Oxford philosopher Nick Bostrom developed a mathematical argument to support the mind-bending theory. A week ago, UC Berkeley mathematician Edward Frankel, author of Love and Math: The Heart of Hidden Reality, summed up the Simulation Argument in the New York Times Sunday Review and asked whether we can test the hypothesis.

Is the Universe a Simulation? *(Thanks, Marina Gorbis!)*]]>
*The Simpsons *is arguably the most successful television show in history. Inevitably, its global appeal and enduring popularity have prompted academics (who tend to overanalyze everything) to identify the subtext of the series and to ask some profound questions. What are the hidden meanings of Homer's utterances about doughnuts and Duff beer? Do the spats between Bart and Lisa symbolize something beyond mere sibling bickering? Are the writers of *The* *Simpsons *using the residents of Springfield to explore political or social controversies?

One group of intellectuals authored a text arguing that *The Simpsons *essentially provides viewers with a weekly philosophy lecture. *The Simpsons and Philosophy*, edited by William Irwin, Mark T. Conard, and Aeon J. Skoble, claims to identify clear links between variousepisodes and the issues raised by history's great thinkers, includingAristotle, Sartre, and Kant. Chapters include "Marge's Moral Motivation," "The Moral World of the Simpson Family: A Kantian Perspective,"and "Thus Spake Bart: On Nietzsche and the Virtues of BeingBad."

One group of intellectuals authored a text arguing that *The Simpsons *essentially provides viewers with a weekly philosophy lecture. *The Simpsons and Philosophy*, edited by William Irwin, Mark T. Conard, and Aeon J. Skoble, claims to identify clear links between variousepisodes and the issues raised by history's great thinkers, includingAristotle, Sartre, and Kant. Chapters include "Marge's Moral Motivation," "The Moral World of the Simpson Family: A Kantian Perspective,"and "Thus Spake Bart: On Nietzsche and the Virtues of BeingBad."

In this video, Mariano Tomatis shows how to create chocolate out of nothing. Here is his explanation of this wonderful phenomenon, known as a missing square or vanishing area puzzle. *(Thanks, Ferdinando Buscema!)*]]>

In this video, Mariano Tomatis shows how to create chocolate out of nothing. Here is his explanation of this wonderful phenomenon, known as a missing square or vanishing area puzzle. *(Thanks, Ferdinando Buscema!)*]]>

[π] is a lovely and simple page that "explores the musical rhythm within 100,000 digits of π, an irrational number. #1 = Day | #0 = Night | #2–9 = La Musica." [π] *(3.14-pi.net)*]]>

[π] is a lovely and simple page that "explores the musical rhythm within 100,000 digits of π, an irrational number. #1 = Day | #0 = Night | #2–9 = La Musica." [π] *(3.14-pi.net)*]]>

The Evil Mad Scientists were presented with a challenge: inscribe one of Cliff Stoll's hand-blown Klein bottles, an object of surpassing beauty and odd topology. They modified an Eggbot plotter to etch the surface of a Klein bottle with a diamond engraver attachment.
(more…)

The Evil Mad Scientists were presented with a challenge: inscribe one of Cliff Stoll's hand-blown Klein bottles, an object of surpassing beauty and odd topology. They modified an Eggbot plotter to etch the surface of a Klein bottle with a diamond engraver attachment. (more…)]]>

The Cartoon Introduction to Statistics is a new book by Grady Klein and Alan Dabney that is a top-notch introductory grounding in statistical concepts told through a series of witty, funny cartoons that relate stats to everything from fish populations to alien opinion surveys. This is a

The authors do a great job of conveying the source material in clear, stepwise fashion, and made the wise decision to put the equations at the back of the book in an appendix called "The Math Cave." They don't delve deeply into any intermediate subjects like assessing correlation (for this, I highly recommend 1993's The Cartoon Guide to Statistics by Larry Gonick and Woollcott Smith, about which I can't say enough great and enthusiastic things), but that's probably a wise tactical decision. Confining the material to basics makes the whole work into an unqualified success.

The Cartoon Introduction to Statistics
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The Cartoon Introduction to Statistics is a new book by Grady Klein and Alan Dabney that is a top-notch introductory grounding in statistical concepts told through a series of witty, funny cartoons that relate stats to everything from fish populations to alien opinion surveys. This is a *very* introductory text, and it assumes that you know nothing about stats -- not even why you'd want to know more about the subject. The book tackles both the task of providing a grounding in statistical concepts (mean/median, standard deviation, null hypothesis, random sampling, confidence intervals, etc) and explaining in clear and exciting ways why you'd care about any of this stuff.

The authors do a great job of conveying the source material in clear, stepwise fashion, and made the wise decision to put the equations at the back of the book in an appendix called "The Math Cave." They don't delve deeply into any intermediate subjects like assessing correlation (for this, I highly recommend 1993's The Cartoon Guide to Statistics by Larry Gonick and Woollcott Smith, about which I can't say enough great and enthusiastic things), but that's probably a wise tactical decision. Confining the material to basics makes the whole work into an unqualified success.

The Cartoon Introduction to Statistics
]]>

Here's a great video pondering the objective reality of mathematics, and running down all the different schools of thought on where mathematical truth comes from -- does it exist outside of systems of codification by intelligent beings, as an eternal part of the universe; or is it something that we invent through codification?

Is Math a Feature of the Universe or a Feature of Human Creation? | Idea Channel | PBS
(*Thanks, Dad!*)
]]>

Here's a great video pondering the objective reality of mathematics, and running down all the different schools of thought on where mathematical truth comes from -- does it exist outside of systems of codification by intelligent beings, as an eternal part of the universe; or is it something that we invent through codification?

Is Math a Feature of the Universe or a Feature of Human Creation? | Idea Channel | PBS
(*Thanks, Dad!*)
]]>

Beast Academy is a set of grade three math textbooks and practice books structured as comic books about monsters. The books are "aligned to the common core state standards for grade three," if that matters to you. What's more significant is that they're actually really good math textbooks that introduce their subjects in a clear and easy-to-follow fashion, carefully linking each concept to the last; and the exercises are lively, fun, and built around stories that dovetail smoothly into puzzles, games, and other ways of putting the knowledge into practice. The monsters are great, too -- wonderful illustrations from Erich Owen, whose work you may recognize from the graphic novel adaptation of my story I, Robot.

Beast Academy is a set of grade three math textbooks and practice books structured as comic books about monsters. The books are "aligned to the common core state standards for grade three," if that matters to you. What's more significant is that they're actually really good math textbooks that introduce their subjects in a clear and easy-to-follow fashion, carefully linking each concept to the last; and the exercises are lively, fun, and built around stories that dovetail smoothly into puzzles, games, and other ways of putting the knowledge into practice. The monsters are great, too -- wonderful illustrations from Erich Owen, whose work you may recognize from the graphic novel adaptation of my story I, Robot. ]]>

Here's glassblower Alan Bennett's astounding triple-nested Klein bottle, a beautiful thing:

A single surface model made by Alan Bennett in Bedford, United Kingdom. It consists of three Klein bottles set inside each other to produce, when cut, three pairs of single-twist Mobius strips. A Klein bottle has no edges, no outside or inside and cannot be properly constructed in three dimensions.

Klein bottle, 1995.
(*via Neatorama*)

(*Image: Science Museum/Science & Society Picture Library*)
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Here's glassblower Alan Bennett's astounding triple-nested Klein bottle, a beautiful thing:

A single surface model made by Alan Bennett in Bedford, United Kingdom. It consists of three Klein bottles set inside each other to produce, when cut, three pairs of single-twist Mobius strips. A Klein bottle has no edges, no outside or inside and cannot be properly constructed in three dimensions.

Klein bottle, 1995.
(*via Neatorama*)

(*Image: Science Museum/Science & Society Picture Library*)
]]>