CLICK ON A YEAR TO JUMP TO THE ANNOTATED LIST
OF THE “DEVLIN’S ANGLE” POSTS FOR THAT YEAR
The posts are listed in chronological order below. All the published posts for this period were lost during an MAA system upgrade in 2023. The posts in this archive were reconstructed from the original files stored on my laptop. Some external links no longer work.
IMPORTANT NOTE REGARDING 1996: The original files I submitted to the MAA for publication in 1996 were all written in a word-processing package that is long out of date (I don’t recall what I used), and when I managed to open them in a simple text editor it was hard to locate the original text among the acres of weird characters, and I had to re-construct the order in which the various clauses, sentences, paragraphs, and the like had actually appeared. (I was clearly getting the internal code that had been generated during my writing and self-editing. It seems I make many changes as I write.) The twelve posts published here are the best I could do to reconstruct the originals. I am confident they will differ only in minor ways from what was originally published. Reading them now, it is clear we were all learning to use this new online medium as we went along. By 1997, I was composing posts in HTML (which I learned for the purpose) in plain-text files, so the remainder of these archives will be as they originally appeared apart from (usually minor) editorial changes made by the MAA Online editor.
1996
JAN Good Times. Socially spread virus
FEB Base considerations Medieval English measuring units and modern computer arithmetic
MAR Reflections on Deep Blue Computer chess and the Turing Test
APR Are Mathematicians Turning Soft? Soft mathematics, with Chomskian linguistics as an example
MAY The Five Percent Solution Using mathematics in business and industry
JUN Laws of Thought Stoic propositional logic
JUL Tversky’s Legacy Revisited Witness identification and the taxicab problem
AUG Of Men, Mathematics, and Myths Eric Temple Bell’s account of the death of Galois versus the reality
SEP Dear New Student Educational advice for incoming college students
OCT Wanted: A New Mix The need for a science of information; what will it involve?
NOV Spreading the word The growth of mathematics exposition and the negative view some leading British mathematicians had towards it
DEC Moment of Truth The nature of mathematical proof. An imaginary exchange between a student and a professor
1997
JAN Why 2001 Won’t be 2001. Early work on AI, going back to Boole; possible limitations of AI
FEB Eskimo Pi The legislating the value of pi myth, and how its growth resembled that of the “Eskimo words for snow” myth
MAR How to Get Into the Newspapers Advice on how to get math stories into the news media
APR When mathematics has to be theater The challenges of adapting a calculus course to run on an interactive digital platform
MAY Clash of the chess titans Ramifications of the chess match between Gary Kasparov and IBM’s Deep Blue computer
JUN Weighing the evidence Bayes rule and the reliability of eye-witness testimony (Tversky and Kahneman’s taxi-cab scenario)
JUL-AUG Performance evaluation A satirical dean’s performance evaluation letter that was circulating on the early Internet
SEP Seeing red Using mathematics in the development of computer vision systems
OCT The K-12 view from Oregon Four mathematicians spend a day with 400 K-12 math teachers to discuss the goal and challenges in advancing school math education
NOV A Nobel formula The development of the Black-Scholes formula to value financial derivatives
DEC Move over Fermat, Now It’s Time for Beal’s Problem A proposed generalization of Fermat’s Last Theorem that has a cash prize for a solution
1998
JAN Math + Rigor = College A US Dept of Education report says rigorous high school math courses have significant positive effects on college performance whatever the major
FEB … Before This Decade Is Out … The director of the NSA, the US Secretary for Education, and the President of the NCTM all addressed attendees at the Joint Mathematics Meetings in Baltimore
MAR Forget “Back to Basics”. It’s Time for “Forward to (the New) Basics” The third TIMMS report showed that US 12th-graders scored poorly compared to many other nations. What should be done to rectify that weakness?
APR Mathematics: As Seen on TV A new PBS television series, Life By The Numbers, provides a valuable resource for mathematics educators
MAY Is that a fact? A startling recent discovery by brain scientists highlights a difference between scientific and mathematical truth. But are they really that different?
JUN The Bible Code that wasn’t A bestselling new book about hidden messages in the Bible was recently proved to be nonsense
JUL Buttered Toast and Other Patterns The oft-repeated claim that buttered toast tends to land butter-side down when knocked from the breakfast table turns out to have a scientific explanation
AUG Mathematicians and Philosophers – Chalk and Cheese? A discussion of the differences between philosophy and mathematics, and the nature of interactions between the practitioners of the two disciplines
SEP Kepler’s Sphere Packing Problem Solved Mathematician Thomas Hales solved this old problem recently; his proof made unavoidable use of a computer
OCT Why Does Back-to-School Imply Back to Math? Why does the US, and other nations, make mathematics an obligatory school subject?
NOV Math Becomes Way Cool Recent years have seen the production of a number of major movies where the lead character is a mathematician
DEC A Good Year for Math? The latest issue of the AMS’s glossy pamphlet What’s Happening in the Mathematical Sciences provided an accessible summary of the many advances in mathematics over the previous twelve months, though for the most part the developments stretched over a longer timeframe, which is typical in mathematics
1999
JAN No post this month
FEB Stardust Equations A lengthy, in-depth look at NASA’s Stardust mission, and some of the mathematics required to make it work
MAR New Mathematical Constant Discovered A recent result showed that if you modify the generating rule for the Fibonacci sequence by using a coin flip to determine whether you add or subtract the last to numbers in the sequence to generate the new one, then with probability 1, the resulting sequence exhibits a regularity in that the Nth number in the sequence is approximately equal to the Nth power of the number 1.13198824
APR What’s Going On During Mathematics Awareness Month? Mathematics Awareness Week has become Mathematics Awareness Month. The theme this year is mathematics biology. We take a look at some of the activities being organized
MAY The Greatest Math Teacher Ever The first of a two-part post about the legendary University of Texas mathematician R. L. Moore, whose discovery learning teaching method became known as “the Moore Method”
JUN The Greatest Math Teacher Ever, Part 2 A continuation of the May column.
JUL-AUG Supermarket Math A description of Jean Lave’s study (the Adult Math Project) of the arithmetic methods people used when shopping and the degree to which they used—and were able to use—methods learned in school
SEP What Can Mathematics Do For the Businessperson? How much mathematics do you need to be a successful CEO? Many CEOs claim to have few or no math skills, but evidence suggests they might have been better CEOs if they had
OCT Those Amazing Flying Mathematicians The mathematics that migrating birds and other creatures implicitly use to navigate. How do they do it?
NOV When mathematics is plain sailing The mathematics required to win the America’s Cup yacht race
DEC About time On the eve of a new millennium, we look at the long history of time-keeping
2000
JAN Johnny might not be math-challenged; his problem could just be that he’s an auditory learner A California Community College study examined the effectiveness of a test of learning styles
FEB The legacy of the Reverend Bayes A description of Bayes’ theorem with example applications
MAR Stealing Copernicus The recent report of the theft of a rare first edition copy of a classic Nicolaus Copernicus text stimulated this look at Copernicus’s literary legacy
APR The Law of Small Errors Many authors report that as soon as they receive the first copy of their new book, the immediately spot a glaring error that somehow managed to escape not only the author but the published and all the various editors involved
MAY Will the real continuous function please stand up? An examination of some of the subtle errors in understanding that can cause problems for students trying to understand the formal definition of continuity
JUN Lottery Mania How can you visualize the odds against winning a lottery jackpot?
JUL-AUG How to sell soap Whimsical story about a Hollywood studio boss pitching Euclid’s Elements as the concept for a television soap opera
SEP The Strange Case of Emily X A surrealistic description of what it’s like to enter the world of abstract mathematics
OCT Do software engineers need mathematics? Software engineers often claim they make no use of mathematics, but everything they do involves mathematical thinking; they are misled by a common school-based perception of mathematics that’s wrong
NOV The perplexing mathematics of presidential elections A comparison of different voting systems in use around the world
DEC The Mathematics of Christmas If Santa were to fulfil his mission as believed by children all over the world, he would break a number of basic limitations of physics
2001
JAN Mathematics, Limited How much of Stanley Kubrick and Arthur C. Clarke’s 1960s movie 2001: A Space Odyssey has come to pass? In particular, what is the current state of AI?
FEB As others see us What is the most common perception of a “mathematician” among 12- and 13-year old schoolchildren? A recent study provided an answer. It wasn’t pretty. How can we change that? Do we need to?
MAR Claude Shannon Claude Shannon died last month. We take a quick look back at his life, and his groundbreaking theory of communication
APR Knotty Problems A recent result in knot theory might help explain why it can take so much effort to untangle last year’s Christmas tree lights
MAY Car Talk Woes One of the hosts (Tom) on NPR’s popular Car Talk program recently sounded off that the math taught in school is a waste of time. His rant was prompted by a statement a teach made about the purpose of calculus. We agree with Tom’s negative opinion of that statement, but his resulting tirade was way off base
JUN How many real numbers are there? A brief discussion of Cantor’s Continuum Hypothesis and an axiom of Set Theory considered by Goedel (but not widely accepted as a fundamental axiom of mathematics) that proves the hypothesis
JUL-AUG Witten at 50 The famous mathematical physicist Edward Witten turns 50 in August. We provide a brief look at the groundbreaking nature of his work
SEP Untying the Gordian Knot Researchers have been examining knots that have physical reality, where the thickness of the string can prevent come known untying move of abstract knot theory from being completed, and have created a computer program to simulate untying procedures for such knots
OCT The music of the primes. We attempt to revive interest in Euler’s amazing expression for the zeta function as an infinite product over the primes, which tends to be overshadowed by Riemann’s work on the complex version of the function
NOV The math of stuff Throughout history, mathematicians have proposed various mathematical objects as being the fundamental elements of matter
DEC A Beautiful Mind With the much anticipated movie A Beautiful Mind coming out next month, we reflect on the way movies portray mathematicians
2002
JAN A Beautiful Portrayal and a Confused NYT Reviewer A hapless movie critic for the New York Times was by no means alone in missing the movie’s dual thread structure of the world John Nash was living in and the world inside his troubled mind, which meant much of the action would seem a senseless melodrama. But for those who paid attention to director Ron Howard’s obvious clues, it came across as an effective way to tell Nash’s story. I enjoyed it
FEB The Math of Online Music Trading We look at the mathematics involved in coding music into digital signals
MAR The Shrimp and the Mathematician We examine some of the ways mathematics plays a role in understanding how living creatures move
APR Mathematics and Homeland Security We look a the ways mathematics is used to help prevent terrorist attacks
MAY Randomness at the Airport Why random security checks at airports are probably not random
JUN The words we use Why scientific precision has to take a low priority when mathematicians and scientists talk on general-audience radio and television programs
JUL-AUG The mathematical legacy of Islam We look back at the key role played by Islamic mathematicians in the development of mathematics in early medieval times
SEP The crazy math of airline ticket pricing With airlines competing for passengers, mathematical algorithms determine ticket prices in real time. From a passenger’s perspective, the results can be confusing, and occasionally wild
OCT The 800th birthday of the book that brought numbers to the west We look back at Leonardo Fibonacci, whose 13th Century book Liber abbaci introduced modern arithmetic to Europe
NOV The inaccessibility of modern mathematics Writing my new book The Millennium Problems, which sent on sale recently, meant I had to face the fact that much of present-day mathematics is virtually inaccessible to a non-mathematical reader. Unlike, say physics or biology, there are often no simple ways to describe what the main problems are, let alone how they are solved
DEC Why are equations important? Though students view equations as problems to be solved, their main importance is to provide formal and precise descriptions of our world
2003
JAN Dear President Bush My response to this year’s Edge Question: applying for an advisory position to the US President
FEB Squaring the circle How do I respond to people who send me claimed solutions to unsolvable problems? Plus, why do mathematicians do mathematics?
MAR The Forgotten Revolution The 19th Century revolution that changed the very nature of mathematics; but few people outside the field knew it ever happened
APR The Double Helix On the fiftieth anniversary of Crick and Watson’s Nobel Prize winning discovery of the shape of the DNA molecule, we look at the different things in our world that have helical shape
MAY The shame of it In mathematics, there is no place for shame when you make an error in a proof. The only thing that should bring shame is not trying again
JUN When is a proof? An analysis of the nature of mathematical proof, with reference to some famous examples
JUL-AUG Monty Hall Another outing for this perennial puzzler
SEP Galileo-Galileo This month, the spacecraft Galileo will crash land on Jupiter, ending a journey that began in 1989. We look at the man whose name the vessel carries
OCT Not-not We look at double negation in particular, and negation more generally; it can be a problem in formulating major policy questions to be put before voters
NOV Contexts of Paradox Many classical logical paradoxes can be resolved by making explicit an unstated context
DEC John von Neumann: The Father of the Modern Computer This month sees the 100th anniversary of John Neumann’s birth. We look at his life, and his contribution to the design of the modern computer
2004
JAN The mathematics of human thought This year marks the 150th anniversary of the publication of the book that set the scene for the introduction of the computer a century later: George Boole’s The Laws of Thought. We look back at the man and his algebra of thought
FEB The Archimedes Cattle Problem This classical problem from antiquity was not solved until sufficiently powerful computers became available
MAR A Year of Anniversaries The anniversary I focus on is the 350th of the Fermat-Pascal correspondence that marked the beginning of modern probability theory. Plus I give an update to the Archimedes Cattle Problem story I presents last month
APR The Abel Prize Awarded: The Mathematicians’ Nobel In addition to reporting the winner, we take a look at the prize and its relationship to the Nobel Prizes and the Fields Medal
MAY The best popular science essay ever After summarizing how I became a “mathematics writer” I present what I view as the best popular science essay ever written: K.C. Cole’s Murmurs, about the birth of the universe
JUN Good stories, pity they’re not true What is true about the Golden Ratio, and what is not. I try to separate fact from fiction
JUL-AUG The Two Envelopes Paradox I pose this initially startling puzzle, and then show why it’s not the paradox it first seems
SEP A game of numbers The many roles played by mathematics in America’s favorite game, baseball
OCT When Google becomes ePlay The playful relationship between the Google co-founders and some of the world’s favorite numbers
NOV Election Math A comparison of the various methods of counting election votes in use around the world
DEC The Amazing Ahmed The navigational feats of the Tunisian Desert Ant
2005
JAN Last doubts removed about the proof of the Four Color Theorem A new computer system called a mathematical assistant has been used to verify a proof of the Four Color Theorem
FEB NUMB3RS gets the math right I look at the new television crime series in which the hero is a mathematician
MAR Mathematics: a natural pursuit A look at the navigational feats demonstrated by many creatures; exhibiting innate mathematical skills
APR What does “DOING MATH” mean? When we look at some of the navigational skills of various creatures, we have to acknowledge that in their own way, they are solving math problems. So to does is computer when its running Mathematica. So what do we really mean when we speak of “doing math”?
MAY Street Mathematics A study carried out in a Brazilian street market found that teenagers managing a stall exhibited near perfect mental arithmetical skills in negotiating sales, but when presented with the same problems expressed in the familiar symbolic language of mathematics, they were unable to produce correct paper-and-pencil solutions. What does this tell us about math learning?
JUN Staying the course My experience in teaching university math courses is that most students give up far too quickly. But my recollection is that this was far less prevalent twenty-five ears ago. Has there really been a change, and if so what caused it?
JUL-AUG When numbers matter Scary newspaper headline statistics about percentage risk increases caused by some environmental factor often appear pretty tame when you look at the actual numbers. And there may be other factors at play than the one the article focuses on. We always need to approach numerical data with a questioning mind
SEP Naming theorems We look at the variety of circumstances that lead to names being given to theorems
OCT Common Confusions One difficulty readers sometimes have with popular mathematics books is a result of their now fully understanding the concepts. Seemingly simple notions often involve subtle distinctions. We present some examples
NOV Common Confusions II In this follow up to last month’s column, we look at the tricky issue of confusions about probability theory; in particular the distinction between frequentist probability and epistemic probability—a distinction that trips up many people
DEC Monty Hall revisited The mailbag I got from readers of last month’s column, where I mentioned the Monty Hall problem, prompted me to attempt, once again, to clarify the confusion many people have with this seemingly simple puzzler
2006
JAN Infinity and intuition Infinite (mathematical) trees have some surprises in store regarding our intuitions about infinity
FEB Cracking the Code Cryptographer Xiaoyun Wang at Tsinghua University in Beijing recently made massive advances in cracking security codes that were previously thought to be beyond reach
MAR How do we learn math? I make a brief foray into the ongoing Math Wars to offer my own perspective (informed by my mathematical experience; I have no background as a K-12 teacher) on what effective math teacher requires. I will likely annoy both camps
APR How a wave led to a prize A report on the awarding of the Abel Prize to Swedish mathematician Lennart Carleson, for his work on wave analysis that effectively completed the work begun by Joseph Fourier over a hundred years earlier
MAY The Mathematics of Aircraft Boarding We report on a study of the mathematically most efficient way to board an aircraft, and comment on all the other factors that the airlines have to consider
JUN Letter to a calculus student When you go beyond all the techniques and the symbolic manipulations you start to see calculus as a subject with inherent beauty, which allows you, in the words of the poet William Blake, to “hold infinity in the palm of your hand”
JUL-AUG Ten Years On Devlin’s Angle is ten years old this month. We take the opportunity to look back and forwards into the future. The particular focus in the article is the increasing use of video games in education
SEP Statisticians not wanted In August, the California Supreme Court ruled that in certain legal cases that hinge on statistical calculations, it is not the business of professional statisticians to decide how to evaluate the statistical data; the courts should decide what statistical analysis is appropriate and what is not. The proper job for statisticians, the Court opined, is simply to plug numbers into a formula and turn the crank to produce an answer. The case involved DNA profiling. What could possibly go wrong? This post is an informed rant
OCT Damned lies A follow up to my September column. The title reflects the old adage, “There are lies, damned lies, and statistics.” It’s unfair. But statistics is a powerful tool, and like all powerful tools it can be misused; it is often misused to blind people with a mass of mathematics they don’t understand
NOV Will the real continuous function please stand up? A rerun of my May 2000 column on the confusing (to beginning) student concept of continuity (or more precisely, the definition of that concept). A message definitely worth regular recycling
DEC The biggest science breakthrough of the year It was, without doubt, the proof of the Poincare Conjecture; a mathematical result
2007
JAN DNA math and the end of innocence A sort-of follow up to my September and October columns last year about the use of statistics in DNA profiling. I observe that a common way to try to raise doubts about a strong argument (in this case, my Cold Hit DNA profiling commentary) is to take one element from the argument and misrepresent it, knowing that a (strong, simple, populist) argument presented against that misrepresented item will lead less-than-careful readers to dismiss the entire original—my column in this case. Hence my title for this month’s post
FEB How to stabilize a wobbly table There’s a simple mathematical argument (using the Intermediate Value Theorem) that claims to prove you can stabilize a wobbly, four-legged table simply by rotating it around its center. Unfortunately, turning that intuitive (to mathematicians) idea into a rigorous proof is not a simple matter. It was finally accomplished in 2005
MAR E8 Mapped Easiest math story I ever wrote; and it’s a deep one in advanced mathematics.
APR Finding Musical Beauty in Euler’s Identity A choral group from Santa Cruz, California, has put Euler’s identity into song. And it’s really good
MAY The myth that will not go away I return to the irrepressible myths about the Golden Ratio that continue to do the rounds. I think each of we popular-math writers have been seduced by them—until someone points out the error of our ways!
JUN The trouble with math The title refers to the fact that until you get to high school, it’s impossible to provide a satisfying answer to the question “Why is this important?” All the teacher or parent can do is say, “It leads on to things that are important.” That changes with high school math, and by the time you get to sophomore college level, practically everything in the syllabus is useful (though in some cases only experts know of the uses)
JUL-AUG The professor, the prosecutor, and the blonde with the ponytail Mistrials and bad judgements can result from misuse or misunderstanding of math in the courtroom. The case referred to in the title was one example where the California Supreme Court issued a scathing overturn of an outrageous judgement in a lower court.
SEP What is conceptual understanding? What do we mean by conceptual understanding (of mathematics), is it important, if so why, and then how do we help students achieve it (assuming we do think it is important)? When you dig into this, you find these are by no means easy questions to answer
OCT Kinds of math People who need to use mathematics in their daily lives (such as shopkeepers in the days before automatic cash registers) rapidly become proficient, but remain unable to do even elementary level school math using paper and pencil. Why is that? And can we leverage the common ability to acquire math skills through use in the math classroom?
NOV The smallest computer in the world The topic is the Turing machine. Not a computer you can buy (though people have constructed them), rather the original mathematical conception that opened the gates to the computer revolution
DEC Predicting mathematical ability Recent research by psychologist Daniela O’Neill of the University of Waterloo in Canada suggests that there is a way to predict if a 3- or 4-year old will do well at math in school. Early ability in arithmetic is not that predictor. Far better, O’Neill found, is narrative skill—the ability to tell a story
2008
JAN American mathematics in a flat world A new one-hour advocacy documentary film says the US needs to wake up to the dire condition of its K-12 education system compared to our major economic competitors. The flat world referred to in the title is the one we live in, as described by Thomas Friedman in his book The World Is Flat
FEB Mathematics for the President and Congress A follow up to last month’s column where I lay out the goals we need to set for college-level math education to ensure the US does not fall too far behind. I argue in particular for one goal that I believe has been overlooked. It’s the one I list first
MAR Lockhart’s Lament Possibly the most significant column I ever published. I did not write it. Rather I simply arranged to publish a dynamite essay that I stumbled across
APR The Napkin Ring Problem This is the first of two forays I make into this classic puzzler. I also remark on the massive response I had to my Lockhart’s Lament post the previous month
MAY Lockhart’s Lament—The Sequel I list some of the many responses I received to Lockhart’s Lament, and then hand my platform to Lockhart to respond directly. The column actually begins with a clever, non-calculus solution to the Napkin Ring problem from the previous month. I did so since I think it is emblematic of the kind of curiosity-driven exploration into problems that I see Lockhart advocating
JUN It ain’t no repeated addition I did not know it at the time, but this column was about to ignite a firestorm of debate that would rage for months, and in some quarters still smolders to this day. Prepare for the initial three-part saga, published over successive months, as I try to rid the world of a dangerous misconception about multiplication. (If this is all new to you, you should realize that in Episode 3 I bring receipts! Lots of them. Big ones. This is not an opinion piece)
JUL-AUG It’s still not repeated addition MINRA Episode 2. I go into far greater depth as to the problems with the false MIRA definition of multiplication, and try to articulate more clearly what multiplication actually is
SEP Multiplication and those pesky British spellings In episode 3 of my MINRA miniseries, I bring in the heavy artillery, citing some of the masses of research that backs up what I have been saying. Much of the research I am familiar with (and hence cite) is by British scholars; hence the post’s title. (Many readers assumed I was simply presenting my personal opinion, and said so, totally unaware that I was simply relaying many decades worth of scholastic research. This entire debate should not have arisen in the first place with better mathematics education.) Though I resolved at the time to leave the issue alone after this post, in response to continued emails, I addressed it again four more times, in JAN 2009, JAN 2010, JAN 2011, and NOV 2011.
OCT The big mortgage surprise With a nod to the recent global financial meltdown due to the massive overreach of the folks who deal in mortgage-backed securities, I reflect on the mathematics that makes it possible for organizations to advance mortgages in the first place. (The problem arose because lenders went well beyond the safety cushion the math provides.)
NOV Polling, polling, polling With a US general election imminent, the nation has been inundated with results of opinion polls predicting the outcome. I note that the possibility of polling began with a mathematical result in the seventeenth century
DEC How do we learn math? I take a look at some of the latest (scientifically informed!) thinking among cognitive scientists and math education researchers as to what is involved in learning mathematics
2009
JAN Should children learn math by starting with counting? In western countries, children’s first encounter with mathematics is the counting numbers and their arithmetic. But in a system that was used in the USSR, know as the Davydov Curriculum, they began with measurement (i.e., the real numbers), with the teacher guiding their development based on their innate sense of (in particular) length and volume. (Area is a bit more problematic, it appears.)
FEB When the evidence deceives us We look at some examples where numerical evidence can lead us to form incorrect conclusions. A reminder that in mathematics, you can’t assume something is true unless it has been rigorously proved
MAR What is Experimental Mathematics? Last month’s column set the scene for this month’s topic. In the newly emerging discipline of Experimental Mathematics, computers are used to gather numerical evidence in order to increase our understanding of various phenomena
APR Stanislaw Ulam—a Great American We celebrate the 100th anniversary of the birth of one of America’s greatest mathematicians: Stanislaw Ulam
MAY Do you believe in fairies, unicorns, or the BMI? I take aim at the much touted “body mass index”, one of the most egregious packages of mathematical snake oil you are likely to come across; indeed, it’s hard to avoid the wretched thing. This post, and a subsequent interview I did on the topic for NPR, led to a number of requests for media interviews on the topic
JUN What’s the real story? Newspaper stories are usually written in great haste, to meet a deadline, and the journalist may have limited background knowledge of the topic the story is about. Stories that begin by announcing that a teenager somewhere has cracked a math problem that had stumped the world’s best mathematicians for hundreds of years are almost always wrong. (But note that “almost”.) That was true in this case. It was still a great human achievement story; just not a big math story
JUL Trisecting Devlin’s Angle This month’s column and next’s are the result of a live exercise in mathematics writing/editing what was part of a workshop on mathematical organized by the MAA, at which I was one of the four “instructors”. If you are a mathematics writer or are interested in becoming one, this is a MUST READ pair of articles. For the rest of humanity (at least those who read Devlin’s Angle, it may have curiosity value: it shows how the expository-mathematics-articles sausage is made
AUG In praise of good editors. The second part of a two-part report of an MAA mathematics writing workshop exercise
SEP Reaching out—with style A report on a new mathematics museum in Sweden
OCT Soft mathematics I present a summary of “Grice’s Maxims” (for everyday human conversations) as an example of what for some years I have been calling “soft mathematics”
NOV Cross Talk A short, simple example to highlight one of the major problems we encounter when trying to write educational standards
DEC Strictly for the birds Two math puzzles to bring up at the dinner table on Christmas Day (if you are in that kind of family) that look like you don’t have enough information to solve them; but you do
2010
JAN Repeated addition—one more spin Prompted by ongoing objections to my posts on MIRA, I return briefly to the issue to give one more example that demonstrates MINRA. I also give the solutions to the two birds problems from the December 2009 column
FEB Is math a socialist plot? Online responses to a NPR Math Guy piece I did on a math formula for parking a car demonstrated a worrying lack of awareness of how math is used in today’s world. General discussion of the need to make our students aware of the role of math, and to counter the idea, advanced by some media commentators that anything beyond a bachelors degree is “over-educated”
MAR The hidden math behind Alice in Wonderland The release of the movie Alice in Wonderland prompted me to write about the strong connections between the Alice stories and developments in mathematics in the 19th Century when the mathematics teacher Charles Dodgson (aka Lewis Carroll) wrote his books. I included several new observations from a recent article on the math in Alice by Melanie Bayley of Oxford University
APR Probability can bite I provide some notoriously tricky examples that show how poor is our ability to estimate certain kinds of probabilities
MAY The problem with word problems A follow up to April’s column about probability calculations, after some readers objected to the solution I gave to the “boy born on a Tuesday” problem. That led me to reflect on the degree to which word problems assume we read them a certain way. That can be a problem when word problems are presented to young children in school who have not yet learned the “code”
JUN In math you have to remember, in other subjects you can think about it I look at some of the work on mathematic education done by Stanford professor Jo Boaler. The title of the post is a quote from a student interviewed by Boaler in one of her studies. I find it very telling
JUL Wanted: Innovative Mathematical Thinking A number of reports on the current state of US student mathematics performance point to a revamp of our education system. In particular, our nation’s future prosperity depends on developing innovative thinkers, particularly in mathematics
AUG 2010: A Space Odyssey I look at some of the growing number of mathematics museums and expositions
SEP A Fibonacci photo-album I make public the photo album I put together when researching my forthcoming book on Fibonacci
OCT Twist or bust I look at the counter-intuitive results we get when we pose seemingly simple questions about long pipes, hypothetical belts round the Equator, and the like
NOV The other thing Fourier did Known for his work on waves (Fourier Series, the Fourier Transform), Fourier was the first person to predict the greenhouse effect that we now know has led to major climate change. (The mechanism he proposed was actually wrong, but the greenhouse effect is very real.)
DEC The innumeracy behind airline security A primary duty of the government is the protection of American lives. The current airline boarding security system is not the way to allocate resources, as a few simple simple calculations indicate
2011
JAN What exactly is multiplication? Faced with continued requests from readers, I sat down and tried to articulate my concept of multiplication
FEB Bad math, bad thinking: the BMI and DNA identification revisited I provide additional insights into those two issues covered in earlier columns
MAR Learning Math with a Video Game I summarize my own approach to designing math learning video games
APR Finger counting This column consists entirely of an embedded video from the talented Vi Hart. I posted it purely to promote her amazing, and highly unique work in mathematics outreach
MAY The Keyring Problem: NCTM fumbles the ball We rarely put much effort into posting a tweet, but I could not pass on commenting on a tweet by NCTM that posed a puzzle for which I suspected they were looking for what I would say is the wrong answer to the problem as posed. Not because I wanted to score a point against NCTM. Rather, being from NCTM, the tweet provided a great hook to raise an important issue about the kinds of problems we present to students and the expectation we have of how the students will understand the problem
JUN Wanted: a mathematical iPod This post is a teaser to the topic I ran the following month
JUL Students should learn everyday math the way they learn to play a musical instrument I propose a strategy of creating an “orchestra” of “mathematical instruments” that students can “play” to learn math the way they can learn music by playing musical instruments. I gave two specific examples of such “instruments”, and knew that others can be created, since I was already doing just that
END OF INDEX
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