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Posts Tagged ‘Mathematics

“I may be going nowhere, but what a ride”*…


Nine salvaged bikes were reassembled into a carousel formation. The bike is modular and can be dismantled, transported and reassembled. It is normally left in public places where it can attract a variety of riders and spectators.

From artist Robert Wechsler, the Circular Bike.

* Shaun Hick


As we return to where we started, we might send carefully-calculated birthday greetings to Stephen Smale; he was born on this date in 1930.  A winner of both the Fields Medal and the Wolf Prize, the highest honors in mathematics, he first gained recognition with a proof of the Poincaré conjecture for all dimensions greater than or equal to 5, published in 1961.  He then moved to dynamic systems, developing an understanding of strange attractors which lead to chaos, and contributing to mathematical economics.  His most recent work is in theoretical computer science.

In 1998, in the spirit of Hilbert’s famous list of problems produced in 1900, he created a list of 18 unanswered challenges– known as Smale’s problems– to be solved in the 21st century.  (In fact, Smale’s list contains some of the original Hilbert problems, including the Riemann hypothesis and the second half of Hilbert’s sixteenth problem, both of which are still unsolved.)



Written by LW

July 15, 2015 at 1:01 am

“The camera is an instrument of detection. We photograph not only what we know, but also what we don’t know”*…


When top chemists and engineers at Harvard and MIT are preparing to reveal new research in the world’s premier journals, they call Felice Frankel.  For over two decades, Frankel has had a front-row seat at some of the biggest discoveries emerging from both ends of Cambridge, photographing experiments within the labs that created them.

Read her extraordinary story in “Photographer has front-row seat for big scientific discoveries“; and check out her work– from daisy-colored yeast colonies through rainbow-colored quantum dots to soft. flexible electronics that can be tattooed onto the skin– on her site.

* Lisette Model


As we find focus, we might remark that today is the birthday of not one but two extraordinary mathematicians:  Gottfried Wilhelm Leibniz (1646; variants on his date of birth are due to calendar changes), the German  philosopher, scientist, mathematician, diplomat, librarian, lawyer, co-inventor, with Newton, of The Calculus, and “hero” (well, one hero) of Neal Stephenson’s Baroque Trilogy…  and  Alan Turing (1912), British mathematician, computer science pioneer (inventor of the Turing Machine, creator of “the Turing Test” and inspiration for “The Turing Prize”), and cryptographer (leading member of the team that cracked the Enigma code during WWII).

Go figure…

Liebnitz (source: UNC)

Turing (source: Univ. of Birmingham)

Written by LW

June 23, 2015 at 1:01 am

“God made the integers; all the rest is the work of Man”*…



From Alex Bellos: the results of his global online poll to find the world’s favorite number…

The winner?  Seven—  and it wasn’t even close…

Leopold Kronecker


As we settle for anything but snake eyes, we might send symbolic birthday greetings to John Pell; he was born on this date in 1611.  An English mathematician of accomplishment, he is perhaps best remembered for having introduced the “division sign”– the “obelus”: a short line with dots above and below– into use in English.  It was first used in German by Johann Rahn in 1659 in Teutsche Algebra; Pell’s translation brought the symbol to English-speaking mathematicians.  But Pell was an important influence on Rahn, and edited his book– so may well have been, many scholars believe, the originator of the symbol for this use.  (In any case the symbol wasn’t new to them:  the obelus [derived from the word for “roasting spit” in Greek] had already been used to mark passages in writings that were considered dubious, corrupt or spurious…. a use that surely seems only too appropriate to legions of second and third grade math students.)


Written by LW

March 1, 2015 at 1:01 am

“Prime numbers are what is left when you have taken all the patterns away”*…


Der Hl. Augustinus und der Teufel


1, followed by 13 zeros, then 666, and then another 13 zeros, and a final 1:  a palindromic prime number named for Belphegor (or Beelphegor), one of the seven princes of Hell.  Reputed to help people make discoveries, Belphegor is the demon of inventiveness.  He figures in Milton’s Paradise Lost as the namesake of one of the “Principalities of the Prime”… So it is only fitting that these devilish digits bear his name.

The symbol of Belphegor’s Prime resembles Pi, only upside down. It is derived from a bird glyph first seen embedded in the Voynich Manuscript.


More prime provocation at Cliff Pickover‘s “Belphegor’s Prime: 1000000000000066600000000000001.”

* Mark Haddon, The Curious Incident of the Dog in the Night-Time


As we try to divine divisors, we might recall that it was on this date in 1968 that the first-ever 9-1-1 call was placed by Alabama Speaker of the House Rankin Fite, from Haleyville City Hall, to U.S. Rep. Tom Bevill, at the city’s police station.

Emergency numbers date back to 1937, when the British began to use 999.  But experience showed that three repeated digits led to many mistaken/false alarms.  The Southern California Telephone Co. experimented in 1946 in Los Angeles with 116 for emergencies.

But 911– using just the first and last digits available– yielded the best results, and went into widespread use in the 1980s when 911 was adopted as the standard emergency number across most of the country under the North American Numbering Plan.

And yes, “911” is a prime…


Written by LW

February 16, 2015 at 1:01 am

“The day after tomorrow is the third day of the rest of your life”*…


French Republican Calendar of 1794, Philibert-Louis Debucourt


… The Earth’s orbit is almost — but not quite — a round number, and so we continually try to fit the natural world into a mathematical order that makes sense. Even though the Gregorian Calendar solved one major problem (a year now aligned with the time of the Earth’s orbit), in the eyes of many it’s still far from perfect, and two quirks of its construction have continued to nag those inclined towards a more rational calendar. First is the inconsistent number of days in each month, and second, the fact that 365 is not divisible by seven, so that each year calendar dates fall on different days of the week…

Colin Dickey explores some the modern attempts to “correct” these short-comings in “Tempo Shifts.”

… As the Sumerian God Gozer tells Bill Murray and friends at the climax of Ghostbusters, we choose the means of our destruction. The End we imagine, Kermode writes, “will reflect [our] irreducibly intermediary preoccupations,” which is why the Apocalypse is always assumed to be happening within years or decades, rather than centuries or millennia. The plain fact being that no matter how we try to organize and structure the calendar — be we French Revolutionaries, post-Soviet mathematicians, or American evangelicals — we design it so that we are the center of history. Time and tide may wait for no man, but the calendar always revolves around the calendar-makers.

The full– and fascinating– story here.

* George Carlin


As we count the days, we might spare a thought for Immanuel Kant; he died on this date in 1804.  One of the central figures of modern philosophy, Kant is remembered primarily for his efforts to unite reason with experience (e.g., Critique of Pure Reason [Kritik der reinen Vernunft], 1781), and for his work on ethics (e.g., Metaphysics of Morals [Die Metaphysik der Sitten], 1797) and aesthetics (e.g., Critique of Judgment [Kritik der Urteilskraft], 1790).  But he made important contributions to mathematics as well:  Kant’s argument that mathematical truths are a form of synthetic a priori knowledge was cited by Einstein as an important early influence on his work.

There is … only a single categorical imperative and it is this: Act only on that maxim through which you can at the same time will that it should become a universal law.

– Chapter 11, Metaphysics of Morals


Written by LW

February 12, 2015 at 1:01 am

“A child[’s]…first geometrical discoveries are topological…If you ask him to copy a square or a triangle, he draws a closed circle”*…


Topology is the Silly Putty of mathematics.  Indeed, sometimes, topology is called “rubber-sheet geometry” because topologists study the properties of shapes that don’t change when an object is stretched or distorted. As Cliff Pickover explains, this leads to the creation of some pretty confounding shapes…

Mathematicians continue to invent strange objects to test their intuitions. Alexander’s horned sphere [above] is an example of a convoluted, intertwined surface for which it is difficult to define an inside and outside. Introduced by mathematician James Waddell Alexander (1888 – 1971), Alexander’s horned sphere is formed by successively growing pairs of horns that are almost interlocked and whose end points approach each other. The initial steps of the construction can be visualized with your fingers. Move the thumb and forefinger of each of your hands close to one another, then grow a smaller thumb and forefinger on each of these, and continue this budding without limit!

Although this may be hard to visualize, Alexander’s horned sphere is homeomorphic to a ball. In this case, this means that it can be stretched into a ball without puncturing or breaking it. Perhaps it is easier to visualize the reverse: stretching the ball into the horned sphere without ripping it. The boundary is, therefore, homeomorphic to a sphere…

Read more at “The Official Alexander Sphere Appreciation Page.”

* Jean Piaget


As we twist and turn, we might send artfully-folded birthday greetings to Sir Erik Christopher Zeeman; he was born on this date in 1925.  While he is probably most-widely known as a popularizer of Catastrophe Theory, his primary contributions to math have been in topology, more particularly in geometric topology (e.g., in knot theory) and in dynamical systems.  The Christopher Zeeman Medal for Communication of Mathematics of the London Mathematical Society and the Institute of Mathematics and its Applications is named in his honor.


We might also spare a thought for Satyendra Nath Bose; he died on his date in 1974.  A physicist and mathematician, he collaborated with Albert Einstein to develop a theory of statistical quantum mechanics, now called Bose-Einstein statistics.  Paul Dirac named the class of particles that obey Bose–Einstein statistics, bosons, after Bose.



Written by LW

February 4, 2015 at 1:01 am

“What is the difference between a taxidermist and a tax collector? The taxidermist takes only your skin”*…


A Ferris wheel of chipmunks, formerly part of the Dead Pals of Sam Sanfillippo


Last October, Atlas Obscura co-presented a Rogue Taxidermy Fair with its fellow Brooklyn-based (and former Roughly Daily subject) Morbid Anatomy in celebration of a new book on “rogue taxidermy.”

The Crucified Sheep


Read more about– and see more of– the Fair at “The Crucified Sheep, Tattooed Frogs, and Crocheted Skeletons of a Rogue Taxidermy Fair in Brooklyn,” and revisit (R)Ds earlier look at rogue taxidermy here.

* Mark Twain


As we strike a pose, we might recall that it was on this date in 1697 that Isaac Newton received and solved Jean Bernoulli’s brachistochrone problem.  The Swiss mathematician Bernoulli had challenged his colleagues to solve it within six months.  Newton not only solved the problem before going to bed that same night, but in doing so, invented a new branch of mathematics called the calculus of variations.  He had resolved the issue of specifying the curve connecting two points displayed from each other laterally, along which a body, acted upon only by gravity, would fall in the shortest time.  Newton, age 55, sent the solution to be published, at his request, anonymously.  But the brilliant originality of the work betrayed his identity, for when Bernoulli saw the solution he commented, “We recognize the lion by his claw.”



Written by LW

January 26, 2015 at 1:01 am


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