Posts Tagged ‘Number theory’
What’s (the) matter?…
On the heels of yesterday’s film recommendation, another… albeit somewhat different: Stanford physics professor, Leonard Susskind, one of the fathers of string theory, articulator of the Holographic Principle, and explainer of the Megaverse, has a gift for making science accessible… a gift that is on display in this lecture, “Demystifying the Higgs Boson“:
(email readers, click here)
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As we say “ahh,” we might spare a thought for Pierre de Fermat; he died on this date in 1665. With Descartes, one of the two great mathematicians of the first half of the Seventeenth Century, Fermat made a wide range of contributions (that advanced, among other fronts, the development of Calculus) and is regarded as the Father of Number Theory. But he is best remembered as the author of Fermat’s Last Theorem.* Fermat had written the theorem, in 1637, in the margin of a copy of Diophantus’ Arithmetica– but went on to say that, while he had a proof, it was too large to fit in the margin. He never got around to committing his proof to writing; so mathematicians started, from the time of his death, to try to derive one. While the the theorem was demonstrated for a small number of cases early on, a complete proof became the “white whale” of math, eluding its pursuers until 1995, when Andrew Wiles finally published a proof.
* the assertion that no three positive integers a, b, and c can satisfy the equation an + bn = cn for any integer value of n greater than two
Pieces of pi…
In 2010, Japanese engineer Shigeru Kondo set a record, calculating the value of pi to 5 trillion digits… then last October, he smashed his own mark, identifying the first 10 trillion decimal places. (He used a home-made computer that ran so hot that the temperature in his apartment was over 100 degrees…)
The quest will no doubt continue– pi is an irrational number that exerts an irrational fascination. Meantime, readers can take a peek at this work-perpetually-in-progress. Web design firm firm Two-N has created this nifty visualization and search tool, allowing one to find any one of the first 4,000,000 digits of pi:
Bonus: “50 Interesting Facts About Pi”
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As we ruminate on randomness, we might send carefully-calculated birthday greetings to Hermann Minkowski; he was born on this date in 1864. Minkowski developed the geometry of numbers and used geometrical methods to solve difficult problems in number theory and mathematical physics; he is probaly best remembered for realizing that his former student Albert Einstein’s special theory of relativity (1905), presented algebraically by Einstein, could also be understood geometrically as a theory of four-dimensional space-time. Einstein embraced the geometric approach in the development of his theory of general relativity– and the four-dimensional space (the three physical dimensions plus time) involved has since been known as “Minkowski spacetime.”
Minkowski’s best friend was “mathematical hotelier” David Hilbert.
Infinitely cool…
How to Count to Infinity (or “Yes, Virginia, some infinities are bigger than others…”)
Many more sixty-second epiphanies at MinutePhysics’ You Tube channel (or via New Scientist TV)
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As we check in to Hilbert’s Hotel, we might spare a thought for Joesph Fourier; the French mathematician, physicist, Egyptologist and administrator who died on this date in 1830. Fourier introduced Jean-Francois Champollion to the Rosetta Stone, which Champollion subsequently decoded/translated. And after calculating that a body the size of earth, at earth’s distance form the sun, should be cooler than our world is, discovered what we now call “the greenhouse effect.” But Fourier is best remembered for his contributions to mathematical physics through his Théorie analytique de la chaleur (1822; The Analytical Theory of Heat), which introduced an infinite mathematical series to aid in solving conduction equations. (The technique allowed the function of any variable to be expanded into a series of sines of multiples of the variable– now known as “the fourier series.”)
True greatness is when your name is like ampere, watt, and fourier—when it’s spelled with a lower case letter.
– Richard Hamming (in a 1986 Bell Labs Colloquium)
Spiraling into control…
The Fibonacci spiral (source)
As we remark that math really is beautiful, we might send elegantly parsimonious birthday greetings to one of Fibonacci’s spiritual descendants, a father of Pure Mathematics, Leonhard Euler; he was born on this date in 1707. While crafting “the most remarkable formula in mathematics,” Euler made foundational contributions to number theory, graph theory, mathematical logic, and applied math; he originated many commonly-used figures of mathematical notation, and invented the concept of the “mathematical function.” And he was no slouch in physics either, making renowned contributions in work in mechanics, fluid dynamics, optics, and astronomy.
The dog 8 my homework…
[TotH to Geaux Keegan]
As we celebrate symmetry, we might send dusty birthday greetings to paleontologist Barnum Brown; he was born on this date in 1873 in Carbondale, Kansas. Brown (who was named after the famous showman) discovered the first documented remains of Tyrannosaurus rex during a 66-year career in which he became the most famous fossil hunter in the world.
Though most of his work was sponsored by the American Museum of Natural History (where most of his finds reside), some was underwritten by the Sinclair Oil Company– which adopted an image of the Apatosaurus (then known as Brontosaurus) in its logo.
Brown often worked on-site in fur coat, tie, and fedora (source)
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