Two Beautiful Mathematical Documentaries
Two beautiful mathematical documentaries are “Fermat’s Last Theorem” and “Dangerous Knowledge”. Both take a popular science style approach to describing compelling and emotional stories about great mathematicians.
The first narrates the story of Andrew Wiles, who proved Fermat’s last theorem in 1994. It’s a relatively short documentary, coming in at about 45 minutes, but I find it to be both inspiring and a nice aid to better understanding Andrew “as a person”, before thinking of him as a superb mathematician. This documentary is based on Simon Singh’s excellent book
Fermat’s Enigma: The Epic Quest to Solve the World’s Greatest Mathematical Problem.
The second documentary focuses on the obsessive quest for knowledge shared by Georg Cantor, Ludwig Boltzmann, Kurt Gödel and Alan Turing. The basic idea behind “Dangerous Knowledge” is that the genius of these outstanding mathematicians and their obsession ultimately lead to their madness and tragic deaths. In truth, I feel that the underlying thread that tries to tie the four stories together is forced.
For example, Alan Turing was persecuted for his homosexuality, and it is believed that this had a significant impact on his eventual suicide. The filmmakers are trying to lead the viewers to come to the certain conclusion that the quest for understanding infinity is what led these mathematicians to insanity, which is entirely unsupported. Nevertheless, if you’re aware of the agenda behind this film, you’ll get a beautiful 1h 29m documentary that is absolutely worth watching. It poses interesting questions about the nature of knowledge, our understanding of nature, and other puzzling dilemmas that encompass mathematics, physics and philosophy.
What other mathematical documentaries are you fond of? If various titles are suggested, we could definitely start a nice must-watch math documentary list here on Math-Blog.com.
There is a video lecture about Alan Turing, which I enjoyed very much:
Alan Turing – Codebreaker and AI Pioneer by B. Jack Copeland
http://mitworld.mit.edu/video/423
[...] Vídeos en Inglés Vía Math-blog, les presento dos documentales que se relacionan con el Último teorema de Fermat y sobre la [...]
The BBC’s website has here and there fascinating little radio documentaries like the series 5 numbers.
Hi everyone, I found this kind of movie called Dimensions. You can download it or watch it online:
http://www.dimensions-math.org/Dim_E.htm
It is not a documentary, but it is really cool!
You can watch it in various languages, too. I enjoyed it very much! and hope you will enjoy it too.
People can’t understand the academic world or tell it apart from cheap publicity overkill.
Whatever Wiles did seems remotely required in possibly the worst example in all of implication logic–you can assert anything by raw contradiction, and when I mean raw it doesn’t get any worse than what was passed of as a proof of Fermat’s Last Theorem.
In the first video, notable mathematician John Conway registered some qualified doubt in the alleged proof’s inability to approach unique factorization. And probably it was because the gymnastics went nowhere near the Fundamental Theorem of Algebra.
A valid proof should at least demonstrate the existence of Pythagorean Triples by satisfying that case along with all the other infinite many of them. But then it would have the proof derived from the form of that equation and not an elliptic form. We could suppose the quadratic equation could be composed into the elliptic form to tell us something; but it doesn’t add anything to just having the quadratic equation.
Another documentary about Julia Robinson brings up FLT in Hilbert’s 10th Problem, again another form of restating the general problem, but one so open ended they could have taken a hint from Godel Incompleteness.
That result doesn’t place any curbs on single forms of diophantine equations even if a free variable may range infinitely, as does Fermat’s.
The real proof is 3 pages and must employ recursion under the property of association. It is a little challenging.
But Fermat probably saw the way though it by his own method of reducing parameters vis a vis the discrete indexing of simple well ordered bipartition over the integers. You get two equations in two unknowns and you know that’s exactly what you get in a complex quadratic solution.
Don’t forget the MSRI video about the proof. MSRI people did demonstrations of basic math, later there was some discussion about all the excitement.
If you look at the Clay Mathematics Institute sight you may notice new research in L functions that has found several contradictions to the Riemann Hypothesis in a challenging new computation; and you should know it only takes one.
Wiles’ proof assumes R.H. under what’s called the Artin Conjecture form of it.
Yes the piltdown proof of wildly regarded professor Wiles (accent on how cluelessly wild it is) is sinking and taking on water fast. It isn’t mathematics it is a pendantic obscurantism, utterly useless to the body of scholarship considering the bona fide methods put to the subject. There is utterly nothing of it any mathematicians will ever by tempted to apply for any practical use; however deriving the alternator to nested recursive associative property in the reduced equivalent of FLT has valid direct applications on any diophantine system. -b^n (-/+) b^n = Cap(Delta’) + Cap(Delta”) the minus over plus sign is key to indicating wheither n is even, -, or odd (+). Use it to exhause the few quick cases of Catlan’s Conjecture. Cap refers to the uppercase Greek character delta, hack marks count on the level of recusive nesting displacing the addition of zero from one level into the next one under, i.e. -b and +b just like deriving the quadratic formula. Try it if you’re not chicken.)
Anti-intellectualism surmounting the academic establishment of mathematics, its Hollywood character assassination in a slew of propaganda movies is a disgusting and worrisome trend. It will only gather the bad rep deserved of its usual suspects–big omnivorous and hated state monopolism, or the buffoons of our modern crumble to tyranny.
Max Planck Institute’s rejection of Yoshi Miyaoka’s 1988 FLT proof should be a standard of refusal on continuum based argument equally applied to shoesting and bubble gum nonsense from Fry to Ribet to Wiles. Namely the Ribet stability arena (foul!) the fry systems solution (foul!) and the vast uncharted or cared for baloney of Wiles, so loathed it was just easier to pronounce him king than address any adjudication of his proof what-so-ever. (laugh)
I am sorry the Wiles-Ribet-Fry bunk has taken so many of you for a ride, but your indignance there could be anything wrong with it is not one founded in the least bit of familiarity with what is going on in the subject matter. You just want your rock-star and he has to be British. Totally beneath commenting on any further. You ‘Occupy’a fantasy you fluff-heads.
So, I hate to have to be the bearer of two disappointing pieces of information in light of the L-form research to date.
Professor Andrew Wiles not only failed to prove FLT, but this also leaves the Tanayama-Shimura Conjecture open to present and future generations of those inspired by the great history of mathematics.
Use Delta to group the operator dervied from the center truncation of the binomial expansions just taking off the ‘bookends’ raised to the nth power.
The rest fits on three pages but is too involved to go into here.
B.W. morefocusandprecision@hotmail.com, I’ll send you a rough draft.
A Note on nested displacement or shift of addition of zero between recursive levels of binomial law bipartitions:
i. (b+(d-b))^N
FLT must be implicit in derivation of the correct formula, i.e.
a^n + (D + b^n) =c^n,
where D is the central truncate of the binomial sequence, thus unavoidably:
ii. (D + b^n) = d^n
and we’re looking at difference of nth powers in two relations i and ii.
Wiles-Ribet-Fry’s efforts are what could qualify as a form of persuasive evidence, in terms of stability theory arguments or very close calls with three integer system solution basins of attraction. However as they go discovered it still doesn’t qualify as a method of eliminating counter examples quantitatively.
Let’s not forget the basis of the proof was to contradict basically another result presumed valid on its own meager case restrictions (Serre-Ribet); and did nothing to disprove it in terms of its own model. Composition of functional systems seems on the surface to baffle any antecedent direct homomorphism to FLT in any number theoretical sense.
We could make up a range function for trigonometric series and many theorems of Fourier Analysis would apply regardless, dependent not so much on what is put in but how it transforms. Choice should be overruled out of valid adjudication procedures for proof, such as departures from any arbitrary choice. Working from the binomial theorem provides the most generic rule for integers raised to a power. You see already that Fry omits this by begging the question of the form under analysis, starting with it instead of deriving it.
Recursion is standard course material in any computer programming language, yet strangely is never discussed in mathematics texts in the context of recursive functions.
Plain enough sense suggest FLT in no way amalgamates with elliptic curve theory or the Tanayama-Shimura conjecture on their replete class modularity. There is no compelling reason not to try any three numbers or actually plug them into the Fry equation. As it stands, the effective restriction or constraint FLT imposes can’t argue against that fact regarding an unrestricted open domain for Fry, further more the root of the Fermat conjecture can’t extend beyond that schema itself or transfer to whatever non-linear system which contracts its artificially imposed correlation. It is still the same question, remains the same question.
Besides, it is only arguing up the end the FLT holds by itself in a contrived variety combined with elliptic forms. Remove it and they are just elliptic forms. FLT as its own form does not transfer governance beyond an arbitrary system(s) binding in the L form. It retains exclusive antecedent predicate over a hypothetical solution for n>2. The ivory tower knows this. And it was chastised so badly in A. C. Clarke’s last novel it might have actually hurt that book’s reviews on its release.
So why is it gotten away with anyway? It is a crude attempt to steal thunder away for an ethnic racial chauvinism. Case in point the 1988 Japanese proof rejected by the Max Planck Institute scholars on grounds which were not equally levied against their multiple occurrences in Wiles Ribet Fry.
On this publicity campaign to demonize mathematics, “Dangerous Knowledge”, it hardly ends there. It has its own genre of major motion pictures. For instance, foul play is suspected in Ramanujam’s bad ending, a piece of evidence was withheld by the British until the 70′s when their American colleague George Andrews of Pennsylvania State University was invited to pick through the remains of a plundered notebook in damaged condition. Steven Hawking appeared to take part in campus protesting during his school years, perhaps he protested too much. If he spoke against their government he would have been hit and they have a diseased fancy for poisoning and other cloak and dagger obviously. David Kelly. There’s always a body in the hedges there.
You know that book about retractions in scientific publication, “Not Even Wrong”..?
How about for W-R-F FLT, “Not Even Modus Ponens”?
One-man forum discussion, nice, haha.