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
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:
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. [email protected], 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:
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.
Viktor, finally you wake up in class. So nice you could attend.
Seriously though, numerical analysis even, could prove that order two or higher convergence searches for close counter-cases can never produce one in integers. They’re never going to round off those least upper bounds. They are more like chaotic attractors; but nothing substantiating a hedge off Ribet’s purely indempotent restrictions.
The matter is a great embarrassment to the mathematics community, who basically are not the aggressive, confrontational types. What do they care, obviously we stagnate in yet another dark protracted age.
University staff are hounded by micro country dictatorships, nothing gets in or out that isn’t monitored by the rough equivalent of matriculating hitler youth in a high security monitoring section somewhere. Dialog with the outside world will cost them a job. Even saying anything negative about anything in context with the university in the newspapers will. Let’s face it, teachers are dogs bullied by the original jerks who disrespected them when they were students.
Vic, people are sick of the brand of smirk you’re so cowardly hocking long after the person posting has evidently left it to no regards or interest.
The maggot industry of this deviant fraud has been well exposed recently in the Edward Snowden makeshift fall guy softener.
We know self absorbed pirates such as you hate the very idea of a free and open society able to associate by internet more than your idea of your worst foreign ethnic rival.
We’re onto your trivial game, your stupidity. Please do something else and stop pretending to hold humanity in a cage.
Model Theory needs reexamination to determine the stead of arbitrarily roped in relations to a system of equations as opposed to conjunctive omitting types epistemic from the definition of TSM i.e. integer modular residue. FLT does only qualify dysjunctive union of the proposed Fry system in correspondent term definition.
Perceived defect in the proof program of WRF can begin with more succinct examination of allowable omitting types to which the flipping of FLT went allegedly gained. These are going to be conjunctive, like tautological valid argumentative proof. The implicit ‘forcing’ type is dysjunctively arbitrary system assignment for the all purpose tools which comprise it; and there is a transfinite set order lapse two ways in fashioning the binding governance of this model.
System solution sets of finite peculiarity as with any assortment of linear equations, vs. the solvability of GL in continuum section.
Limiting case expectation would predict the glancing, near perfect coincidence with any number of fixed integer three space lattice points off any given infinite projection or affine projection subset, actually any number of said points to mock a ‘counterexample’–which is in this articulation at its weakest, i.e invalid. What isn’t arbitrary however is repetitive modular residue occurrence in TSM ‘modularity sense, as it would appear something like a tunnel of opposing mirror reflection to span the continuum or aleph one, overlapping the three space lattice of XYZ integer graduation of scale on three orthogonal axis.
So these arbitrary system assortments are purposeful, adequate for finitary co-agreement but also represent a general purpose tool entering a probability of satisfiability, good for a language model. However it’s not about the tools in particular until it is about whichever among those tools, particularly. The rest of it is reaching into an urn randomly to withdraw system relation elements as if they were colored balls. Then the question is more one of how they can color or ZKP in finite net without perfect knowledge as to conjunct every one of them into a single unifying form. For this we have other examples in Logic solidifying Incompleteness which should actually reaffirm a language model versatility, generic competence etc.
These ideas of Incompleteness vs. Generality are duals.
It may as in fact it turns out FLT renders a subtler property of algebra so far as binomial expansion this way, separating two opposite parts of zero in different nested sub-associative association. This would still remain true and is in fact true. But for the coloring of the WRF model it would have to remain a shade apart from its Fry curve modeling, like a standard algebraic property that has always been there, staple goods as much as divisibility.
Then wherever they are with their elliptic toil is totally their frustration, not that of algebra. The rules were there before them and shall remain after their example of falsehood in false times.
Complex analysis admits a many complex variable reality to its workings. Basically a new complex variable is created every time the log of another complex number is taken. This is telling.
Instead of assuming zeta series is complex, let’s find out for real. The modulus of the zeta function ought to lose information same way the modulus of a complex number does.
I have a hunch there is more to this complexity in complex numbers that we have foreseen.
Let’s start by synthetically taking zeta apart. And here’s what we’ll do: first make it alternating with a series exponented minus one for every term; and then make another offshoot of it simply shifting the alternator of the other one, rotate the sign forward in the same alternation. Now you have pair of conjugate alternators based on the zeta function.
Create an equality using the special synthetic versions of zeta with the original zeta.
You might find this a delightful chore. Go for the usual formula for modulus and mimic its procedures of norm extraction.
It could get weird, it could fall into what’s called indeterminate form. So if and when it does follow L’Hopital’s rule to interpret limits of ratios.
We might find for example that zeta holds remarkable symmetry between its even and odd indexed terms. And it might even be just because the harmonic series does that automatically.
But there is a challenge how we will ever portrait the zeta function as a complex number when it is this difficult reciprocal exponented term summed to infinity.
It could belong to a complexity class all its own for what we’re begging of it.
I don’t know how to place the complex arrow on it, do you?
The zero search tools don’t regard the fact their mush is devoid spatial information as in a complex range value out of a complex domain function. And it hangs them up on the critical strip right there in the middle, at 1/2.
It’s not even a complex number component they have extracted; but the fake like it is.
They have no idea where the real or the complex dissolves under function of taking the modulus of zeta. They’re just concerned with where their bouncing ball curve of modulus strikes the x axis. And it is a fact that a function’s zeros by whether it complex or real happen to indicate where it would be zero if complex–just without all that complexity.
That’s cheating and unsatisfactory.
..but ( they ) fake like it is”, 3rd paragraph from end. (line 8 counted from the end)
..I have a hunch..(etc)..there is more this..(etc)..than we have foreseen. ….
…The spell checking slays us on on these tidbits. (line 7 down from tag: Reimann .
There are other ways to unpack the zeta series.
I was going to add that the approach to this elementary problem is nearly identical in apprehension at least to the age old problem of quadratic completion of the square… This is like the last hurdle of preparatory algebra education in American public school curriculum.
Think about it though. Complete the obvious open n-limited discrete binomial. Is that obvious enough? You don’t have to worry about n, it’s like an open set, you just have to make what it goes assigned to make algebraic sense.
Complete this simple square. You can do it, anyone could if I did.
A Proof YOU CAN DO
…like, the original separation of variables, kind of?
Makes sense, less filling?
We could ask the question whether famous unsolved elementary mathematics questions are not a source of contention or rivalry among peoples.
For another example, it is obvious Reimann was used to lay claim to Complex Analysis by overstepping what could be inferred about the modulus of the zeta function’s roots.
..and since this is just playing to an empty house over a contraption help hostage, it serves the purposes of proof to indicate what a sore point of contention and ignorance math truly is and remains.
Meanwhile, your credit cards and passwords have been effortlessly swept by what Edward Snowden really leaked, what they don’t want you to suspect.
The noise of their mooing about civil liberties while picking everyone’s pockets.
I’d have to appraise the media flap of him as typical manipulation.
So was Assange.
You have all been taken for fools while enormities either went disguised, covered up or waiting in the wings.