UP Math prof proves Princeton man wrong
Edgar Escultura, a professor of mathematics at the University of the Philippines, proved that Andrew Wiles' proof of Fermat's last theorem is false.
Escultura's refutation sparked much discussion on the Internet that has spilled over to other fields such as physics, astronomy, cosmology, intelligence, learning, chaos, turbulence, gravity and nonlinear analysis.
He took the position that the failure to resolve the problem for over 360 years reveals the inadequacy and defects of foundations, number theory and the real number system. He undertook a thorough critique-rectification of these fields and found, among others, that the real number system in basic algebra, the foundation of mathematics, is defective. Specifically, two of its axioms (the trichotomy and completeness axioms, for those who took basic algebra in high school and college) are false. More >>
Is this true? Can someone help me verify this? I don't want to let out a nationalistic whoop and help spread the news if this turns out to be a hoax, much like the girl named Faye who allegedly won an international contest but whose story turned out to be a big fat lie. Even legitimate and respected newspapers get fooled, much like Philippine Star which carried the Faye article written by that infernal Patricia Evangelista.
In-N-Out's website has a new look! Ooh, I love In-N-Out.
After watching Encantadia last night, my dad gave a dissatisfied grunt, remarking on how stupid Amihan is for not being able to tell that her "daughter" isn't, well, her daughter at all.
Might I also say that it's interesting how Nancy Castiglione has been cast once again as a tiny fairy. This trend in her career may be the reason why she appears to have been wasting away lately, possibly in an effort to keep in step with the pixies she portrays.
To the person who typed in the keywords "what are diwatas" and got to this website: I hope no Philippine mythology enthusiast will shoot me for this guess, but I reckon they'd be about the same as elves (the tall gorgeous kinds) or fairies even (tall gorgeous fairies, not the mischievous giggling kind who trick wayward travelers). I might even say they're like nymphs, except they're not enormous flirts and teases. If one would imagine what a diwata looks like, one would be put in mind of slim women with long hair, wearing wreaths of flowers on their head and wearing filmy long dresses.
5 Comments:
Hello.
The Queen and her sister were looking for Muyak. That was how they got to the Asnamon Tree and discoverd that Pirena had given them the slip.
Amihan did not see her child after he delivery as she was exhausted. She fell asleep. The only one who really saw the child was Alena, and this was perhaps why she was the one who noticed the difference.
14/5/05 09:06
Hey, thanks! ^_^ I was telling my dad that Alena was the only one who saw the baby, but he wouldn't listen.
I missed the episode wherein they were looking for Muyak. I had to forgo Encantadia in favor of the The Amazing Race 7 finale.
14/5/05 19:12
andrew wiles letter to the math professor sounds sarcastic (e.g. "let's make a perfect proof great professor...").
i'm glad to find the engcantadia commentary..i and my housemates enjoy watching it, despite its recent slide to predictable melodrama :) i hope they develop the original characters instead of adding a whole bunch of new ones. the episode you missed was one of the good ones.
18/5/05 13:40
pcij's take on this
22/5/05 15:08
Alecks Pabico of pcij claims to have received a letter from Andrew Wiles written in Filipino English.
He then proceeded to go around the internet with Roy Choco spreading nonsense about FLT for both of them are totally ignorant of what the issue is all about. When I pointed this out he cried, moTHERRRR.......!!!! and threatened to sue me for slander. I told his lawyer, Atty. D'Campanilla to send me the subpoena immediately so I can tell it to the Marines.
Below is the documentation of my feat: proving Andrew Wiles wrong and resolving
FLT by countably infinite counterexamples.
MY STRATEGY FOR CAPTURING FLT.
I wondered why FLT remained unresolved for centuries and concluded that its underlying fields foundations, number theory and the real number system are defective. In particular, number theory is flawed because its subject matter, the integers have no valid axiomatization. Therefore, I embarked on their critique-rectification that yielded the following:
1) There are sources of contradiction in mathematics including ambiguous and vacuous concepts, large and small numbers (depending on context), unbounded or infinite set and self-reference. Here is an example of vacuous concept: A triquadrilateral is a plane figure with three vertices and four edges. The Richard paradox is an example of self-reference: The barber of Seville shaves those and only those who do not shave themselves; who shaves the barber? Incidentally, the indirect proof is flawed, being self-referent.
2) Among the requirements for a contradiction-free mathematical space are the following:
a) It must be well-defined by consistent axioms and every concept must be well-defined by them. A concept is well-defined if its existence, properties and relationship with other concepts are specified by the axioms. A false proposition cannot be an axiom as it introduces inconsistency. For example, this proposition cannot be used as an axiom of any mathematical space: There exists a triangle with four edges.
b) The rules of inference (mathematical reasoning) must be specific to and well-defined by its axioms.
c) Any proposition involving the universal or existential quantifiers on infinite set is not verifiable and, therefore, cannot be used as an axiom for it would not endow certainty to the conclusion of a theorem.
3) The real number system does not satisfy the requirements for a contradiction-free mathematical space. In particular, the trichotomy axiom is false since it is equivalent to natural ordering which the real number system has none because most of its concepts are ill-defined. Therefore, the real number system is ill-defined or nonsense and FLT being fomulated in it is also nonsense. Consequently, to resolve FLT the real number system must be fixed first and FLT must be reformulated in it. Andrew Wiles failed to do this and his work collapses althogether.
4) It is alright to introduce ambiguity provided it is 'approximable" by certainty. For example, a nonterminating decimal is ambiguous since not all its digits are known but it can be approximated by a segment at the nth decimal digit at margin of error 10^-n.
5) The rectification is to build a new real number system R* with three simple axioms and two operations + and x: 1) R* contains the basic integers 0, 1, ..., 9, and the operations + and x are well-defined by 2) the addition and 3) multiplication tables of arithmetic that we learned in primary school. The rest of the elements of R* are the terminating decimals first which are later extended to the nonterminating decimals.
A new real number is well-defined if every digit is known or computable, i.e., there is some rule or algorithm for determining it uniquely.
6) The new elements of the new real number system are the dark number d* = 1 0.99 - N (N1), N = 0, 1, (the ordinary integers), and u* the equivalence class of divergent sequences. The integers are mapped into the decimal parts of the decimals; this is the needed rectification to number theory. Then the integers are embedded in R* by the mapping 0 > d*, N > (N1).99 , the new integers, to well-define them. The well-defined real numbers are embedded in R* as terminating decimals (note that the well-defined real numbers are the terminating decimals. Nonterminating decimals cannot be added or multiplied because the operations + and x require the last element to carry out. In R* the nonterminating decimals are well-defined Cauchy sequences and the operations + and x are well-defined accordingly.
7) Then the counterexamples to FLT are as follows: Let x = (0.99...)10^T, y = d*, z = 10^T, where T is an ordinary integer, T = 1, 2, ... Then x, y, z satisfy Fermat's equation, for n > 2,
x^n + y^n = z^n.
Moreover, if k = 1, 2, ..., is ordinary integer, kx, ky, kz also satisfy Fermat's equation. They are the counterexamples to FLT. They prove that FLT is false and Wiles is wrong.
The critique-rectification of the underlying fields of FLT, the construction of the counterexamples and applications of this new methodology, especially in physics, are developed in the following articles in renowned refereed international journals and conference proceedings:
[18] Escultura, E. E. (1996) Probabilistic mathematics and applications to dynamic systems including Fermat's last theorem, Proc. 2nd International Conference on Dynamic Systems and Applications, Dynamic Publishers, Inc., Atlanta, 147 152.
[19] Escultura, E. E. (1997) The flux theory of gravitation (FTG) I. The solution of the gravitational n-body problem, Nonlinear Analysis, 30(Cool, 5021 5032.
[20] Escultura, E. E. (1998) FTG VII. Exact solutions of Fermat's equation (Definitive resolution of
Fermat's last theorem, J. Nonlinear Studies, 5(2), 227 254.
[21] Escultura, E. E. (1999) VIII. Superstring loop dynamics and applications to astronomy and biology, J. Nonlinear Analysis, 35(Cool, 259 285.
[22] Escultura, E. E. (1999) FTG II. Recent verification and applications, Proc. 2rd International Conf.: Tools for Mathematical Modeling, St. Petersburg, vol. 4, 74 89.
[23] Escultura, E. E. (2000) FTG IX. Set-valued differential equations and applications to quantum gravity, Mathematical Research, Vol. 6, 2000, St. Petersburg, 58 69.
[24] Escultura, E. E. (2001) FTG X. From macro to quantum gravity, J. Problems of Nonlinear Analysis in Engineering Systems, 7(1), 56 78.
[25] Escultura, E. E. (2001) FTG XI. Quantum gravity, Proc. 3rd International Conference on Dynamic Systems and Applications, Atlanta, 201 208.
[26] Escultura, E. E. (2001) FTG. XII. Turbulence: theory, verification and applications, J. Nonlinear Analysis, 47(2001), 5955 5966.
[27] Escultura, E. E. (2001) FTG III: Vortex Interactions, J. Problems of Nonlinear Analysis in Engineering Systems, Vol. 7(2), 30 44.
[28] Escultura, E. E. (2001) FTG IV. Chaos, turbulence and fractal, Indian J. Pure and Applied Mathematics, 32(10), 1539 1551.
[29] Escultura, E. E. (2002) FTG V. The mathematics of the new physics, J. Applied Mathematics and Computations, 130(1), 145 169.
[30] Escultura, E. E. (2003) FTG VI. The theory of intelligence and evolution, Indian J. Pure and Applied Mathematics, 33(1), 111 129.
[31] Escultura, E. E. (2003) FTG XVII: The new mathematics and physics, J. Applied Mathematics and Computation, 138(1), 127 149.
[32] Escultura, E. E. (2003) FTG XVIII. Macro and quantum gravity and the dynamics of cosmic waves, J. Applied Mathematics and Computation, 139(1), 23 36.
[33] Escultura, E. E. (2001) FTG. XIV. The mathematics of chaos, turbulence, fractal and tornado breaker, deflector and aborter, Proc. Symposium on Development through Basic Research, National Research Council of the Philippines, University of the Philippines, 1 13.
[34] Escultura, E. E. FTG XIX. Recent results, new inventions and the new cosmology, accepted, J. Problems of Nonlinear Analysis in Engineering System.
[35] Escultura, E. E. FTG XV. The new nonstandard analysis and the intuitive calculus, submitted.
[36] Escultura, E. E. (2002) FTG VI. The philosophical and mathematical foundations of FLTs resolution, rectification and extension of underlying fields and applications, accepted, J. Nonlinear Differential Equations.
[37] Escultura, E. E. (2002) FTG XXII. Extending the reach of computation, submitted.
[38] Escultura, E. E. (2003) The theory of learning and implications for Math-Science Education, submitted.
[39] Escultura, E. E. (2003) FTG XXIII. The complex plane revisited, accepted, Journal of Nonlinear Differential Equations.
[40] Escultura, E. E. (2002) FTG XXIV. Columbia: the crossroads for science, accepted, J. Nonlinear Differential Equations.
[41] Escultura, E. E. (2003) FTG XXV. Dynamic Modeling and Applications, Proc. 3rd International Conference on Tools for Mathematical Modeling, State Technical University of St. Petersburg, St. Petersburg.
[42] Escultura, E. E. (2004) FRG XXVII XXVIII. Part I. The new frontiers of mathematics and physics. Part I. Theoretical Construction and Resolution of Issues, Problems and Unanswered Questions.
[43] Escultura, E. E. (2005) FRG XXVII XXVIII. The new frontiers of mathematics and physics. Part II. The new real number system: Introduction to the new nonstandard analysis, Nonlinear Analysis and Phenomena, II(1), January, 15 30.
[44] Escultura, E. E. (2005) FTG XXVI. Dynamic Modeling of Chaos and Turbulence, Proc. 4th World Congress of Nonlinear Analysts, Orlando, June 30 July 7, 2004.
[45] Escultura, E. E. FTG. XXVII (2005). The theory of everything, Nonlinear Analysis and Phenomena, II(2), 1 45.
[46] Escultura, E. E. Escultura (2006) FTG XXXIV. Foundations of Analysis and the New Arithmetic,
Nonlinear Analysis and Phenomena, January 2006.
[47} Escultura, E. E. FTG XXXV (2006) The Pillars of FTG and some updates, Nonlinear Analysis and Phenomena, III(2), 1 22.
[48] Escultura, E. E. FTG XXXVI (2006) The New Nonstandard Calculus, accepted, Nonlinear Analysis.
For more info see my website: http://home.iprimus.com.au/pidro/
WHAT IS THE TAKE ON FLT?
Since 1997 my work in Math and Physics, especially, FLT, has been widely discussed and debated across the Internet in various fora, websites and newsgroups. In the math forum Sci Math I have several threads on topics related to FLT. One of the earliest was the thread, Is 1 = 0.99 ? This alone generated about 700 posts and has been resolved in my favour. Since January I posted in Sci Math the thread, Contradiction-Free Mathematical Space, The Adics and Other Nonsense, My Strategy for Capturing the Basic Constituent of Matter and The State-of-the-Art in Mathematics. The first thread alone generated 153 posts and all of them were resolved in my favour. They are all quiet now and consigned to the archives with me having the last words. All threads in Sci Math since 1997 have generated over 2,000 posts. I also have several threads in Mathforge that generated about 700 posts and another in ISCID (International Society for Complexity, Information and Design), New Approach to Physics, covering 5 pages. Now, all is quiet not just in the Western Front but in all Fronts for these threads and websites because the issues have all been resolved in my favour with me having the last words.
When the Manila Times carried the news story, UP Prof Proves Princeton Man Wrong, Blogs and threads sprouted like mushrooms attacking my work as a hoax, calling me names and chastising me for taking the Manila Times for a ride. None of them knew the issues involved and they all blurted nonsense all along. Unfortunately, I knew about them only last April. Now that I have responded to them, except the monologues or blogs that disallow posts of contrary opinions, they are also quiet now. But their booh-boohs have come home to roost and one of the bloggers, Alex of pcij, after having slandered me for over a year, cried, moTHERRRR .!!!!! and threatened to sue me for slander. I told him to send the subpoena soon so that I can tell it to the Marines. His threat is posted on my Message Board at http://home.iprimus.com.au/pidro/ .
But here is the rub:
After more than 9 years of discussion and debate NOT A SINGLE HOLE HAS BEEN PUNCH ON MY WORK. A blog reported that my name ranks 4th in successful searches next to the mathematician Euler and followed by analyst Danzig, a poor 5th, with my share of 1.7%. On top of these, neither Andrew Wiles nor his three supporters, Ribet of UC Berkeley, Mazur of Harvard and Saranak of Princeton, refuted my criticisms of Wiles work or challenged my counterexamples to FLT to prove it false and Wiles wrong.
Where, oh, where art thou smart guys from the UP Math Department? Enliven this blog and debate with me. You dont have to identify yourself if you are embarrassed by your own feeble ideas and empty publication list.
For the benefit of the doubting Thomases, here is an aspirin:
The ScienceDirect TOP25 Hottest Articles is a free quarterly service from ScienceDirect. When you subscribe to the ScienceDirect TOP25, you'll receive an e-mail every three months listing the ScienceDirect users' 25 most frequently downloaded journal articles, from any selected journal among more than 2,000 titles in the ScienceDirect database, or from any of 24 subject areas.
TOP25 articles within the journal:
Nonlinear Analysis
OCT - DEC 2005
1. Initial value problems for higher-order fuzzy differential equations Article
Nonlinear Analysis, Volume 63, Issue 4, 1 November 2005, Pages 587-600
Georgiou, D.N.; Nieto, J.J.; Rodriguez-Lopez, R.
2. Fixed point solutions of variational inequalities for asymptotically nonexpansive mappings in Banach spaces Article
Nonlinear Analysis, Volume 64, Issue 3, 1 February 2006, Pages 558-567
Shahzad, N.; Udomene, A.
3. Variational approach to nonlinear problems and a review on mathematical model of electrospinning Article
Nonlinear Analysis, Volume 63, Issue 5-7, 1 November 2005, Pages e919-e929
He, J.-H.; Liu, H.-M.
4. Approximation of common fixed points for a family of finite nonexpansive mappings in Banach space Article
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Wu, D.; Chang, S.-S.; Yuan, G.X.
5. Nonlinear differential equations with nonlocal conditions in Banach spaces Article
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Xue, X.
6. A survey on piecewise-linear models of regulatory dynamical systems Article
Nonlinear Analysis, Volume 63, Issue 3, 1 November 2005, Pages 336-349
Oktem, H.
7. Fixed point theorems in metric spaces Article
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Proinov, P.D.
8. Dynamic modeling of chaos and turbulence Article
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Escultura, E.E.
9. Existence result for periodic solutions of a class of Hamiltonian systems with super quadratic potential Article
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Karshima Shilgba, L.K.
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Guo, D.
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Nonlinear Analysis
Dhompongsa, S.; Kirk, W.A.; Sims, B.
12. High regularity of the solutions of the telegraph system subjected to nonlinear boundary conditions Article
Nonlinear Analysis, Volume 63, Issue 4, 1 November 2005, Pages 491-512
Apreutesei, N.
13. Viscosity approximation methods for a family of finite nonexpansive mappings in Banach spaces Article
Nonlinear Analysis
Jung, J.S.
14. New modelling approach concerning integrated disease control and cost-effectivity Article
Nonlinear Analysis, Volume 63, Issue 3, 1 November 2005, Pages 439-471
Tang, S.; Xiao, Y.; Clancy, D.
15. Existence and approximation of solutions of second-order nonlinear four point boundary value problems Article
Nonlinear Analysis, Volume 63, Issue 8, 1 December 2005, Pages 1094-1115
Khan, R.A.; Lopez, R.R.
16. Autonomous steering control for electric vehicles using nonlinear state feedback H"~ control Article
Nonlinear Analysis, Volume 63, Issue 5-7, 1 November 2005, Pages e2257-e2268
Moriwaki, K.
17. A Petri net-based object-oriented approach for the modelling of hybrid productive systems Article
Nonlinear Analysis, Volume 62, Issue 8, 1 September 2005, Pages 1394-1418
Villani, E.; Pascal, J.C.; Miyagi, P.E.; Valette, R.
18. Existence and uniqueness of a wavefront in a delayed hyperbolic-parabolic model Article
Nonlinear Analysis, Volume 63, Issue 3, 1 November 2005, Pages 364-387
Ou, C.; Wu, J.
19. Positive solutions of second-order two-delay differential systems with twin-parameter Article
Nonlinear Analysis, Volume 63, Issue 4, 1 November 2005, Pages 601-617
Bai, D.; Xu, Y.
20. Multiple positive and sign-changing solutions for a singular Schrodinger equation with critical growth Article
Nonlinear Analysis, Volume 64, Issue 3, 1 February 2006, Pages 381-400
Chen, J.
21. Strong convergence of the CQ method for fixed point iteration processes Article
Nonlinear Analysis
Martinez-Yanes, C.; Xu, H.-K.
22. Nonlinear analysis of arterial blood flow-steady streaming effect Article
Nonlinear Analysis, Volume 63, Issue 5-7, 1 November 2005, Pages 880-890
Jayaraman, G.; Sarkar, A.
23. Existence and exponential stability of periodic solution for impulsive delay differential equations and applications Article
Nonlinear Analysis, Volume 64, Issue 1, 1 January 2006, Pages 130-145
Yang, Z.; Xu, D.
24. Uniqueness results for nonlinear elliptic equations with a lower order term Article
Nonlinear Analysis, Volume 63, Issue 2, 1 October 2005, Pages 153-170
Betta, M.F.; Mercaldo, A.; Murat, F.; Porzio, M.M.
25. Positive solutions of a second-order singular ordinary differential equation Article
Nonlinear Analysis, Volume 61, Issue 8, 1 June 2005, Pages 1383-1399
Bonheure, D.; Gomes, J.M.; Sanchez, L.
View this website at: http://top25.sciencedirect.com/index.php?subject_area_id=16&journal_id=0362546X
Paper No. 8, Dynamic Modelling of Chaos and Turbulence, presented by the author at a plenary session of the 4th World Congress of Nonlinear Analysts, Orlando, FL, July 5, 2004, provides, for the first time, the most comprehensive explanation of gravity as part of the dynamics of turbulence, specifically, vortex flux of superstrings (the superstring is the basic constituent of matter), such as galaxy, star, planet and moon (note their spins as vortices). Dynamic modelling (an off-shoot of the resolution of FLT), the new methodology introduced by the author as an alternative to the present methodology of physics called mathematical modelling (that describes nature in terms of numbers, equations, functions, etc.) explains nature in terms of its laws. To-date 43 laws of nature have been discovered using this new methodology.
E. E. Escultura
14/6/06 18:08
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