Abstract:
As an application of the grand unified theory (GUT) to medicine, this paper introduces two natural nanomaterials—the gene and electromagnetic wave. They are involved in the proposed treatment of genetic and infectious diseases. It introduces the superstring as the fundamental building block of matter and the basic constituent of dark matter, one of the two fundamental states of matter. It also introduces the primum, unit of visible or ordinary matter, the other fundamental state of matter. They are convertible to each other by the action of basic cosmic or electromagnetic waves. Eleven biological laws define biology as a biological and physical theory. The gene is the primitive ingredient of living things and, therefore, the beginning of biological life and the virus the simplest living thing. Treatment ranges from genetic modification and alteration to remove undesirable symptom through genetic sterilization to stop the spread of the disease and outright destruction of the disease. Genetic sterilization and outright destruction apply also to infectious diseases. The paper concludes with a blueprint for research and development of appropriate technologies for the treatment.

Abstract:
The paper reviews the most consequential defects and
rectification of traditional mathematics and its foundations. While this work
is only the tip of the iceberg, so to speak, it gives us a totally different
picture of mathematics from what we have known for a long time. This journey
started with two teasers posted in SciMath in 1997: 1) The equation 1 = 0.99…
does not make sense. 2) The concept ？does not
exist. The first statement sparked a debate that raged over a decade. Both
statements generated a series of publications that continues to grow to this day. Among the new findings are: 3) There does not exist
nondenumerable set. 4) There does not exist non-measurable set. 5) Cantor’s
diagonal method is flawed. 6) The real numbers are discrete and countable. 7)
Formal logic does not apply to mathematics. The unfinished debate between
logicism, intuitionism-constructivism and formalism is resolved. The resolution
is the constructivist foundations of mathematics with a summary of all the
rectification undertaken in 2015, 2016 and in this paper. The extensions of the
constructivist real number system include the complex vector plane and
transcendental functions. Two important results in the 2015 are noted: The
solution and resolution of Hilbert’s 23 problems that includes the resolution of Fermat’s last theorem and proof Goldbach’s conjecture.

Abstract:
Creativity and critical thinking are the core values of science. Since mathematics is its primary language, the student of mathematics must imbibe and consolidate them. Critical thinking is consolidated in the critique of current mathematics and its foundations, creativity in the construction of a mathematical space or system. Therefore, the student of mathematics must go through the twists and turns of the critique-recti- fication of current mathematics and its foundations which in this paper focuses on the real and complex number systems that results in the construction of the contradiction-free new real number system and the complex vector plane. Since this is an expository paper on creative education much of the content is quoted from the Author’s previous works.

Abstract:
The paper offers an overview of quantum and macro gravity, two of the three pillars of the Grand Unified Theory (GUT), the other thermodynamics, developed in a series of papers since the solution of the gravitational n-body problem in 1997 (J. Nonlinear Analysis, A-Series: Theory, Methods and Applications, Vol. 30, No. 8, 1997, pp. 5021 - 5032) and consolidated in the paper, The Grand Unified Theory (J. Nonlinear Analysis, A-Series: Theory: Method and Applications, Vol. 69, No. 3, 2008, pp. 823 - 831). GUT is further advanced by the paper, The Mathematics of GUT (J. Nonlinear Analysis, A-Series: Theory: Method and Applications, Vol. 71, 2009, pp. e420 - e431) and the discovery of more natural laws in the course of analyzing and explaining the disastrous final flight of the Columbia Space Shuttle in 2004 (J. Nonlinear Studies, Vol. 14, No. 3, 2007, pp. 241 - 260). Qualitative modeling was the key to the development of GUT and its theoretical and practical applications. The relevant natural laws of GUT that provide the foundations of the Unified Theory of Evolution are stated. GUT provides the basis for the development of the electromagnetic engine and the Unified Theory of Evolution, its theoretical application, for the development of appropriate technology for electromagnetic treatment of genetic diseases such as cancer, systemic lupos erythematosus, diabetes, muscular dystrophy and mental disorder, the central focus of this paper.

The grand unified theory (GUT) originated in mathematics with this
question: why are there long standing unsolved problems in mathematics, e.g.,
Fermat’s conjecture (also known as Fermat’s last theorem (FLT))? The answer
came quickly: its underlying fields—foundations and the real number system—are
defective. In particular, formal logic isinapplicable to
mathematics (language of science) and the real number system is inconsistent.
Critique-rectification of these fields was undertaken leading to a new
mathematical methodology and the consistent new real number system that
provides the main mathematics of GUT. Similar question was posed in physics:
why are there long standing problems, e.g., the gravitational n-body and
turbulence problems? The answer: the present methodology, quantitative modeling
is inadequate and the remedy is a new methodology—qualitative mathematics and
modeling that solved these problems and provided the initial formulation of
GUT. This paper presents the basic logic of GUT and its fundamental concepts,
particularly, the superstring or fundamental building block of matter.

The paper identifies chaos, turbulence and fractal of quantum and
macro gravity and studies their behavior, properties and applications based on
the grand unified theory (GUT) and qualitative mathematics and modeling.
Applications include devising electromagnetic engines, tornado aborter and
terminator and technologies for electromagnetic treatment of genetic diseases
such as cancer, systemic lupos erythematosus, diabetes and mental disorder
without harm to normal cell and side effect. Typhoon in the Western Pacific
which is turbulence is impossible to terminate and impractical to deflect but
prediction can be improved because it follows the Northern Pacific Wind Cycle
(Southern Pacific Wind Cycle in the Southern Hemisphere) and is affected by the
temperature variation over the Philippine Deep and around Mayon Volcano. The
electromagnetic engine uses the clean, inexhaustible, free dark matter,
specifically, the energy of magnetic flux, in place of conventional fuel, e.g.,
fossil, nuclear and geothermal. The tornado aborter and terminator utilize the
gravitational flux of the Earth, its vortex flux of superstrings as a
cosmological vortex which is turbulence. The technologies for electromagnetic
treatment of genetic diseases utilize electromagnetic waves based on resonance.
All of them are GUT technologies because they are applications of GUT. Except
for the magnetic train which is in operation the rest is still at the
conceptual and research and development (R&D) phase but the theory is
complete and the strategy for R&D are laid down in detail in the cited
original papers.

Abstract:
This paper establishes the link between human activity and climate change, e.g., more frequent and devastating typhoons, tornadoes, bushfires, droughts, floods and snowstorms and melting of the norther polar ice cap and recent occurrences of super typhoons and tornadoes. Qualitative mathematics and modeling(QMAM) explains this link and its remarkable verification based on the grand unified theory(GUT).

Abstract:
A blueprint for research and development for design and development of suitable electromagnetic
treatment of genetic diseases (Escultura, Journal of Biomaterials and Nanobiotechnology, 3(2),
2012) known as genetic sterilization is applied to infectious diseases including viruses. It is based
on the Grand Unified Theory (Escultura, Nonlinear Analysis, A-Series, 69(3), 2008) and the Unified
Theory of Evolution (Escultura, The Journal of the Science of Healing Outcomes, 2015). Since every
physical characteristic of living thing is determined by a gene, so is the undesirable symptom of a
disease. For virus, its undesirable symptom is determined principally by the wavelength of the
natural vibration of its gene as sequence of base materials which is equal to its measure as a segment
of a double helix. Radiation with wavelength equal to this measure will resonate with it.
Raising its intensity suitably will sterilize the gene, stop its spread and render it harmless to the
host; then the disease is treated without harm to normal cells. Another treatment is establishing
resonance with radiation of wavelength equal to the measure of the virus (protein strand with the
gene) across; raising its intensity suitably will burn the virus without side effect (since it is much
smaller than normal cells).

Abstract:
The paper resolves the great debate of the 20th century between the three philosophies of mathematics-logicism, intuitionism and formalism—founded by Bertrand Russell and A. N. Whitehead, L. E. J. Brouwer and David Hilbert, respectively. The issue: which one provides firm foundations for mathematics? None of them won the debate. We make a critique of each, consolidate their contributions, rectify their weakness and add our own to resolve the debate. The resolution forms the new foundations of mathematics. Then we apply the new foundations to assess the status of Hilbert’s 23 problems most of which in foundations and find out which ones have been solved, which ones have flawed solutions that we rectify and which ones are open problems. Problem 6 of Hilbert’s problems—Can physics be axiomatized?—is answered yes in E. E. Escultura, Nonlinear Analysis, A-Series: 69(2008), which provides the solution, namely, the grand unified theory (GUT). We also point to the resolution of the 379-year-old Fermat’s conjecture (popularly known as Fermat’s last theorem) in E. E. Escultura, Exact Solutions of Fermat’s Equations (Definitive Resolution of Fermat’s Last Theorem), Nonlinear Studies, 5(2), (1998). Likewise, the proof of the 274-year-old Goldbach’s conjecture is in E. E. Escultura, The New Mathematics and Physics, Applied Mathematics and Computation, 138(1), 2003.

Abstract:
The paper summarizes the contributions of the three philosophies of mathematics—logicism, intuitionism-constructivism (constructivism for short) and formalism and their rectification—which constitute the new foundations of mathematics. The critique of the traditional foundations of mathematics reveals a number of errors including inconsistency (contradiction or paradox) and undefined and vacuous concepts which fall under ambiguity. Critique of the real and complex number systems reveals similar defects all of which are responsible not only for the unsolved long standing problems of foundations but also of traditional mathematics such as the 379-year-old Fermat’s last theorem (FLT) and 274-year-old Goldbach’s conjecture. These two problems require rectification of these defects before they can be resolved. One of the major defects is the inconsistency of the field axioms of the real number system with the construction of a counterexample to the trichotomy axiom that proved it and the real number system false and at the same time not linearly ordered. Indeed, the rectification yields the new foundations of mathematics, constructivist real number system and complex vector plane the last mathematical space being the rectification of the complex real number system. FLT is resolved by a counterexample that proves it false and the Goldbach’s conjecture has been proved both in the constructivist real number system and the new real number system. The latter gives to two mathematical structures or tools—generalized integral and generalized physical fractal. The rectification of foundations yields the resolution of problem 1 and the solution of problem 6 of Hilbert’s 23 problems.