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 o...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.展开更多
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 infectiou...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.展开更多
文摘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.
文摘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.
