Indeed, it reads more like the report of an intuition than a formal proof. Descartes underscores the simplicity of his demonstration by comparing it to the way we ordinarily establish very basic truths in arithmetic and geometry, such as that the number two is even or that the sum of the angles of a triangle is equal to the sum of two right angles. We intuit such truths directly by inspecting our clear and distinct ideas of the number two and of a triangle.

Mathematician — A mathematician is someone who uses an extensive knowledge of mathematics in his or her work, typically to solve mathematical problems.

Mathematics is concerned with numbers, data, quantity, structure, space, models, one of the earliest known mathematicians was Thales of Miletus, he has been hailed as the first true mathematician and the first known individual to whom a mathematical discovery has been attributed.

He is credited with the first use of deductive reasoning applied to geometry, the number of known mathematicians grew when Pythagoras of Samos established the Pythagorean School, whose doctrine it was that mathematics ruled the universe and whose motto was All is number.

It was the Pythagoreans who coined the term mathematics, and with whom the study of mathematics for its own sake begins, the first woman mathematician recorded by history was Hypatia of Alexandria.

She succeeded her father as Librarian at the Great Library and wrote works on applied mathematics. Because of a dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked. Science and mathematics in the Islamic world during the Middle Ages followed various models and it was extensive patronage and strong intellectual policies implemented by specific rulers that allowed scientific knowledge to develop in many areas.

As these sciences received wider attention from the elite, more scholars were invited and funded to study particular sciences, an example of a translator and mathematician who benefited from this type of support was al-Khawarizmi.

A notable feature of many working under Muslim rule in medieval times is that they were often polymaths. Examples include the work on optics, maths and astronomy of Ibn al-Haytham, the Renaissance brought an increased emphasis on mathematics and science to Europe.

As time passed, many gravitated towards universities. Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content. According to Humboldt, the mission of the University of Berlin was to pursue scientific knowledge.

In some universities, a qualifying exam serves to test both the breadth and depth of an understanding of mathematics, the students, who pass, are permitted to work on a doctoral dissertation.

Mathematicians involved with solving problems with applications in life are called applied mathematicians. Applied mathematicians are mathematical scientists who, with their knowledge and professional methodology.

With professional focus on a variety of problems, theoretical systems 2. Supersymmetry — Each particle from one group is associated with a particle from the other, known as its superpartner, the spin of which differs by a half-integer. In a theory with perfectly unbroken supersymmetry, each pair of superpartners would share the same mass, for example, there would be a selectron, a bosonic version of the electron with the same mass as the electron, that would be easy to find in a laboratory.

Thus, since no superpartners have been observed, if supersymmetry exists it must be a broken symmetry so that superpartners may differ in mass. Spontaneously-broken supersymmetry could solve many problems in particle physics including the hierarchy problem.

The simplest realization of spontaneously-broken supersymmetry, the so-called Minimal Supersymmetric Standard Model, is one of the best studied candidates for physics beyond the Standard Model, there is only indirect evidence and motivation for the existence of supersymmetry.

Direct confirmation would entail production of superpartners in collider experiments, such as the Large Hadron Collider, the first run of the LHC found no evidence for supersymmetry, and thus set limits on superpartner masses in supersymmetric theories.As direct-to-consumer marketing of medical genetic tests grows in popularity, there is an increasing need to better understand the ethical and public policy implications of such products.

Learning to analyze and critically evaluate ideas, arguments, and points of view IDEA research has found that it is related to Objectives #6 through #10 and Objective #12, which all address activities at the upper levels of cognitive taxonomies, activities requiring application and frequent synthesis and evaluation of ideas and events (3.

Jul 30, · Concerning Berkeley’s Argument about Pain, Pleasure, and the Existence of Sensible Objects Outside the Mind Posted on July 30, July 30, by Eleven Grams This paper is devoted to Berkeley’s argument concerning the pain and pleasure of certain sensible qualities, such as heat, taste, and odor, as a way to establish that .

Pascal's Wager about God Blaise Pascal () offers a pragmatic reason for believing in God: even under the assumption that God’s existence is unlikely, the potential benefits of believing are so vast as to make betting on theism rational.

Empiricism v. rationalism. THE EMPIRICISTS: Empiricists share the view that there is no such thing as innate knowledge, and that instead knowledge is derived from experience (either sensed via the five senses or reasoned via the brain or mind).

Locke, Berkeley, and Hume are empiricists (though they have very different views about metaphysics). Designed to replace the inadequate editions in Berkeley's Works, the present volume provides complete and critically established texts, with bibliographies and an index.

It will be of particular interest to Berkeley scholars, historians of mathematics, and anyone with an interest in the science and philosophy of the early modern period.

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