Pascal on Analysis

Blaise Pascal (1623-1662) posited the following still useful rules for constructing arguments in what he characterizes as "geometric" analysis (Pascal, 1952, p. 443):

1. Do not leave undefined any terms at all obscure or ambiguous.
2. Use in definitions only terms perfectly well known or already explained.
3. Ask only that evident things be granted as axioms.
4. Prove all propositions, using for their proof only axioms that are perfectly self-evident or propositions already demonstrated or granted.
5. Never get caught in the ambiguity of terms by failing to substitute in thought the definitions which restrict or explain them.

Blaise Pascal (1623-1662)

Pascal's thinking remains instructive to this day for all forms of analysis.

Source: Pascal, B (1952), On Geometrical Demonstration (On the Geometrical Mind) (R Scofield, Trans). In R M Hutchins & M Adler (Eds), Great Books of the Western World (Vol 33, pp. 430-446), Chicago, IL: Encyclopedia Britannica.

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Mathematics, Problem-Solving, and Critical Thinking

The following is extracted from a speech presented by Grace Fu to winners of the Singapore Mathematical Society's Annual Prize Presentation Ceremony in 2008:

Mathematics will imbue you with problem-solving skills such as the ability to understand a problem, identify the relevant information, look for relationships and patterns, make your own conjectures and apply mathematical knowledge and tools to solve or prove them. Mathematics, thus, provides good opportunities for the training of the mind to think critically and adapt to new situations, something that will be valuable to your future careers.

The words above are instructive for anyone seeking to join the ranks of analytics professionals worldwide. The ability to solve complex problems through critical thinking and reasoning is essential in today's analytics-based economy. Singapore is recognized around the world as a leader in the conceptual mathematics movement.

Grace Fu Hai Yien (Chinese: 傅海燕; pinyin: Fù Hǎiyiàn)

Source: Fu, G (2008), Speech at the Singapore Mathematical Society Annual Prize Presentation Ceremony.

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