We humans have a great capacity to embrace a variety of philosophical paradoxes: infinity and nothingness in one breath without having truly experienced either one; belief without empirical evidence; empirical evidence without belief, simultaneous order and chaos, deterministic and random destinies, existential meaning and nihilism.

Blaise Pascal (1623 – 1662) was a French mathematician, physicist, inventor, writer and religious Christian philosopher. In his *Pensées*, he grappled with several philosophical paradoxes: faith and reason, soul and matter, death and eternal life, meaning and vain thinking. He ultimately arrived at no definitive conclusions but did put forward a wager, now called Pascal's Wager, which drew on probability theory for its justification.

A more modern stretch of the human imagination is the evasive answer to the question:

Can mathematics, precariously balanced on only five assumptions, the Peano Axioms which form the formal foundations for the natural numbers, be in fact the language of the universe?

“Astrophysicist and writer Mario Livio, along with a colorful cast of mathematicians, physicists, and engineers, follow math from Pythagoras to Einstein and beyond. It all leads to the ultimate riddle: Is math a human invention or the discovery of the language of the universe?

Join NOVA on a mathematical mystery tour — The Great Math Mystery — a provocative exploration of math's astonishing power across the centuries. We discover math's signature in the swirl of a nautilus shell, the whirlpool of a galaxy, and the spiral in the center of a sunflower. Math was essential to everything from the first wireless radio transmissions to the prediction and discovery of the Higgs boson and the successful landing of rovers on Mars.”

Gottfried Leibniz (1646 - 1716) was a German philosopher, physicist and mathematician. Even as a self-taught mathematician, he is famous for being one of the founders of Calculus, the discoverer of the binary numbers and the invention of an early version of the calculator, the latter two being precursors to the modern computer. However, it was his personal philosophy that led him to probe into the dynamics of the universe around him. Leibniz believed that we were living in a deterministic universe whose rhythm was derived from a ‘pre-established harmony.’ This led him to focus on a formulation of what he called ‘vis viva,’ that unseen ‘life force’ of a moving body, as being a product of its mass times the square of the velocity at which it was moving and that *vis viva* was subject to some kind of law of conservation or state of equilibrium. In mathematical terms, Leibniz considered a body’s *life force* to be = mv^{2}. This is so reminiscent of Einstein’s relativity equation between mass and energy which was introduced to the scientific community some two centuries later. E = mc^{2} where E represents the energy ( ‘life force’) equivalent to a moving body of mass m somewhere in the universe and c is the speed of light. In fact, there is a law of conservation built into this equation. It states that the ratio of a body’s energy over its mass is a constant, implying that energy and mass are in a constant state of equilibrium.

For more on the legacy of Leibniz’s idea of ‘vis viva’ or ‘life force,’ watch the documentary called: Order and Disorder

**Note:** Here the word ‘chaos’ is defined as the infinity of space or formless matter supposed to have preceded the existence of the ordered universe.

*Mathematician, Economist and Nobel Prize Laureate 1994*

It is not often that mathematicians win Nobel Prizes because there is no Nobel Prize in Mathematics. This is the autobiography of one who did. He has 'A Beautiful Mind', the central premise of the 2001 Oscar award winning film of the same name.

Of note is that the Field's Medal, sometimes referred to as the 'Nobel Prize of mathematics' and considered by many to be the most prestigious award a mathematician can receive, was founded as a legacy of a Canadian mathematician, John Charles Fields.

John Napier was a Scottish mathematician and inventor who lived in the latter part of the sixteenth and the early seventeenth centuries. Some of his innovative ideas and devices caused a great stir at the time.

From trying to sketch a walking tour of Konigsberg, Germany by traversing each of its seven bridges only once; to puzzling over primes; to pondering why Zeno's fleet-footed runner can never finish the course; to the seemingly child's play of colouring a clearly distinguishable map with only four colours; to solving inveterate gambling problems: mathematicians world wide have spent a great deal of prime time crunching numbers and symbols into solutions.

Clearly, mathematicians do think differently because when Fyodor Dostoyevsky played away his entire fortune in the elegantly appointed Wiesbaden Casino in 1865, he solved his gambling problems by writing another novel, "The Gambler", and having it published just two years later.

Speaking of thinking differently, some enterprising MIT students apparently used mathematical thinking to win the Massachusetts’ state lottery consistently from 2005 to 2011. Why were they able to “beat the System” for such a long period? A clever combination of number theory and geometry – and the ever-pervasive forces of human psychology and politics – may have been the answers to their success.

How Not to Be Wrong: The Power of Mathematical Thinking (published on June 24, 2015 by The Royal Institution)Updated December 12 2016 by Student & Academic Services

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