Transformational Minds

 

Cantor

Between bouts of insanity and frequent hospitalizations, Georg Cantor laid the foundations of set theory and proved that one infinity could be bigger than another infinity. Cantor put quantitative boundaries on something that was considered to be intrinsically unquantifiable.


Cantor’s works give us insight into putting normative boundaries around infinite state spaces.

 

Hilbert


The 23 problems which German mathematician David Hilbert put forth in Paris in 1900 formed much of the agenda for 20th century mathematical research. Some of these problems remain unsolved.


Theoretical research is in its infancy, with many exciting transformations yet to be discovered.

 
Godel

During his U.S. citizenship interview, Kurt Gödel felt compelled to announce that he had discovered a logical loophole in the framing of the U.S. Constitution that could conceivably enable a dictatorship to be created. What was worse, the eccentric theorist claimed that he had a proof for it.


The two sponsors who had vouched for him, Einstein and Morgenstern, somehow convinced him not to speak further on the matter, and Gödel became a US citizen.


Gödel’s works have given us insight into the power of first order logic and its limitations to capture mathematical induction.

 

Sir Isaac Newton


Newton did foundational work in physics, mathematics, astronomy and natural philosophy, and wrote Philosophiae Naturalis Principia Mathematica still in print (and avidly studied) more than 300 years after its first publication.

 

Archimedes


Archimedes didn’t invent the lever, but he explained the properties of leverage, by which applied force may be multiplied many times over. Archimedes is reported to have proclaimed, "Give me a place to stand on, and I will move the Earth."

Autonomics is a profound force multiplier for IT service management.

 

RussellBertrand Russell’s seminal work, Principles of Mathematics, was a dense tome, nearly 600 pages long. Legend has it that a London newspaper offered a cash prize to anyone who actually read the book — and no one received the prize. Of course, Russell’s writings were highly regarded and later awarded the Nobel Prize.

Russell believed, “Science may set limits to knowledge, but should not set limits to imagination.” Today, his domain of expertise, set theory, applies to triaging incoming exceptions and amortizing the event management load across global network operation centers.

 

Turing

Alan Mathison Turing was a British mathematician noted for his pioneering work on computer theory and artificial intelligence. Among his lesser known works: A failed attempt to use a Fourier series to explain the pattern of a zebra's stripes.


Not all theoretical transforms succeed. Edison was probably right: Genius is 1% inspiration, 99% perspiration.

 

Leibniz


Leibniz's intellectual output in fields ranging from law to logic was characterized by a consistent and clear-eyed rigorousness in reasoning.


Rigorous logical analysis enables us to see things as they are, not as we wish them to be. This knowledge is powerful, and essential to making sound management decisions in any environment, especially IT.

 

Pascal

In collaboration with Fermat, Pascal essentially discovered and developed the discipline of probabilities.


Pascal’s practical application of pure mathematics to solve real-world problems remains a gold-standard model for the application of theoretical research.

 

Fermat


One day in 1637, Pierre de Fermat made a curious note in his copy of Diophantus's Arithmetic: "The equation xn+ yn = zn, where x, y, and z are positive integers, has no solution if n is greater than 2... I have discovered a most remarkable proof, but this margin is too narrow to contain it."


It took mankind over 350 years to prove Fermat’s last theorem.


Bayesian analysis coupled with Fermat’s work on probability theory assists us in statistical learning techniques.

 

Pythagoras


Pythagoras believed that mathematics was the root of all truth and the ultimate reality. Iamblicus, a later Pythagorean follower, quoted the master as saying, “Number is the ruler of forms and ideas and the cause of gods and demons.”


Numbers don’t lie. To understand and control your IT environment, you have to have measurable, accurate and reliable information.

 

LaplacePierre Laplace researched the stability of the solar system, authored several seminal works of probability and observed:  “Probability theory is nothing but common sense reduced to calculation.”

Probability theory is at the foundation of Bayesian models that allow expert systems to adaptively learn by observing the behavior of humans.

 

Euclid


Euclid’s Elements became a foundational text in both mathematics and logic. Euclid created some of the world’s first algorithms — sets of rules for solving problems — inspiring computer scientists as well.


The rigorous application of logic and rule-based reasoning can transform your thinking about any kind of problem, including managing your IT infrastructure.

 

Euler


Euler gave us remarkable works in number theory, including the Euler's number "e." When he grew blind in one eye, he said, "I shall now have fewer distractions" and continued to make noteworthy contributions to calculus and algebra.


Mathematical modeling and deterministic finite state machines hold the keys to several autonomic engines.

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