Science of Mathematics: Passion of Mathematicians.

It’s not an empty-talk of jobless fellow, rather something that we forget to feel while pursuing Mathematics. Mathematics: A smart fabric of arithmetically spun science woven by logical tricks, and at last worn by the Science itself; Truly, complicatedly woven fabric; will look great but to study - baffles. A famous quote of Albert Einstein: “Do not be troubled by your difficulties with Mathematics, I can assure you mine are much greater”. Of course it’s difficult, when you are about to invent something new, but not to pursue the well based Mathematics. Unlike rhetoric literature, by its look of mere symbols determined to its own purpose, Mathematics is boring, I agree! Then for what, the hell is to be learned! Otherwise we cannot enjoy advantages of Science. OK! Then how the hell is to be learned! So, it’s to be considered - The Science of Mathematics. Science is the rhetoric of Mathematics, can also ascribe to its Soul.

The story of Duo: - They were friends since high school, talking about their jobs. One of them became a statistician and was working on population trends. He showed a reprint to his former classmate. The reprint started, as usual, with the Gaussian distribution and the statistician explained to his former classmate the meaning of the symbols for the actual population, for the average population, and so on. His classmate was a bit incredulous and was not quite sure whether the statistician was pulling his leg. "How can you know that?" was his query. "And what is this symbol here?" "Oh," said the statistician, "this is pi." "What is that?" "The ratio of the circumference of the circle to its diameter." "Well, now you are pushing your joke too far," said the classmate, "surely the population has nothing to do with the circumference of the circle."

Have you ever wonder upon persistent usage Mathematical constant ‘π’ and Exponential constant ‘e’ in the equations of discoveries of scientific theories along the history. Actually they are scientific constants. How? They are Transcendental Numbers! Transcendental numbers are any number that is not an Algebraic Number (technically cannot be expressed as the root of any algebraic equation with rational coefficients) means, their existence cannot have pure mathematical form. I said pure mathematical form! Their existence is Real, Physical, or Scientific. Similarly there are certain numbers which have Mathematical form, but no physical existence. Actually they are not numbers, but something abrupt result of algebraic operations bound to Zero. Zero at denominator (anything or zero divided by zero). Technically it’s ‘Not Defined’. Not yet. But it’s not cannot be defined. There is nothing to wonder if, in future, it is defined to be something else. Root of negative unity is defined as imaginary number and kept orthogonal to real axis. Likewise zero at denominator can also be defined as something and be kept at separate set of numbers – an inverse of real & imaginary set. Not a bluff! We accepted that Time is relative; Masses and Energy are different aspects of single thing. Take the case of Dark Matter that still teases the physicists. Science is Wonder! Think again!

Mathematics is the easy way to study Science. Studying Mathematics with these deep understandings, we may not feel the mental/mechanical strain, and also we can find some easy way of studying Mathematics: Passion that the Mathematicians do have. “Necessity is the mother of all inventions”. This is not completely true in the case of Mathematical inventions. Sometimes it’s the passion that leads to invention, like in the case of Analytical Geometry. Take a simple example of equation for locus of circle with radius ‘R’ having center at origin. Any one with knowledge of Pythagoras Theorem & Algebra and having passion to do graphs, can straight way write the equation ‘X2 + Y2 = R2’. Whereas, The Pythagoras Theorem is itself is not basic theorem but, derived from the Principles of Similar Triangles. Practically it’s almost impossible to have passion of graphical application of Principles of Similar Triangles to form the equation for locus of circle. Mathematics is consecutive application such tricks. All one need is passion and consistent work on tricking with basic principles known already. Then you too are Mathematician! And this Blog is meant to discuss such tricks and to enhance the passion towards Mathematics.

Referral Links:

• The 15 most famous Transcendental numbers
• The story of Duo from "The Unreasonable Effectiveness of Mathematics in the Natural Sciences" by Eugene Wigner.

Internal Links:

• The Evolution of Mathematics and the Recreation of Universe.

The Evolution of Mathematics, and the Recreation of Universe…..

Year 35000 B.C.! It had has been Four hundred thousands of years as we, The Human Race, were troubling for our mere existence at present and to expel into better future. Whilst the troubles, over millenniums, we adored the science of creation and enjoyed the arts of creative. But the darkness of ignorance yet remained surrounding us; hiding the Lunisolar Expressions, baffling the Salt Bartering. "Ignorance is Dysphoric". We understood something, but unlabeled to express that: How many? How much? We were let on hunting the Root; At last found the key, The Numbers, more exactly symbolic show-off of numbers, to communicate ourselves and with the nature.

At the unmanned caves in the heart of dense forests and at depths beyond the depth of Deep Ocean…..

Yikes! Here! Baboon’s fibula! It is scratched, evenly. Indeed, as of counting some crucial events. Crucial Events! Weather circumstances? Lunar activities? Women’s menstrual cycle? - Whatever may be! But this shows how primitive men, while 37,000 years ago, kept tracking to manage their threats. Over here! Finely grained stone beads! This might be the record that kept the counts of their pet mates. Count of women mates? Hah! Ha! May be! But for sure – Counts of Catties. So, primitive men were good at numerals! Scientific studies shows that even animals too have the ability to comprehend the numerals, at least one & two. As there were group fights with their competitors, they always care about enemy’s strength in numbers. No wonder that the primitive men know to count. The matter is how they symbolized and then systematized the numbers.

Most of us were known to count up to two, but few were up to four or five. From the two base system, having numerals only one & two were named and symbolized, we developed into twenty base system (Mayas) and even up to sixty base system (Babylon), as the dawn of Christianity were only a millennium ahead. We were not contented with the invention of system of numbers as we are not contented with trading alone. We enthusiastically worked at arithmetic as an application towards banking. We learned to calculate interests, comprehend the concept of division or fraction, as reciprocals. We delighted with our trading as along with goods we also traded cultural customs and official systems of each other’s, for free. Men from Egypt, Greek, Arab, India, and China were all came into hand-in-hand, to do magic with numbers. They were Mathematicians. What they dealt with numbers was Mathematics. Yet something left us worried for centuries together, which was “Nothing” or The Zero. Some convinced and prepared to conceive, but some questioned “How can nothing be something?” At last we saw the light, arising from east that brought us "Sunya" The Zero and "Sthanam Sthanam Dasa Gunam" or The Decimal Place Value System.

Does anybody know 2,700,000,000,001^th decimal value of Pi (π)? Does anybody know 1,000,000,000,001^th decimal value of √2? Does anybody know 500,000,000,001^th decimal value of e (exponential constant)? Not Now! But we know all the preceding digits. Beginning form the mid of Eighteenth century, with the Economic Renaissance, Globalization of trading, and Advancement of technology, all these computations of billions and billions of digits are in accelerating pace. This shows the potential of Mathematics, what it could do to Human Race. Newtonian Calculus is in the application from Municipal’s water supply systems to state’s satellite monitoring systems. Computers of kind at National establishments are available for individual entertainment. Evolutional Biology, Extreme Weather, Enhanced Economy has nothing to frighten us. After Albert Einstein, Erwin Schrodinger, Modern mathematics is engaged at modeling the Universe. Only thing left to us is to end the Evolution of Mathematics at the Recreation of Universe.

Brain Foods:

• The oldest known mathematical object is the Lebombo bone, discovered in the Lebombo Mountains of Swaziland and dated to approximately 35,000 BC. It consists of 29 distinct notches deliberately cut into a baboon's fibula. There is evidence that women used counting to keep track of their menstrual cycles; 28 to 30 scratches on bone or stone, followed by a distinctive marker.
• As of evidences available, the history of trading by Salt Bartering begins around 6000 B.C. But, here author assumes it must be much earlier or at least the trading itself, as evidence of social habitat of human backs to 70000 B.C.
• To marginalize the thoughts of the school of Mozi and for the survival of the thoughts of Confucius. In 212 BC, the Emperor Qin Shi Huang (Shi Huang-ti) commanded all books in the Qin Empire other than officially sanctioned ones be burned. As a consequence of this order little is known about ancient Chinese mathematics before this date.
• It was the Pythagoreans who coined the term "mathematics", and with whom the study of mathematics for its own sake begins.
• In the 5th century AD , Indian mathematician and astronomer Aryabhata stated in his book "Aryabhatiya" that the idea of "Sthanam sthanam dasa gunam" or place to place in ten times in value, which is the origin of the modern decimal-based place value notation.
• In the 7th century, Brahmagupta, Indian mathematician, in his Brahma-sphuta-siddhanta, he lucidly explained the use of zero as both a placeholder and decimal digit, and explained the Hindu-Arabic numeral system.
• A Tally Stick was an ancient memory aid device to record and document numbers, quantities, or even messages.

<--- Split Tally: A tool of the Exchequer for the collection of taxes by local sheriffs (tax farmers “farming the shire”) in medieval England. The split tally of the Exchequer was in continuous use until 1826.

• As the quest for new science blows up, Mathematics has to be accommodative, After Albert Einstein mostly idle “Differential Geometry” techniques, along with new “Spacetime Topology” techniques, is made to use in his gravitational theory.

Referral Links:

• The origin of Mathematics.
• Ishango Bone.
• History of mathematics.
• Tally Sticks.
• How zero was invented?
• Your source for the latest research news.

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• Science of Mathematics: Passion of Mathematicians