## 1729

**I remember once going to see him when he was ill at Putney.** I had ridden in taxi cab number **1729** and remarked that **the number seemed to me rather a dull one**, and that I hoped it was not an unfavorable omen.

“**No**,” he replied, “**it is a very interesting number**; it is the smallest

**number**expressible as the sum of two cubes in two different ways”

— G. H. Hardy

Euler Function on the Complex Plane

Yep, it is ALSO the **first absolute** Euler pseudoprime. Unique. **Sui Generis.**

** ** Just like *The Man Who Knew Infinity:
*

**Srinivasa Ramanujan**:**Sui Generis**

Only the self-educated are free.

DMK

Srinivasa Ramanujan, Architect Rational, (Tamil: ஸ்ரீனிவாஸ ராமானுஜன்; 22 December 1887 – 26 April 1920) was an Indian mathematician and autodidact who, with almost no formal training in pure mathematics, made extraordinary contributions to mathematical analysis, number theory, infinite series, and continued fractions. Living in India with no access to the larger mathematical community, which was centred in Europe at the time, Ramanujan developed his own mathematical research in isolation. As a result, he rediscovered known theorems in addition to producing new work. Ramanujan was said to be a natural genius by the English mathematician G. H. Hardy, in the

same league as mathematicians such as Euler and Gauss.He died at the age of 32. [Wikipedia, revised]

His introduction to formal mathematics began at age **10**. He demonstrated a natural ability, and was given books on advanced trigonometry written by S. L. Loney that he mastered by the age of **12**; he even discovered theorems of his own, and re-discovered Euler’s identity independently. He demonstrated unusual mathematical skills at school, winning accolades and awards. By **17**, Ramanujan had conducted his own mathematical research on Bernoulli numbers and the Euler–Mascheroni constant.

Nobody in British India was qualified to appreciate his work. In the early 1900’s the center of mathematics in English was in the universities in England.

In

1912–1913, he sent samples of his theorems to three academics at the University of Cambridge. The first two returned Ramanujan’s papers without comment. On16January1913, Ramanujan wrote to G. H. Hardy. Hardy noticed that letter contained already know results but also some results were “seemed scarcely possible to believe.” Hardy commented that “they [theorems] defeated me completely; I had never seen anything in the least like them before”. He figured that Ramanujan’s theorems “must be true, because, if they were not true, no one would have the“. Hardy asked a colleague, J. E. Littlewood, to take a look at the papers. Littlewood was amazed by the mathematical genius of Ramanujan. After discussing the papers with Littlewood, Hardy concluded that the letters were “certainly the most remarkable I have received” and commented that Ramanujan was “a mathematician of the highest quality, a man of altogether exceptional originality and power”. Hardy recognizing the brilliance of his work, invited Ramanujan to visit and work with him at Cambridge. He became a Fellow of the Royal Society and a Fellow of Trinity College, Cambridge. Ramanujan spent nearly five years in Cambridge collaborating with Hardy and Littlewood and published a part of his findings there. Hardy and Ramanujan had highly contrasting personalities. Their collaboration was a clash of different cultures, beliefs and working styles. Hardy was an atheist and an apostle of proof and mathematical rigour, whereas Ramanujan was a deeply religious man and relied very strongly on his intuition. While in England, Hardy tried his best to fill the gaps in Ramanujan’s education without interrupting his spell of inspiration.imaginationto invent them

Ramanujan died of illness, malnutrition, and possibly liver infection in 1920. (His age was 32: 32 is the first member of the **31**–aliquot tree.) An interesting number. **32** is the smallest number *n* with exactly **7** solutions to the equation φ(*x*) = *n*. It is also the sum of the totient function for the first **10** integers.

During his short lifetime, Ramanujan independently compiled nearly 3900 results (mostly identities and equations). Nearly all his claims have now been proven correct, although a small number of these results were actually false and some were already known. He stated results that were both original and highly unconventional, such as the Ramanujan prime and the Ramanujan theta function, and these have inspired a vast amount of further research. *The Ramanujan Journal*, an international publication, was launched to publish work in all areas of mathematics influenced by his work.

For **Architects**, the world exists primarily to be analyzed, understood, explained – and re-designed. External reality in itself is unimportant, little more than raw material to be organized into structural models. What is important for Architects is that they grasp fundamental principles and natural laws, and that their designs are elegant, that is, efficient and coherent. **Architects** show the greatest precision in thought and speech of all the types. [Please Understand Me II]

“I quickly came to recognize that my instincts had been correct; that the mathematical universe had much of value to offer me, which could not be acquired in any other way.

I saw that mathematical thought, though nominally garbed in syllogistic dress, was really about patterns; you had to learn to see the patterns through the garb.That was what they called “mathematical maturity”. I learned that it was from such patterns that the insights and theorems really sprang, and I learned to focus on the former rather than the latter.”–– Robert Rosen

In **1919** Ramanujan was **deathly ill** while on a long ride back to India, from February **27** to March **13** on the steamship Nagoya. All he had was a pen and pad of paper, and he wanted to write down his equations before he died.

Ramanujan believed that

17new functions he discovered were “mock modular forms” that looked like theta functions when written out as an infinite sum (their coefficients get large in the same way), but weren’tsuper-symmetric. Ramanujan, a devout Hindu, thought these patterns were revealed to him by the goddess Namagiri.

**“Sir, an equation has no meaning for me unless it expresses a thought of GOD**.”

“**Architects** often seem difficult to know. They are inclined to be shy except with close friends, and their reserve is difficult to penetrate. Able to concentrate better than any other type, they prefer to work quietly at their computers or drafting tables, and often alone. **Architects** also become obsessed with analysis, and this can seem to shut others out. Once caught up in a thought process, **Architects** close off and persevere until they comprehend the issue in all its complexity. **Architects** prize intelligence, and with their grand desire to grasp the structure of the universe, they can seem arrogant and may show impatience with others who have less ability, or who are less driven.” — [David Keirsey]

Ramanujan died before he could prove his hunch. But more than

90years later, mathematicians proved that these functions mimicked modular forms, butdon’t share their defining characteristics, such as super-symmetry. The expansion of mock modular forms helpsphysicists compute the entropy, or level of disorder, of black holes.In developing mock modular forms, Ramanujan was decades ahead of his time; mathematicians only figured out which branch of math these equations belonged to in2002.

“Authority derived from office, credential, or celebrity does not impress them. **Architects** are interested only in what make sense, and thus only statements that are consistent and coherent carry any weight with them.” [Please Understand Me II]

“Ramanujan’s legacy, it turns out, is much more important than anything anyone would have guessed when Ramanujan died”

The findings were presented at the Ramanujan **125** (**5**^**3**) conference at the University of Florida, ahead of the 125th anniversary of the mathematician’s birth on Dec.(**12**th month) **22**, **2012**.

Every positive integer is one of Ramanujan’s personal friends.

John Littlewood

42(forty-two) is the natural number immediately following 41 and directly preceding 43. The number has received considerable attention in popular culture as a result of its central appearance inThe Hitchhiker’s Guide to the Galaxyas the “Answer to The Ultimate Question of Life, the Universe, and Everything“. Doug Adams wrote theGuideas satire.

**Seriously: hey, Doug.** You are one off. 42-1=**41** **Forty-one** is a ** very very interesting number**. {0,1,7,41,71}:24

**Forty-one** is the **13**th smallest prime number. The next is forty-three, with which it comprises a **twin prime**. It is also the sum of the ** first six prime** numbers (

**2**+

**3**+

**5**+

**7**+ 11 +

**13**), and the sum of

**three primes**(11 +

**13**+ 17). Forty-one is also the

**12**th supersingular prime, a Sophie Germain prime and a Newman–Shanks–Williams prime. 41 is the smallest Sophie Germain prime to start a Cunningham chain of the first kind of three terms, {

**41**,

**83**, 167}. It is an Eisenstein prime, with no imaginary part and real part of the form 3

*n*− 1. 41 is a Proth prime as it is

**5**×

**2**+ 1. The number figures in the polynomial

^{3}*f*(

*n*) =

**+**

*n*^{2}*n*+

**41**, which yields primes for

**−40**≤

*n*<

**40**.

**This is also called the lucky number of Euler Prime. It is the biggest of such primes.**Forty-one is the sum of two squares,

**4**

^{2}+

**5**

^{2}. Adding up the

**sums of divisors**for

**1**through

**7**yields 41. 41 is the smallest integer whose reciprocal has a

**5**-digit repetend. That is a consequence of the fact that 41 is a factor of

**99999**. It is a

**centered**

**square**number. The Square root of

**5 (an irrational number) — Squared — is 5.**

Re: Hollywood fantasy, Jeremy Irons is set to co-star in the production of “The Man Who Knew Infinity,” the biopic of Srinivasa Ramanujan, with Dev Patel starring as the revered Indian mathematician. Filming is scheduled for **2014**.

**Any intelligent fool can make things bigger and more complex… It takes a touch of genius – and a lot of courage to move in the opposite direction. – Albert Einstein**

**Other Architect Rationals**: Emmy Noether, Paul Dirac, Robert Rosen, David Keirsey, Albert Einstein, Lonnie Athens, David Bohm

David KeirseyDecember 22, 2014 / 6:44 pmReblogged this on Please Understand Me and commented:

Narendra Modi, Prime Minister of India, paid tribute to Srinivasa Ramanujan: A genius who made a monumental contribution to mathematics, I pay my tributes to the legendary S Ramanujan on his birth anniversary.

127th anniversary.

As a Mersenne prime, 127 is related to the perfect number 8128. 127 is also an exponent for another Mersenne prime 2127 – 1 (2127 – 1), which was discovered by Édouard Lucas in 1876, and held the record for the largest known prime for 75 years – it is still the largest prime ever discovered by hand calculations. Furthermore, 127 is equal to 27 – 1, and because 7 is also a Mersenne prime, this makes 127 a double Mersenne prime.

Ramanujan would have known THIS NUMBER too.

127 is also a cuban prime of the form p = (x^3 – y^3) / (x – y), x = y + 1. The next prime is 131, with which it comprises a cousin prime. Because the next odd number, 129, is a semiprime, 127 is a Chen prime. 127 is greater than the arithmetic mean of its two neighboring primes, thus it is a strong prime.

127 cannot be written as a sum of a power of 2 and a prime, the next is 149.

127 is a centered hexagonal number.

It is the 7th Motzkin number.

127 is a palindromic prime in nonary and binary.

It is the first nice Friedman number in base 10, since 127 = -1 + 27, as well as binary since 1111111 = (1 + 1)111 – 1 * 1.

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goodrumoDecember 22, 2014 / 6:49 pmReblogged this on iheariseeilearn and commented:

127th anniversary for Srinivasa Ramanujan.

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