One such article I read was: Who needs comments? My code is self-documenting! aka: Comment tersely with value-added information.

The author makes the following point:

/* If the first field of the properties record is N... */ IF master_list(l_curr_index).properties_flag.field1 = 'N' THEN

a better way of writing it would be

/* If the customer is not eligible for a discount... */ IF customer_not_eligibility (l_curr_index) = 'N' THEN

As part of the suggestion, he suggests it is better to write a function, and code the business validation. Once that is done, there is no need for the preceding comment. The function is self explanatory.

I know coding style differs. But I am particularly edgy about a function returning TRUE for a negative check (I know, I know, it is just me, but still saying). I would rather rewrite the following:

IF customer_not_eligible (l_curr_index) THEN

into

IF NOT customer_eligible (l_curr_index) THEN

this way, I can use the same function to see if the customer is eligible (otherwise, you would be doing, “IF NOT customer_not_eligible (l_curr_index) ” which is double negation and could be confusing.

How would you do?

]]>The WordPress.com stats helper monkeys prepared a 2011 annual report for this blog.

Here’s an excerpt:

]]>The concert hall at the Syndey Opera House holds 2,700 people. This blog was viewed about

21,000times in 2011. If it were a concert at Sydney Opera House, it would take about 8 sold-out performances for that many people to see it.

Now, that being said, let us look at the specialty of 2012. Being an even-numbered year, and a leap year, 2012 for sure is attractive. Though few can complaint about having one extra day to get through in February.

2012 is named as Alan Turing’s year. Alan Turing was born on 23rd, June of 1912. 2012 will be his birth centenary year. He is widely respected for inventing theoretical computer and much of code breaking in Cryptology. His contribution in war-time Britain saved scores of live and eventually lead allied forces to win world war II.

2012 is also named as international co-operative year. Co-operatives or cooperative unions are special kind of business/non-business establishments. It is special to me, as I have studied a cooperative management diploma for a year.

2012 is also a E-Toothpick sequence number. Last year, 2011, we observed what as a toothpick numbered year. A E-Toothpick is formed by three half toothpicks, like a trident.

The story of 2012 as the end year of Mayan calendar is well-known. Even there are a handful of movies made on it. It is left to see what happens in 2012. Even if we have to go by Mayan’s, we have full year 2012.

2012 is has same calendar as of 1984, 1956 and will have same as 2040, 2068 (that’s +/- multiples of 28 years). On another side note, there is a move to have a permanent calendar. A calendar that has every weekdays of a month identical year after year.

From: http://www.cato.org/pub_display.php?pub_id=13940

Two Johns Hopkins professors are proposing a new calendar in which dates would fall on the same days of the week every year.

The calendar proposed by Richard Conn Henry, an astrophysicist, and Steve H. Hanke, an applied economist, begins each year on Sunday, Jan. 1.

There will one full week added every 5th or 6th year.

Do you like it? I do not. Not just simply for the reason, that there will be no new calendars printed with glossy models. Also for the fact that there will be no surprises in the holidays and leaves. Doesn’t it become monotonous?

]]>ஔவையார் பொருளை பற்றி குறிப்பிடும் போது. ஈவது அறம் என்றவர், பொருள் என்பதற்கு ஈட்டல் பொருள் என்று மட்டும் சொல்லாமல், தீவினை விட்டு ஈட்டல் என்று விளக்கினார்.

ஈதல் அறம். தீவினை விட்டு ஈட்டல் பொருள்

அதியமான் குறித்த ஒரு பாடலில், அவனது பரிசில் தரும் பண்பை, யானையின் வாயிடை பட்ட சோற்று உருண்டையுடன் ஒப்பிட்டு, கைக்கு கிட்டியது பொய்க்காது என்னும் பொருள் பட:

யானை தன் கோட்டிடை வைத்த கவளம் போல

கையகத்தது அது பொய்யாகாதே

அதே மன்னன் பரிசில் மறுத்த போது, வாயில்காப்போனை பார்த்து, புலவர்க்கேயான பெரும்மையுடன் :

எத்திசைச் செலினும் அத்திசைச் சோறே

கற்றவர்க்கு எந்த திசை சென்றாலும் அந்த திசையில் பொருள் சேர்க்க முடியும் என்றார். இன்னுமொரு தமிழ் புலவர்:

வாழ்தல் வேண்டிப் பொய்கூறேன் மெய்கூறுவல்

யானோர் வாணிகப் பரிசிலனலேன்

வாழ்க்கை வாழ வேண்டும் என்னும் ஒரு பொருட்டு பொய் கூறி பொருள் ஈட்டும் வணிகப் புலவன் அன்று, எப்பொழுதும் மெய் மட்டும் உரைப்பேன் என்றான்.

இலக்கியங்களில் அங்கங்கு அறிய உவமைகளை படிக்க இயலும். சில இங்கே:

ஞாயிறு காயும் வெவ்வளை மருங்கிற்

கையில் லூமன் கண்ணிற் காக்கும்

வெண்ணே யுணங்கல் போல

உச்சி வேலையில், திறந்த வெளியில், வெயிலில் காயும் ஒரு பாறை மீது ஒரு கைப்பிடி வெண்ணையை வைத்து, அதை கைகள் இல்லாத ஊமனை கண்களால் மட்டுமே கானும்மாறு காவலுக்கு இருப்பது போல என்று வினை பொருட்டு சென்ற தலைமகனை பிரிந்து இளமையில் வாடும் தலைமகளை காக்கும் முது மகன் நிலைமை சொல்லப் பட்டது.

இன்னும் ஒரு குருந்தொகை பாடலில்:

எம்மிற் பெருமொழி கூறித் தம்மிற்

கையுங் காலும் தூக்கத் தூக்கும்

ஆடிப் பாவை போல

தலைமகன், தலைவியை பிரிந்து பரத்தையுடன் இருந்தான். அது தவறு என்று உணர்த்து தலைவியை பார்க்க சென்றான். அதற்கு பரத்தை சொல்வது போல: என்னிடம் அளப்பரிய வார்த்தைகளை கூறுவதும், தலைவியை பார்த்தவுடன், நிலை கண்ணாடி முன் நிற்பவர் கைகளை தூக்க, கண்ணாடியுள்ளும் இருக்கும் பிம்பம் திரும்ப செய்யுமே, அதை போல தலைவி சொல்வதை, செய்வதை தவறாமல் கேட்பவன் தலைவன் என்று தோழியிடம் பகடியாக சொன்னது.

]]>Another article even attributes geographical / language factors for mastering the mathematical ability of remembering number. If you haven’t read it, here is the summary: the article advocates the certain languages (Asian in this case) have inbuilt advantage in manipulating numbers in mind. Because, the words for the numbers are smaller and easy to store, retrieve, manipulate.

Chinese number words are remarkably brief. Most of them can be uttered in less than one-quarter of a second (for instance, 4 is ‘si’ and 7 ‘qi’) Their English equivalents—”four,” “seven”—are longer: pronouncing them takes about one-third of a second. The memory gap between English and Chinese apparently is entirely due to this difference in length. In languages as diverse as Welsh, Arabic, Chinese, English and Hebrew, there is a reproducible correlation between the time required to pronounce numbers in a given language and the memory span of its speakers. In this domain, the prize for efficacy goes to the Cantonese dialect of Chinese, whose brevity grants residents of Hong Kong a rocketing memory span of about 10 digits.

It could not help me but to compare this with the counting in my mother tongue Tamil. In English, we have to count fourteen, sixteen, seventeen, eighteen and nineteen, so one would think that we would also say one-teen, two-teen, and three-teen. Not the case. It is little bit in a different form: eleven, twelve, thirteen, and fifteen. Compare that to Tamil counting, 11 is pathinoonnu (பதினொன்று or pathu+one; ten+one), 18 is pathinnettu (பதின்னெட்டு or pathu+ettu; ten+eight).

As a result the article concludes Asian children have advantage of storing more numbers in their mind and manipulate them faster.

On that being said, let me point you that, though counting is one of basic skills, easily acquired, gifted, it is the one which is widely misunderstood too. The notion of counting is different from highly debated.

Intuitively when you count something, you will be labeling them with numbers, a one-to-one mapping between the object being counted and the natural numbers. When my grandmother counted coconuts she would have used her fingers to keep track and folded one finger after another, a one-to-one mapping.

Ordering is a different concept. Some how, even small children knew two candies is better than 1 candy. They can order 2 candy and then 1 candy. The ordering is known as “Natural Ordering”. You know which number is bigger to another number fairly to some extend.

Is there a connection between ordering and counting? There seems to be deeper connection then what we could imagine.

Simply put, countability is the ability to count. Not your ability, but the ability of object being counted. Consider this, in young days children often challenge others to count the sand particles in handful of sand or fistful of hair in head or even the number of stars in a quite bright night sky. Most the smaller kids would blink and could not reply. But as you grow older, you would would reply with some huge number and counter-challenge to disprove it by counting. The point to take is, these objects are countable, just not easily. Is a litre of milk countable? It is measurable, but again measurability in mathematics is another field worth separate discussion.

Fine, let us get more abstract, are the natural numbers countable? Assume a bag that contains 10 balls each numbered with one number between 1 to 10 unique. You would pick all of them, not in any particular order, but after picking 10 of them, you could confirm that you have picked all of the balls from bag without seeing into the bag to see whether any thing more is left. How? You would just need to count the balls as you pick, mind you, count without any order. So, are they countable? the fact that you are able to count them one, two, three using your fingers prove they are countable. Are the whole of integers countable? Yes, the same argument finger in the hand applies, only but you have remember the sign for negative numbers. Are the rational numbers (fractions) countable? This is where it gets tricky. Yes, they too. You can always think there could be innumerable rational numbers between 0 and 1, but still the entire set of rational numbers are countable.

The famous mathematician, Cantor, has given the following brilliant demonstration. You have to understand that by counting you mean to can assign an order to objects and make sure nothing gets lost from being numbered, or rather from counted. If by some how you can introduce such an order in the rational numbers (not just lesser then, greater to), and make sure no other number is missed between any given two, the countability of rational numbers can be established.

Cantor used the above pairing method. Start with writing with number in the first column and and so on. Now in the above zig-zag pairing, you will be able to comb all the number (just like counting bag of 10 balls using fingers). Such a zig-zag pairing will not leave any number from being missed out. Though this is not the natural ordering, but this ordering will make sure rational numbers are countable.

Do un-countable numbers exist? They do. Consider the easiest and familiar-est of all: “real numbers”. Consider the below sequence of number (refer below, for better, imagine S1 as big number with all digits separated by comma). S2, S3 and others numbers which are written in some order. The idea is so that, what ever order the numbers are ordered, there will be a number which can be shown not be part of such an arrangement. All it needs to show is, such number arrangement will always leave some numbers uncounted for, and hence uncountable.

*s*_{1}= (**0**, 0, 0, 0, 0, 0, 0, …)*s*_{2}= (1,**1**, 1, 1, 1, 1, 1, …)*s*_{3}= (0, 1,**0**, 1, 0, 1, 0, …)*s*_{4}= (1, 0, 1,**0**, 1, 0, 1, …)*s*_{5}= (1, 1, 0, 1,**0**, 1, 1, …)*s*_{6}= (0, 0, 1, 1, 0,**1**, 1, …)*s*_{7}= (1, 0, 0, 0, 1, 0,**0**, …)- …

*s*_{0}= (**1**,**0**,**1**,**1**,**1**,**0**,**1**, …)

Now, is constructed by taking the diagonal numbers, i.e., 1st digit from , 2nd digit from , 3rd digit from and so on. Call this as . Find the complement (replace all 0s with 1 and 1s with 0) and call it as . Now check whether such a number is present in our collection. It would have not. Since our construction is such it would have taken care, (remember that we took the diagonal number and reversed it, so if such a number had existed in the collection, we would have picked the diagonal digit and reversed it).

If you are not sure, add this number to the collection, call it , and start over again. If you are not able to get the idea, take a paper and pencil, imagine you know only four numbers, and do this exercise.

This method is known as Cantor’s Diagonal argument and was first demonstrated by Georg Cantor (refer here for his interesting rather troublesome life). Diagonal argument is such a profound method it paved in way to much more brilliant ideas and proofs later. Russell’s paradox which shock the base of set theory is based on diagonal argument. Later Alan Turing’s answer to the *Entscheidungsproblem *and Gödel’s incompleteness theorems which spelled the end for David Hilbert’s grand formalization of mathematics, were also developed based on diagonal argument demonstration.

All of the above methods would require detailed explanation and a separate detailed post. Hope you understood it is easy to just keep counting.

]]>First: 2011 is a prime number. The fundamental building blocks of number system, prime numbers are special. It means 2011 can not be expressed a product of smaller prime numbers (or any other numbers for that sake). And then, a friend pointed out 2011 can be expressed as sum of 11 prime numbers.

Further, the number 2011 can also be represented as sum of three consecutive primes as well (661+673+677=2011).

And then, it is also notable, 2011 is a toothpick number.

Toothpick numbers, or toothpick sequences are the number of toothpicks used in particular toothpick arrangement. The steps for generating toothpick sequence is

- Start with a single two dimensional toothpick. Placed on a plane. Parallel to ‘Y’ axis.
- Place two more toothpicks, one each at the end of a toothpick.
- Keep repeating, until you maintain a fractal like symmetric shape.
- the number of toothpicks used in any step is the toothpick number of that state and the sequence is toothpick sequence.

The steps would look like below.

The structure would look like below after 56th step.

It is difficult to find out how many toothpicks are needed for step. And there are generating functions on this. Read this paper for a serious treatment.

Often the toothpick setup is studied in reference with Cellular Automata, Conway’s game of life and universal Turing machine.

Try out several variations online (also called as **toothpick movie** version).

Coming back, 2011 is the number of toothpicks at step 60, it is 25th prime number in toothpick sequence.

Isn’t that cool? Happy new year to all!

]]>The stats helper monkeys at WordPress.com mulled over how “Abstract Confusions” did in 2010, and here’s a high level summary of its overall blog health:

The *Blog-Health-o-Meter* reads Wow.

The average container ship can carry about 4,500 containers. This blog was viewed about **14,000** times in 2010. If each view were a shipping container, your blog would have filled about 3 fully loaded ships.

In 2010, there were **24** new posts, growing the total archive of this blog to 64 posts. There were **81** pictures uploaded, taking up a total of 7mb. That’s about 2 pictures per week.

The busiest day of the year was June 30th with **103** views. The most popular post that day was Haskell – A Functional Programming Language.

The top referring sites in 2010 were **stefano.italians.nl**, **benhutchison.wordpress.com**, **en.wordpress.com**, **google.co.in**, and **cv-templates.info**.

Some visitors came searching, mostly for **tamil horror movies list**, **2009 tamil movies list**, **good tamil movies 2009**, **oracle apex interview questions**, and **funny tamil movies list**.

These are the posts and pages that got the most views in 2010.

1

Haskell – A Functional Programming Language May 2010

2 comments

2

Top Tamil Movies 2009 – The Good, Bad and Ugly December 2009

8 comments

3

Professional Resume Using Latex Templates November 2009

2 comments

4

Oracle Application Express (APEX) Interview Questions June 2010

6 comments

5

Math Games for Children May 2010

6 comments

Historical Failure | Aayirathil OruvanA movie about mystical Chola king defeated by Pandiya king living in an island. The movie did create a wave with people applauding Parthiban‘s acting, Reema Sen‘s portrayal. Did not do well in box offices, but it did make a bold attempt. |

Surprise Success | Tamil Padam
Even the director would have never expected this movie’s success. Tamil padam did make a life out of ridiculing all movies made so far and it was received well by the audiences. It was like watching Vijay TV‘s famous Lollu saba program for 3 hours. This alone was not a reason for the movie’s success, note when similar movie – ‘Va – Quarter Cutting‘ was made, it did not go well with the audience. |

Musical Success | Vinnaithandi Varuvaya
The movie is a through musical treat. About a film maker falling in love with his malayali neighbor. Directed by Gauthum Vasudevan Menon, music composed by A R Rahman, the movie did go well with youngsters. Unlike other Gauthum movies, the heroine did not die in the end and there is no or little fighting sequence. Simbu did get a makeover and making the most of it. |

Bold Success | Angadi Theru
Movie on people who work tirelessly in Ranganathan Street. It did go well with lot of people and created a huge apathy. The movie is critically acclaimed and box office hit as well. There were good songs in the movie. Though it had a sad end, people liked the new actors and Vasantha Balan’s directing as usual. |

Epic Failure | Raavanan
The movie which created a huge hype did not live up to the reputation of haracters it portrayed. Though I found it a new approach, but it is evident that Mani Ratnam did not know how to finish the story in second half. The Tamil version did well compared to Hindi Raavan. |

Epic Success | Madarasapatniam
A movie set in pre-independence India. It appealed to audience for the nice cinematography, simple story and patriotic setup |

Commerical Success | Enthiran
Do I need to say more? Rajini, Sankar and story line from Sujatha. Enthiran created world record opening and business for Tamil movie. Starting from NY Times, all western journals did take up the cue about Rajini. As a fall off, there were steady stream of Chuck Noris-like jokes involving Rajni. |

Critical Success | Mynaa
Keeping with the trend of low-budget movies, dishing out a nice love story and a sad ending. |

Copycat Success | Nandalala
The movie was inspired by a Japanese movie and did well. First movie for Myskin as actor. |

Did I forget any movie? No. I did not. They are just, forgettable movies.

**Sura** – Yet again. Vijay starer and a stereo type movie.

**Paiya** – Another commercial movie.

**Irumbu Kottai Muratu Singam** – Though this movie will be known for the Tamil movie portrayal of wild western cowboys, it was a lengthy movie with known story line.

**Singam** – Commercial, gripping movie. Did have an engaging story but I found it to be as usual.

**Boss Engira Baskaran** – Nanbeanda was the dialogue people would remember for some time, rest would be forgotten soon.

There are few movies which did not live upto the hype they created.

**Goa **– Expected, but turned out to be a flop show by Venkat.

**Rettai Suzhi** – This movie had impressive actors. Both Barathiraja and Balachander, but still dint not make any impression. Barathiraja’s action is mentionable though.

**Va Quarter Cutting** – Horrible movie. No more words.

**Easan** – Sasikumar directed movie. Director Samutharakani’s acting alone was mentionable.

**Manmathan Ambu** – Kamal’s answer to Rajni’s Enthiran.

**Naan Mahan Alla** – Though the movie did well, it doesn’t have any thing interesting apart from the usual masala.

**Ratha Charitharam** – Movie known for too much violence. Slow motion camera, blood oozing into the wet mud, some one has to die in each frame.

There were some nice music through out the year 2010. I liked the following tracks very much.

**Aval appadi onrum alagillai **– Angadi Theru

**Unn perai sollum pothae** – Angadi Theru

**Thaai thindra mannae** – Aayirathil Oruvan

**Hosanna, Aaromale** – Vinnai Thandi Varuvaaya

Actor Vijay’s movie name got changed from Body guard, to Kavalkaran, then to Kaval kadal. Finally the movie name got fixed to Kavalan. Vijay said he does not know the movie name he was acting.

]]>You can use any language you like (except 3rd requirement). I was forced to use PL/SQL because of the project requirements.

The function, say, `foo`

should return only numbers for the following test cases.

Input | Output |

foo(‘123’) | 123 |

foo(‘123a’) | 123 |

foo(‘a123’) | 0 |

So, how would you do that?

create or replace function ret_num (p_str in varchar2) return number is begin --- Try to return, if it is pure number --- , it should go without exception. return to_number(p_str); --- The string contains Aplhabet. --- Return with logic. exception when value_error then --- Now the classic case, --- most of the times this is expected to fire. return nvl( substr(p_str , 1 , regexp_instr(p_str ,'[a-zA-Z]')-1 ) , 0 --- If the string starts --- with aplhabet (not number) --- then return 0. NVL() does that ); end;

Given a line or sentence, the function or program should return the last word.

You can do this in plain SQL, a function is just a convenience.

create or replace function getWord(p_word_in in varchar2) return varchar2 is lv_out varchar2(20); begin --- The logic is to find the last word by --- finding the last space. Reverse the sentence --- find the first space and retrieve the word and --- reverse the word again select reverse(substr(reverse(p_word_in) , 0 , instr(reverse(p_word_in), ' ') ) ) into lv_out from dual; return lv_out; end;

Also, I think there is should be an efficient way of doing this.

**Update:**

The below SQL works, perfectly.

select substr( &sentence , instr( &sentence , ' ' , -1) + 1) from dual

I want to delete set of the rows from a table. I can decide which rows need to be deleted (conditions in WHERE clause). But I want to keep few of the records from deleting. That is, if I have a 100 records, I want to delete 95 rows from table and keep 5 records in table. Remember the records should be deleted only if the count of rows is more than 5 (retention condition).

A condition: You have to do this in plain SQL.

delete from mytable where rowid in (select rowid from (select rowid , row_number() over (partition by col1 , col2 order by id )rn from mytable ) where rn > 5 );

You can also add your own strange question / answer you might want to share.

]]>- Identifying the problem (includes preparation, collecting information, identifying challenges and risks) .
- Attacking the problem (use existing tools, techniques to derive new method). Get vigorous, consciously.
- The problem attacking becomes an unconscious activity from a conscious one, then the problem starts attacking you.
- Either problem is consumed or the attacker is consumed by problem.

Especially at stage 4, one will be thinking only about the problem. While driving, eating, teaching and even in sleep. Archimedes resolved the problem when he was bathing. Isaac Singer, the american inventor of sewing machines was supposed to found solution for the problem of finding where to put hole in needle so that it is easy to stitch, in dream, he dreamt of someone chasing him with strange spear with a hole in the spear head. These are examples of sub conscious mind solving problems.

What happens when you are preoccupied with a problem, little too much, okay, way too much? Either you solve the problem successfully or you loose your mind over it and end up ruining your life.

Mathematics is full of stories like this. And today we will see such stories.

I happened to read about a documentary about mathematicians on BBC and had chance to watch it. “Dangerous Knowledge” is a one-off documentary about four brilliant mathematicians – Georg Cantor, Ludwig Boltzman, Alan Turing and Kurt Godel. After seeing it what struck my mind was, though study of mathematics is seen purely as an intellectual activity with communication with other mathematicians, over the years has become more and more intense on being becoming an personal activity, challenging individual knowledge more than ever. Lets see some strange personalities in mathematical world.

Georg Cantor is known for his deep theories in set theory. His theory includes, importance of one-to-one correspondence, transfinite numbers and infinity of infinities. When he first said that there could be different sizes to infinities, it was totally counter intuitive and created enough uproar (yet to be settled). Henry Poincare declared Cantor’s ideas as a dangerous disease which corrupts the young mind. Leopold Kronecker, Hermann Weyl and few other mathematicians joined in tarnishing Georg Cantor’s mathematical reputation. Cantor also strained his professional relationship with Mittag Leffler and Richard Dedekind. All through this Cantor never worried but only about the mathematical theories he was producing. He was so much occupied by ‘Continuum Hypothesis‘.

Cantor tried proving continuum hypothesis all through his life. Couple of times he claimed wrongly that he was able to prove only to withdraw the claim later. Cantor was so occupied with the continuum hypothesis problem, that he knew that could not solve it easily. Through his mid-career he considered abending mathematical career and pursuing a career in philosophy. He was also admitted to mental sanatorium couple of times for five or more years. When ever he tried fixing continuum hypothesis he had nervous break down and would lose his mental health.

He suffered from depression and nervous breakdown. Cantor declared the theory of transfinite number was given to him by god (another mathematician who attributed his knowledge to god was Srinivasa Ramanujan). Cantor died in a mental asylum in 1918.

David Hilbert during one of his famous speech said:

No one shall expel us from the Paradise that Cantor has created.

Continuum hypothesis is still not proved.

Kurt Godel‘s life too is linked with continuum hypothesis. Godel was a German. He proved one of Hilbert’s mathematical question. Albeit in a negative assertion, he proved that there will be in-complete systems. This is known as incompleteness theorems.

Godel published many papers in logic, set theory and theology. During his hearing for US citizenship, when asked whether there is possibility of dictator ship in US, he answered a strange but possible loop-hole, thus putting his appeal in jeopardy. Albert Einstein was a great friend to Godel. During his last days came to Princeton University only to have a walk with him in campus. Godel tried solving Continuum hypothesis. He did make advancement by proving that adding certain axioms wont prove / disprove the hypothesis.

However, though being a perfect logician, Godel always suspected someone would kill him by poisoning. He always wanted his wife to eat the food before he would eat. Godel is also an introvert. He would restrain from touching people and body contacts. After his wife passing out, Godel never had a proper food. He concentrated on solving the open problems more vigor only to worsen his health. He was admitted to hospital several times for malnutrition. When he passed out in his 70s, the doctor observed Godel died of malnutrition and starving.

Here is a mathematician, a perfect logician, a wealthy person, tried to solve problems late till his age dying of starving.

John Nash is a genius mathematician. He perhaps would have affected our worldly understanding more than anyone else would have. Starting from complex systems, evolutionary biology, market economics to sociology, he had a far more impact. Nash also awarded Nobel prize.

John Nash too had his part of mental paranoia. His story is explained in Hollywood movie – ‘A Beautiful Mind’. He was admitted in hospital for treatment and remained there for close to 12 years. Nash said he started seeing delusional characters, an agency, in which all of them wore a red tie and chasing him.

Nash’s story is that of a successful one with lot of struggle. After his return from hospital for treatment for paranoid schizophrenia. He did further advancement of game theory, economics and market study. He published close to 25 papers after returning from mental asylum.

There are some strange habits among mathematicians:

Andrew Whiles, who proved Fermat’s last theorem, did all the math hiding in attic. He would never tell to his wife of what he was doing and hide in attic for close to 8 years.

Srinivasa Ramanujan declared few equations / proofs were given to him by his family goddess ‘Namakal’.

Really strange!

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