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 21,000 times 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.

Click here to see the complete report.

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 – Alan Turing year

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 – Cooperative year

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 – Mathematical significance

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.

2012 : E-Toothpick number

2012 – Mayan Calendar

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.

Mayan Calendar ends at 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?

கற்றோர், பொருள் பெருமை

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.

உவமை நயம் 

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.

Asian Advantage in Counting

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.

Counting and Ordering

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.

Countability

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.

Ordering of Rational Numbers - Countable Rational Numbers

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.

Uncountability

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.

s₁ = (0, 0, 0, 0, 0, 0, 0, …)

s₂ = (1, 1, 1, 1, 1, 1, 1, …)

s₃ = (0, 1, 0, 1, 0, 1, 0, …)

s₄ = (1, 0, 1, 0, 1, 0, 1, …)

s₅ = (1, 1, 0, 1, 0, 1, 1, …)

s₆ = (0, 0, 1, 1, 0, 1, 1, …)

s₇ = (1, 0, 0, 0, 1, 0, 0, …)

…

s₀ = (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.

2011 is a prime number & sum of 11 consecutive prime #'s: 157+163+167+173+179+181+191+193+197+199+211=2011—
SREE GURUPARAN PA (@guruparan18) January 02, 2011

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 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.

toothpick number 1 to 10

Toothpick number - t(56)

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.

Crunchy numbers

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.

Where did they come from?

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.

Attractions in 2010

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

Haskell – A Functional Programming Language May 2010
2 comments

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

Professional Resume Using Latex Templates November 2009
2 comments

Oracle Application Express (APEX) Interview Questions June 2010
6 comments

Math Games for Children May 2010
6 comments

Forgettable Movies

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.

Disappointing Failures

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.

Music

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

Comedy For this year… and Next year

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.

Kavalan Vijay

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

Return Number

The function, say, foo should return only numbers for the following test cases.

So, how would you do that?

Solution

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;

Last Word

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

Solution

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

Delete All But Some Records

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.

Solution:

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.

1. Identifying the problem (includes preparation, collecting information, identifying challenges and risks) .
2. Attacking the problem (use existing tools, techniques to derive new method). Get vigorous, consciously.
3. The problem attacking becomes an unconscious activity from a  conscious one, then the problem starts attacking you.
4. 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.

Problem with problems

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: (1845 – 1918)

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‘.

Georg Cantor

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: (1906 – 1978)

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: (1928 *)

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.

Others

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!

Earliest Mathematicians

No one know where the first class in mathematics was held. But all of us know for pretty sure what could have been the first theorem proved. Pre historic math was used for studying geometry and planetary. Greeks mastered this field of mathematics. Euclid, Aristotle, Archimedes and Pythagoras were the most noted mathematicians. They all are philosophers too. For good, once, a great mastery over written and oratory skill of a language was needed to practice mathematics.

In India, Baskara wrote Lilavati, a book written in poetic verses about mathematics. But the scene shifted slowly. As math became more abstract words and verses gave away to numbers and symbols.

Modern Mathematicians

I would say the most successful and interesting mathematicians were from late 18th century and 19th century. I would call them modern-day mathematicians, most of them went on to make a lot. If Newton was considered as amateur mathematician, Euler, Gauss, Galois, Reimann, Weirstrauss, Hardy, Ramanujan and Einstein were considered as the celebrities in mathematics.

My favorite mathematicians would be Galois, Gauss, Ramanujan and Euler. Galois and Ramanujan in spite of being poor achieved so many things, died young and left quite lot of impact.  Where as Gauss and Euler lived up to ripe age, achieved great amount of deeds, left behind rich literature and good students.

Evariste Galois – A Revolutionist Mathematician

Galois lived up for twenty years and was able to achieve many things when he was in his teens. He was active in French revolution too. Galois was killed in a street dual, allegedly fighting for his lover. What we know today as his contributions were written in a night before the eventual duel. In the letter he wrote that night, he was desperate to prove theorems but has left side notes saying there is no time to prove them.

Galois is responsible for an entire field of study in mathematics itself. He questioned and answered about reducibility of a polynomial. The field is known as Galois theory. Two hundred years later Andrew Wiles used Galois theory to solve Fermat’s last theorem, a problem every mathematician desired to solve. Today Galois theory is used in computer security to rocket science.

Perhaps Galois is the only mathematician who can be associated with revolution, guns, duels, love, girls and abstract algebra.

Srinivasa Ramanujan – The Indian Clerk

Ramanujan is a mathematical prodigy, he did not have a formal training in mathematics. Yet Ramanujan produced gem of theories in number theory, continued fraction and analysis.

When Paul Erdos asked G. H. Hardy, what was his greatest contribution to mathematics? Without hesitation Hardy replied it was finding Ramanujan. The relation Ramanujan and Hardy shared was a special one. Ramanujan attributed his mathematical insights to goddess Namakal. Where as Hardy is an atheist and would always ask for rigorous proof, Ramanujan would some times jot down proofs based purely on intention.

Hardy would write letters, seal the envelope, claiming that he has solved Reimann hypothesis before setting out for a journey or boat ride. Hardy believed if God existed, he would not like Hardy getting fame as some one who were able to solve the Reimann hypothesis posthumously. Hardy would argue because of this, God would always take care of his safe journey.

Hardy considered his relationship with Ramanujan as one of the romantic incidents.

Carl Friedrich Gauss – The Prince among Mathematicians

Gauss is considered as the prince of mathematics. Gauss was able to contribute most of mathematical fields. Reimann is his famous student.

Leonhard Euler – The Master Mathematician

Euler is known as the most productive mathematician ever. Euler contributed to most of mathematics and physics. An interesting story involving his eye sight is very famous.

When Euler started loosing eye sight in one of his eyes and asked about how he feels, he replied, now I have less distraction. Very soon he lost his total eye sight, but he did not stop writing. In fact this period was the most productive period of Euler’s life. Some one said, since Euler lost eye sight and could not see the outside world, he started seeing the inside world of mathematics and discovering the hidden connections.

So, tell me, who is your favorite mathematician?