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Posts Tagged ‘Mathematicians’

I have never done anything useful. No discovery of mine has made or is likely to make, directly or indirectly, for good or for ill, the least difference to the amenity of the world. Judged by all practical standards, the value of my mathematical life is nil. And outside mathematics it is trivial anyhow. The case for my life then, or for anyone else who has been a mathematician in the same sense that I have been one is this: That I have added something to knowledge and helped others to add more, and that these somethings have a value that differ in degree only and not in kind from that of the creations of the great mathematicians or any of the other artists, great or small who’ve left some kind of memorial behind them. 

I still say to myself when I am depressed and and find myself forced to listen to pompous and tiresome people “Well, I have done one thing you could never have done, and that is to have collaborated with Littlewood and Ramanujan on something like equal terms.” — G. H. Hardy (A Mathematician’s Apology)

Yesterday I  discovered an old (1987) British documentary on Srinivasa Ramanujan, which was pretty recently uploaded. I was not surprised to see that the video was made available by Christopher J. Sykes, who has been uploading older documentaries (including those by himself) on youtube (For example – The delightful “Richard Feynman and the Quest for Tannu Tuva” was uploaded by him as well. I blogged about it a couple of years ago!). Thanks Chris for these gems!

Since the documentary is pretty old, it is a little slow. But if you have one hour to spare, you should watch it! It features his (now late) widow, a quite young Béla Bollobás and the late Nobel Laureate Subrahmanyan Chandrasekhar. The video is embedded below – in case of any issues also find it linked here.

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[Ramanujan: Letters from an Indian Clerk]

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I could have written something on Ramanujan, but decided against it. Instead, I’d close this post with an excerpt from a wonderful essay by Freeman Dyson on Ramanujan published in Ramanujan: Essays and Surveys by Berndt and Rankin

Ramanujan: Essays and Surveys (click on image to view on Amazon)

A Walk Through Ramanujan’s Garden — F. J. Dyson

[…] The inequalities (8), (9) and (10) were undoubtedly true, but I had no idea how to prove them in 1942. In the end I just gave up trying to prove them and published them as conjectures in our student magazine “Eureka”. Since there was half a page left over at the end of my paper, they put in a poem by my friend Alison Falconer who was also a poet and mathematician. […]

Short Vision

Thought is the only way that leads to life.

All else is hollow spheres

Reflecting back

In heavy imitation

And blurred degeneration

A senseless image of our world of thought.

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Man thinks he is the thought which gives him life.

He binds a sheaf and claims it as himself.

He is a ring through which we pass swinging ropes

Which merely move a little as he slips.

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The Ropes are Thought.

The Space is Time.

Could he but see, then he might climb.

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There are two kinds of truths: those of reasoning and those of fact. The truths of reasoning are necessary and their opposite is impossible; the truths of fact are contingent and their opposites are possible. (The Monadology of Leibniz)

The past few months have made me realize more and more about the sheer number of fundamental ideas that can be traced back, atleast in part to Gottfried Leibniz. The ones that I find most striking (other than his countless other contributions in calculus, geology, physics, philosophy, rationality, theology etc.) given what has been on my mind recently are his ideas in formal systems, symbolic logic and Kolmogorov Complexity.

It is not incorrect to think that Leibniz could be considered the first computer scientist to have lived. His philosophy centered around having a universal language of symbols combined with a calculus of reasoning, something from which modern symbolic logic and notation has directly descended from. An interest in mathematical logic also directly leads to an interest in the “mechanization of thought”, the same could be seen in Leibniz who was a prolific inventor of calculating devices.

His elucidation of what might be called the earliest ideas in Algorithmic Information Theory/Kolmogorov Complexity is equally intriguing. While he explicates them in depth, what he essentially talks about is the complexity of an “explanation” (basically Kolmogorov Complexity). And that an arbitrarily complex explanation is no explanation at all. I also find this idea similar to the bias-variance tradeoff in machine learning and the problem of overfitting. What I find striking is the clarity with which these ideas had been expressed and how little they have changed in essence in 3 centuries (though formalized).

In my intrigue, I have tried to read his very short works – Discours de métaphysique and The Monadology. While these have been debated over the centuries, their fundamental nature is unquestioned and are a recommended read. More recently I mentioned that I had been really intrigued by Leibniz for some months to my teacher from the undergraduate days. He was instrumental in getting me to read Cybernetics (by Norbert Wiener) and in Signal Processing in general. He was quick to point to this paragraph from Wiener’s book that I did not even remember reading:

Norbert Wiener

Since Leibniz there has perhaps been no man who has had a full command of all the intellectual activity of his day. Since that time, science has been increasingly the task of specialists, in fields which show a tendency to grow progressively narrower. A century ago there may have been no Leibniz, but there was a Gauss, a Faraday, and a Darwin. Today there are few scholars who can call themselves mathematicians or physicists or biologists without restriction.

A man may be a topologist or an acoustician or a coleopterist. He will be filled with the jargon of his field, and will know all its literature and all its ramifications, but, more frequently than not, he will regard the next subject as something belonging to his colleague three doors down the corridor, and will consider any interest in it on his own part as an unwarrantable breach of privacy.

Norbert Wiener, Cybernetics or the Control and Communication in the Animal and the Machine. 1948.

Since the mention of Wiener has occurred, it might also be useful to consider his trenchant advice just before the start of the above passage:

For many years Dr. Rosenblueth and I had shared the conviction that the most fruitful areas for the growth of sciences were those which had been neglected as a no-man’s land between the various established fields […]

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N is a Number : A Portrait of Paul Erdős is one of the most delightful, endearing and probably one of the best documentaries I have seen on an individual. I have always regarded Paul  Erdős as one of my personal heroes and hence It seems weird that I had not seen this rather old documentary earlier. Especially given it’s extremely high quality, appeal and not to mention the character it is based on.  However, it is never late to discover something so good.

There is an extremely good wikipedia entry on Paul Erdős. However I would still write a few words on him before linking to the videos.

A Mathematician is a machine for turning coffee into theorems.

— An extremely famous quote attributed to Alfréd Rényi. It was originally intended for Hungarian mathematicians and the mathematical-circles culture that flourished there giving the world so many mathematical giants.

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Erdős was an extremely prolific and famously eccentric mathematician, producing more papers and collaborating with more people than anybody in history. His eccentricity made him an extremely lovable character, and he made a fair share in contributing to human comedy.

He had no home and no full time job, he traveled around the world for half a century. Surviving on living with collaborators, fees from lectures and other appearances. His dis-interest in anything carnal or materialistic was almost Zen like I would dare say. Just having two pairs of half empty suitcases as his only belongings as he moved along from one location onto another.

It is often said (and quite correctly) that if you finish all bees in the world, the world would not survive for long. We could use that as an allegory for the sciences /mathematics as well. Erdős was essentially a bee. Brilliant in many areas of mathematics, he traveled from place to place using one idea from one area into another, cross-pollinating them, generating interest with his lovable anecdotes and enriching Mathematics as a consequence. A welcome departure from the so called purists.

His mathematical output was so prolific that a tribute is the famous Erdős number that gives the collaborative distance of a mathematician with him. The reason for such astounding output was not just his love for only mathematics but a brilliant memory. Colleagues have remarked that he could remember problems discussed years ago and exactly what the details that were talked about. If a mathematical problem was left half way, he could still remember where was the point they stopped, even if revisited after years. Not just that, he had this knack of knowing the mind of other mathematicians in where their interests lay. So he knew who would like to work on what kind of problems.

Though Mathematics was his only love, his knowledge was extremely wide and he could talk with most people about most things they might be interested in. Almost educated in the classical European style, with interests spreading across other basic sciences, politics, history. literature etc.

His work was not rich just in quantity. He displayed an extremely good taste in choosing and posing problems. The solutions to some of which have resulted in entirely new areas of Mathematics. Paul Erdős had been a towering figure even while he was alive, but as more time passes by, he only grows taller.

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N is a Number : A Portrait of Paul Erdős – Videos

Total Runtime : 57 Minutes

[View Here]

– Based on the book “The man who only loves numbers” by Paul Hoffman.

– Made by George Paul Csicsery 1993

– Narrated by James Locker

– Music by Mark Adler (I have to mention the music as I thought it was pretty beautiful, especially towards the end)

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Hat Tip : To Dr Vitorino Ramos’ ever thoughtful blog

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At the end of this post is a funny anecdote about American theoretical and applied mathematician Norbert Wiener. He was a pioneer in the study of stochastic and noise processes, contributing work relevant to electronics and communication engineering. He is also known and probably best known for being the founder of cybernetics.

His 1948 book, Cybernetics: Or the Control and Communication in the Animal and the Machine is a must read though i have not been lucky enough to read it myself as it is very difficult to find. This book is very high on my list of “books that MUST be read”. I wouldn’t be shy in admitting that the single most important reason on why i would want to read it is that this book came as a seminal work in that field! and is considered the authority to this day!

norbert_wiener_3.jpg

The anecdote to this rather eccentric and great man follows and is as recounted by Howard Eves and is on his forgetful nature:

Norbert Wiener was renowned for his absent-mindedness. When he and his family moved from Cambridge to Newton his wife, knowing that he would be of absolutely no help, packed him off to MIT while she directed the move. Since she was certain that he would forget that they had moved and where they had moved to, she wrote down the new address on a piece of paper, and gave it to him. Naturally, in the course of the day, some insight occurred to him. He reached in his pocket, found a piece of paper on which he furiously scribbled some notes, thought it over, decided there was a fallacy in his idea, and threw the piece of paper away in disgust.

At the end of the day he went home – to the old address in Cambridge, of course. When he got there he realised that they had moved, that he had no idea where they had moved to, and that the piece of paper with the address was long gone. Fortunately inspiration struck. There was a young girl on the street and he conceived the idea of asking her where he had moved to, saying, “Excuse me, perhaps you know me. I’m Norbert Wiener and we’ve just moved. Would you know where we’ve moved to?” To which the young girl replied, “Yes Daddy, Mommy thought you would forget.”

In later posts i will try to write on cybernetics and Wieners work as a follow-up and will try to read that book as soon as possible! :)

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