Senthil Kumaran (Posts about mathjax)http://www.xtoinfinity.com/enMon, 21 Jun 2021 05:13:20 GMTNikola (getnikola.com)http://blogs.law.harvard.edu/tech/rssThe Man Who Knew Infinityhttp://www.xtoinfinity.com/posts/the-man-who-knew-infinity.htmlSenthil Kumaran<div><blockquote>
"An equation for me has no meaning, unless it represents a thought of God." - Srinivasa Ramanujan</blockquote>
<p>"The man who knew infinity" is the story of <a class="reference external" href="https://en.wikipedia.org/wiki/Srinivasa_Ramanujan">Srinivasa Ramanujan</a>. This phrase, associated with Ramanujan should be
familiar to many due to a <a class="reference external" href="http://www.amazon.com/Man-Who-Knew-Infinity-Ramanujan/dp/B00C7F17OE/">very popular book</a> with the same title. There is a motion picture directed by Matt Brown
based upon this book.</p>
<p>I watched his movie on a Saturday at Berkeley. I was excited to listen to the QA with the director, and Mathematicians
such as <a class="reference external" href="https://en.wikipedia.org/wiki/Richard_Borcherds">Richard Borcheds</a> , <a class="reference external" href="http://www.cs.berkeley.edu/~oholtz/">Olga Holz</a> and <a class="reference external" href="https://math.berkeley.edu/~ribet/">Ken Ribet</a> following the screening.</p>
<p>In India, we have been exposed to Ramanujan quite early in our lives. I had stories in school book about great Indian
mathematicians like Aryabhata, Brahmangupta, and Bhaskaracharya. Indian Satellites to Space launched by ISRO bear their
names too. Along with those personalities, we have Srinivasa Ramanujan and whom we know for his invention of <a class="reference external" href="https://nrich.maths.org/1380">Magic
Squares</a>, and <strong>Ramanujan Number</strong>, <strong>the smallest number expressible as sum of two cubes.</strong></p>
<div class="math">
\begin{equation*}
1729 = 1^3 + {12}^3 = 9^3 + 10^3
\end{equation*}
</div>
<p>Beyond that, I had not known much about the significance of this number or Ramanujan's work.</p>
<p>Years later, when taking <a class="reference external" href="https://youtu.be/h_9WjWENWV8?t=14m48s">online courses</a>, I had come to know about Hardy and Ramanujan's research in Number Theory
being at the core of secure communication and cryptography. Do you use Credit Cards online and feel confident that
someone will not maliciously take your money? All this is was because of the research in number theory.</p>
<p>There is also famous anecdote associated with Ramanujan, known to many from South India, Ramanujan prayed to a goddess,
and she gave inspiration for his work. He mentions that his theorems had come up like a dream, a boon granted by the
Goddess, and he would write formulae in his book. That's how he invented those theorems.</p>
<p>If it happened like that, imagine how excited young students from Madurai will
be, where there a temple every hundred feet. :) It needs to be clarified that,
Ramanujan was a genius and he also worked very hard on his subjects.</p>
<p>A better understanding of this phenonmemon, in general, is now known. The style of discovery is called
" <a class="reference external" href="https://www.youtube.com/watch?v=hbRc8uUKSHM">diffused mode</a> learning", wherein after an intense work on challenging
problem, the solution suddenly comes up during a restful time.</p>
<p>All these are portrayed well in this movie. The relationship between Hardy and Ramanujan, the scientific culture at
Trinity College, London revealed in real detail. The movie has a significant portion dealing with how Hardy mentors
Ramanujan, and strives to bring his work to the modern world.</p>
<p>In the question and answer session that followed, two questions were of interest to me.</p>
<p><strong>How do mathematicians study Ramanujan's work when he has not left many formula proofs with his equation?</strong></p>
<p><a class="reference external" href="https://en.wikipedia.org/wiki/Richard_Borcherds">Richard Borcheds</a>, who is an accomplished mathematician, replied that Ramanujan's work was published in the form of
series of <a class="reference external" href="http://www.amazon.com/Ramanujans-Notebooks-Bruce-C-Berndt/dp/1461270073/">notebooks</a>. He left behind three notebooks containing almost 3000 theorems, virtually all without proof. The
reason he could have done that is perhaps he grew up in a time when the paper was very expensive for him and he wanted
to be economical.</p>
<p>(It did not answer the question, but provided a good perspective).</p>
<p><strong>Question 2: In the movie, Ramanujan is shown to be desisting writing formal proofs. Is that true?</strong></p>
<p>Richard Borcheds shared that, it is bit exaggerated in the movie. Ramanujan always knew the proof of his work and
could state it if he wanted to. But he usually did not.</p>
<p>I enjoyed watching this movie and listening to the perspectives associated with the genius from kumbakonam.</p></div>http://www.xtoinfinity.com/posts/the-man-who-knew-infinity.htmlMon, 27 Jun 2016 04:12:17 GMT