You are currently browsing the monthly archive for December 2013.

As such, I cant tell much about the dynamics behind Google buying Boston Dynamics, but I am excited to hear this news. All I can say is that, there is still life for innovation! Knowing Google, they will do a good job with this new addition. We will have to wait and see the big day.

If you haven’t seen, you must watch the Cheetah Robot, the Usain Bolt equivalent in machine form:-)

With Scott in all smiles:-)

Sadly, the great man has left us. The world becomes a lesser place. Nelson Mandela, has been a remarkable symbol of  peace, determination and humility. A champion leader for humanity. Perhaps, no one since Mahatma Gandhi will have a legacy like Mandela. I vividly remember holding a placard in one of the  school day processions, with a message “Free Nelson Mandela”.  Little would I have known the true greatness of this man, back then… An absolute hero.

The most striking thing about Mandela to me, is the way he composed himself, after release from 27 years of prison. 27 long years.. think of it! 18 of that 27 years  in the isolated Robben Island. He held himself, dumped all vengeance against the very people who took away a golden slice of precious life. For the world, we had a great leader in him for years since then! His release could easily have turned into a bloodshed like never before, but he instead chose the path of peace. Talk about leadership. He is something beyond special.

I can feel the deafening feeling in South Africa and Africa in general, the world by and large too. What a sacrifice! Hope we can continue his legacy. BBC has this nice obituary on him. RIP.

If you have not seen this before, here is a must watch page from PBS.

So, the number has descended down from 70 million to a mortal 600! Expectedly, there is a new Polymath initiative to improve this further and who knows, perhaps 2 indeed is that number. Well, we are talking about the new result by James Maynard on the asymptotic gap between prime numbers.

Just to recap, the problem statement is as follows: If $p_n$ and $p_{n+1}$ are the $n$th and $(n+1)$th prime numbers (e.g., $p_1=2,p_2=3,p_3=5, \ldots$). On cursory counting, the gap $p_{n+1}-p_{n}$ appears to grow larger as $n$, but not necessarily, because there are these well known twin prime pairs such as $\left(3756801695685 \times 2^{666669} \pm 1 \right)$. Will this gap of $2$ stay good forever as $n \to \infty$? If not as low as $2$, will that be something low enough? i.e.,  How small can $G$ be, where

$G=\lim_{n \to \infty} \inf \left(p_{n+1}-p_{n}\right).$

Earlier this year, Zhang proved that $G$ is no more than $70$ million. That in a way proved that, the prime gap is bounded as we move along the number line. A bunch of mathematicians including Terrance tao worked further (polymath project on this) and improved that gap to as a few thousands. The latest result from Maynard brings in an independent proof for $G=600$. Maynard also claims that if the Elliott–Halberstam conjecture (See this nice blog post on prime tuple theory this by Terry Tao) is indeed true, then, $G=12$. Stunning!

What is stated here is just one avatar of the prime tuple theorem. More general results are also being discussed within the community. Terrance Tao again has this nicely articulated and maintains a polymath page for us. As an onlooker, I am as excited as many others to see this progress.