{\huge Predictions For The New Year}

For 2014, that is \vspace{.5in}

Isaac Asimov was one of the most prolific writers of all times---he wrote or edited over 500 books. In his Foundation series a mathematician finds out that the future can be predicted based on equations.

Today Ken and I want to make several predictions about the new year, without using any equations.

In previous years we tried to make serious predictions, well we thought they were serious. So this year we plan on making less serious ones. Perhaps, based on Murphy's Law, these will all come to pass. Some jokes on this blog do run parallel to serious research ideas, as we sometimes say if our own second thoughts haven't shot them down already.

In this spirit, Asimov wrote a joke paper, ``The Endochronic Properties of Resublimated Thiotimoline,'' at the time he was finishing his own PhD in biochemistry. He intended it to help him transit from the style of his already-successful fiction to serious academic writing. It was supposed to appear in the magazine Astounding Science Fiction under a pseudonym, but appeared under his real name. One of his examiners noticed it, and queried how his time-reversing molecule squared with the laws of thermodynamics. Happily there was hilarity all around and Asimov earned his ``Dr.''

Of course, as Kurt Gödel remarked at the end of our last interview with him, we need a new time-reversal mechanism to re-contact him. The system could also enable us to make perfect predictions. So let us proceed to last year's and next year's business.

Last Year's Predictions

Another hitch with serious predictions is that sometimes it is seriously hard to verify them, especially when there is difference of opinion. Probably we should crowdsource the results. At least we began with a slam dunk.

1. No circuit lower bound of $latex { 1000n}&fg=000000$ or better will be proved for SAT. True.

2. A Computer Scientist will win a Nobel Prize. As usual, close but no. The Chemistry Nobel centered on computerized models of chemical systems, but none of the three winners has an official CS affiliation.

3. An important advance will be made on understanding barriers either to proving $latex {\mathsf{P = NP}}&fg=000000$ or proving the opposite, $latex {\mathsf{P \neq NP}}&fg=000000$. Depends. The improved ``chasm'' results for arithmetical complexity are certainly relevant, but it is not clear which way the support goes. There was ongoing significant work on polytopes for TSP and other problems, but they merely speak against one approach to $latex {\mathsf{P = NP}}&fg=000000$.

4. A new simple group will be discovered. By the classification theorem, such a group must be infinite. Apparently no, nor have we heard about a new result about finitely generated ones.

5. Another gap will be found in Shinichi Mochizuki's claimed proof of the ABC Conjecture. (Note that Mochizuki released updates to his papers on Dec. 16th, including acknowledgments to Vesselin Dimitrov and Akshay Venkatesh who had found a gap in two of them.) We claim half-credit: all five ``Inter-universal Teichmüller Theory'' papers at the bottom of his papers page have 2013 modification dates, with two updates just recently on Dec. 18th.

6. The ABC claimed proof will be found to be correct. Not yet.

7. Experiments scaling up boson sampling from $latex {3 \times 3}&fg=000000$ to $latex {4 \times 4}&fg=000000$ permanents will be published by year's end. Apparently yes; indeed per this Jan 8, 2013 item, $latex {4 \times 4}&fg=000000$ may already have been done as we wrote. However, according to Scott Aaronson's Nov. 8 post on his blog, ``...so far, BosonSampling has only been demonstrated with 3-4 photons,'' amid proposals for larger-scale computation of permanent-related quantities. We should stress that computing the permanent itself, or anything NP-hard, is not the object. The latest news we find is this Nov. 17 paper on techniques for verifying experiments that may put 25--30 photons in reach, pushing the limit of brute-force classical simulation, and that furthers interesting issues of matrix and polynomial symmetry. Scott has just posted notes of 5 lectures he gave in Rio de Janeiro.

8. A new conditional relation will be found tying the difficulty of scaling up boson sampling to that of scaling up full universal quantum computation. Not that we see. Closest we find is this paper giving an elementary argument against classical methods scaling up to simulate boson sampling.

9. A best seller will be published by a noted blogger on the $latex {\mathsf{P = NP}}&fg=000000$ question.

   Does Top-14,000 count? Lance Fortnow's book The Golden Ticket made Amazon's 2013 Best Books in Science list. Congratulations, Lance.

10. Work will begin on a major motion picture whose plot is based on finding a polynomial time algorithm for factoring. It will audition Angelina Jolie as the brilliant mathematician who solves the problem and Tom Hanks as the villain. Our script is still looking for a buyer, while Jolie and Hanks are tied up with Disney.

11. Noted progress toward solving another Clay Problem will be released on the ArXiv this year. Maybe. Closest we find is this paper showing a sense in which a positive fraction of elliptic curves over the rationals have an analytic rank of $latex {0}&fg=000000$, and hence meet a long-known criterion for satisfying the Birch/Swinnerton-Dyer conjecture.

12. A planet no more than twice Earth's size will be detected orbiting within the habitable zone of its single star. Apparently still no. Major headlines were made by a study released last month giving what appears to be an overwhelming probabilistic proof of their existence, but the best that stories about it such as this one seem to give are planets that are still too big or too hot.

The Predictions

Here are our predictions for the new year, 2014. They are just predictions, so there is no way to tell today if they will come true---that is why we call them predictions.

$latex {\bullet }&fg=000000$ Two integers $latex {p/q}&fg=000000$ of over one million digits each, in decimal, will be discovered so that

$latex \displaystyle p/q = \sqrt{2}. &fg=000000$

$latex {\bullet }&fg=000000$ Trading in Bitcoins will be stopped when an anonymous team posts an algorithm that breaks the scheme. Social media will be abuzz with the question: why did they post it? They could have made billions in real dollars. $latex {\bullet }&fg=000000$ A new field of computer science called computational football will be one of the hottest areas of research. At least one university president will be quoted by the New York Times as saying: Finally a research area I can understand and get behind. As a result MIT will create a college football team in the NCAA Division I Football Bowl Subdivision. Their team will win no games their first season under coach Mike Shanahan. The MIT president will say, jokingly, ``next year we will win twice as many games.'' MIT students will love the quote, and it will appear on t-shirts all over campus.

\includegraphics[width=2in]{shirt.png}

$latex {\bullet }&fg=000000$ A proof that there is a proof that there is a proof that there is no proof that there is a proof that there is a proof in Peano Arithmetic of $latex {\mathsf{P} \neq \mathsf{NP}}&fg=000000$ will be found. No one will be able to referee the proof. The author, who is famous, will appeal to the formal proof checking community to get involved, but they will demur.

$latex {\bullet }&fg=000000$ Computer scientists will sweep the all the Nobel Prizes except Peace and Literature. The Nobel committee will say in a press release: Computing is now a lens for all of science, so we had little choice. When the board of ACM's {\sc SigNobel} group is interviewed by the New York Times on why computer scientists missed out on the Literature prize, they will say: ``Surely your joking.''

$latex {\bullet }&fg=000000$ A company called Braincloud LLC will announce a competitor for Google Glass that is controlled directly by brain pulses. The first release will include apps for cryptographically secured remembering of your passwords and phone numbers, hands-free texting, playing chess, visualizing GPS directions, and (for panicky new parents) having Dr. Spock's Baby Guides fed right to the brain. It will be worn in the ears not the eyes, using vulcanized rubber ear tips.

$latex {\bullet}&fg=000000$ A new massively-multiplayer online role-playing computer game called ``DoS Survivor'' will take the world by storm. Each player connects a pair of computers to the game. One runs a licensed simulation of a famous online server, while the other is used to generate Denial-of-Service attacks on other players' servers. Survivors progress to higher levels and are enabled to run more advanced servers. The two finalists square off with one running healthcare.gov and the other running Silk Road. Results of field tests this week indicate that the game is close to alpha release.

$latex {\bullet }&fg=000000$ MOOCs will adopt a ``human-centered support structure.'' This will involve geographically localized cells of up-close instruction at regularly spaced time intervals, with generous time in-between for absorbing material and practicing non-bubble exercises. Advanced-intelligence scanning of exercise submissions for quality points will be an implementable option. Accompanying each course will be a device predicted 40 years ago by Isaac Asimov himself in his essay, ``The Ancient and the Ultimate'':

``[It] can go anywhere, and is totally portable. Something that can be started and stopped at will along its data stream, allowing the user to access the information in an effective, easy manner ... and requir[ing] no electrical energy to operate ... minimum technology for maximum interaction.''

Ken and I have been extra-busy with Asimov's devices, as we will shortly reveal.

Open Problems

Our final prediction is that 2014 will be another great year for mathematical research, and another fun year for all of us at GLL. We thank you again for your support and wish you all a joyous new year.