# 2012 Survey Results

* What would your favorite theoretician be doing? *

Antea is a fictional young aspiring mathematical physicist in the epilogue of Roger Penrose’s book *The Road to Reality*. She experienced the rare green flash phenomenon while watching the sunrise, and “then an odd [remarkable] thought overtook her…”

Today we wish to thank the 259 people who took our survey posted last week, and present the results. Of course Antea could not be among the great thinkers listed, not at that stage, but our purpose was to see where the greats would seek remarkable thoughts today.

The Antea shown in the painting detail is not Penrose’s, but was painted by Giuseppe Mazzola, called Parmigianino, around 1530. She belongs to the Museo di Capodimonte in Naples, Italy, but has traveled much. During World War II she was taken by German forces to a salt mine near Salzburg, Austria, where Ken’s family spent part of a holiday during Christmas week. She was loaned to the Frick Collection in New York City in 2008.

Parmigianino himself pursued materials science, so much as to neglect his contract creating art for a church. Being the 1500s this meant *alchemy*, but his motive seems to have been art rather than greed for gold. He was one of the first Italians to do etching as an art form. He sought a metal that would respond more easily to the technique than copper.

## The Questions and Results

1. What would Euclid be doing in 2012?

- Writing the best blog: 16.1%
- Writing a new edition to his famous book: 36.9%
- Working on factoring: 49.0%
- Other: 9.4%. The most amusing answer was “working on non-Euclidean geometry” from two responders. Two people put him on the front line of the Greek protests. The most ironic response was “Formalizing the foundations of ill-defined fields,” a service David Hilbert performed for Euclid. There were also: engineer, solving math, String Theory, breaking RSA, writing an undergraduate text on Category Theory, writing world-class surveys, synthesizing 20th-century mathematics, encouraging young mathematicians a-la Bourbaki, meditating in Tibet, enjoying the beach, re-founding geometry in topos theory, other math logic, running a hedge fund, tax attorney, blogging, using the Coq theorem prover, and the one denotational truth: requiescatting in pace. There was also a neat riff on debating with Cicero on Greek versus Roman contributions, which is welcome to be put in as a comment.

2. What would Gauss be doing in 2012?

- Working on quantum computation: 36.1%
- Working on complexity theory: 29.0%
- Working on P=NP: 31.0%
- Other: 21.0%, making 53 responses. A general drift was that this universal mind would not be confined to computer-science topics; one had him working on what we take to be mag-lev trains, recalling that “gauss” is a unit of magentism. Riemann, Navier-Stokes, and ‘all’ Clay problems came up. The most wicked answer was that he would name all arXiv published papers after himself. The most “real” answer IMHO (Ken) was “Doing the Langlands program,” while someone else had him zoned in on the Collatz problem, and another had him making good on a proof by constructing a regular 65,537-gon. One had him fixing the world’s economy, while another anointed him chair of the Federal Reserve, not too far from a job in the British Government actually held by our next man.

3. What would Newton be doing in 2012?

- Working on string theory: 39.8%
- Creating a new branch of mathematics: 56.1%
- Working on P=NP: 4.1%
- Other: 15.4% Lots of economic vocation for this former Master of the Mint—one connected his concern for counterfeit and shaved-down coins into work on unforgeable quantum money. Some had him into polemics against quantum theory and Leibniz. Others noted his paranormal and alchemy interests. Teaching theology was a given—Newton wrote over a million words on theology. The most topical response was that Newton would have worked on the 3-body problem—note that our next man identified a meaty special case that is solvable in closed form. However, what we note most is that the founder of so much continuous mathematics drew no truck with a ‘discrete’ problem like P=NP.

4. What would Euler be doing in 2012?

- Working on everything: 73.6%
- Solving the Navier-Stokes Clay problem: 20.1%
- Working on P=NP: 6.3%
- Other: 5.0% One of the twelve “Other” responses said “everything and two or three other things too.” Another said he would co-author a paper with Erdős “(pretend Erdős is still alive)” but the qualifier was hardly necessary—Erdős has maintained a stellar publication record since his death in 1996. This all creates a higher
*polymath*impression than Gauss. One had him helping with global-warming satellites, another with elementary school math teaching, and another living like Grigory Perelman in St. Petersburg. I once wrote a short story in Italian about a man who dies trying to move a rock with his mind, and someone (else) put Euler up to that, while another said worse. The most elevative respondent had him resolve P vs. NP from results on complex power series. But no mention of theology, despite Euler being the only mathematician on the Lutheran Calendar of Saints.

5. What would von Neumann be doing in 2012?

- Working on peta-scale computing: 27.1%
- Working on quantum computing: 55.0%
- Working on P=NP: 17.9%
- Other: 9.2% More “everything” including housing computer server rooms on the Moon for better thermal regulation. When not working on “something beyond our imagination,” he campaigns for Barack Obama and becomes his science advisor or runs for his job. Global-scale synthetic biology and regenerative medicine, patterns of resemblance, computational fluid dynamics, alternative energy sources, people got real specific with Johnny. Only one “pure math” topic came up, non-commutative geometry, though two mentioned game theory of course. However, the main categories show the degree to which quantum computing rules!

6. What would Gödel be doing in 2012?

- Thinking: 58.3%
- Finally writing up his solution to the P=NP question: 46.0%
- Working on string theory: 7.9%
- Other 9.1% Theology made a comeback with three responses, in-tandem with proving his Third Incompleteness Theorem or the Comtinuum Hypothesis. The cleverest logical answer was “He would prove that deciding whether P = NP would imply that P = NP iff P != NP”—though this is equivalent to others’ responses that he’d prove P vs. NP undecidable. Honorable mention to “Using the fact that Euclid works on Non-Euclidean geometries as a contradiction to prove that P=NP.” Others addressed his paranoia and conspiracy theories, including the pithy reply, “Dieting.” Another had him viewing endless reruns of the movie “Inception”—while another put it more philosophically: “Applied transcendental epoché.” Category theory, new foundations for mathematics, and ordinal analysis of (strength of) theories harked back to what for him was his real world, along with “depression at having killed Hilbert’s program” and “hiding in his office at the Institute.” The most upbeat answer was, “Co-authoring some papers with ME!” Note also that the answers for Gödel add up to more than 100%, as also with Euclid but not the others.

7. What would Turing be doing in 2012?

- Working on AI: 65.8%
- Working on the Riemann Hypothesis: 6.9%
- Working on P=NP : 27.3%
- Other: 9.0% Being able to marry legally and greeting former Prime Minister Gordon Brown who delivered a formal British Government apology for the treatment leading to his suicide topped the list topically. One respondent with several “Creating a new branch of…” responses followed here with simply “…science,” while four others noted a branch Turing did help create: the computational study of morphogenesis. He was tabbed for (CEO of) Google or Apple or Facebook, or somewhere he could “invent the Turing machine.” Straight-arrow answers had him working on AI/robotics/brain science, and this gives me opportunity to note that Scott Aaronson has posted the culmination of his Philosophy and TCS course, including a student project showing the Turing Test remains very much alive. Skiing, winning second-tier marathons, and hobnobbing with celebrities seemed to be wishes for the “good life” unknown, though one can follow Turing’s real life in the online scrapbook maintained by his biographer Andrew Hodges. Another had him attracted to parallel computing, which made me think more of how Turing would have weighed in on Jim Backus’ 1977 Turing Award article, “Can Programming be Liberated from the von Neumann Style?” And a healthier percentage than anyone except Gauss thought he would take a crack at the time-bounded NTM version of the Halting Problem, our last subject.

8. Will 2012 see the end of the P=NP question?

- Yes: 5.9%
- No: 49.4%
- Perhaps: 9.9%
- No way: 28.5%
- I hope so: 6.3%

I’d be curious to know what the 15-of-253 answering “yes” may have up their sleeve—after all, even Donald Rumsfeld famously skipped over the case of “unknown knowns.” But most were confident in the question’s staying power, and nobody mused that extra-terrestrials might give the answer away. Instead, having belatedly realized we could have invited other luminaries to be mentioned in a catchall “Other” field, I became the only one to mention someone of the same gender as Antea.

## Other Folks, Other Strokes

These were the 18 general suggestions, including one from the comments.

- Ramanujan doing in 2012 : Celebrating National Mathematical Day in India, creating more number theoretic formulas.
- Hilbert: would attack Perm vs Det via polynomial ideal theory, with help from Em. Lasker and Em. Noether
- Leibniz: working on Lie groups to show the identity of indiscernibles
- What would Claude Shannon be doing in 2012?
- I would ask what John Horton Conway would be doing, but he is still with us.
- Which part of AI would Dijkstra be studying? None of it..
- Whether P = NP is only the beginning of the P vs. NP question.
- Maybe a proof will be found, but we would have to wait more than a year for validation.
- None of the seven Euclid–Turing will be working on
*any*standard problem—they are too creative for*that*. - Hilbert would design his own automated proof assistant.
- Depends on how long it takes me to flesh out all the details in my paper.
- P=NP question will see the end of the world! Remember it’s 2012! :-p
- Only dishonest people would say it is still unsolved.
- I think it’s more likely that society crumbles, rendering this question irrelevant [plus some encomium for this blog]
- I will prove that parity games can be solved in polynomial time. Mark my words.
- Perhaps you can add Hilbert and Einstein to the list.
- [Terence] Tao will be working on things I don’t understand
- [On P=NP ending] I hope not.

Although our survey was meant to be lighthearted, there were interesting correspondences between a researcher’s proclivities and future areas. We are all for diversity in science: different strokes from different folks.

## Open Problems

What areas might be primed for a stroke of creativity? What should priorities be?

What would your favorite research mentor be doing?

We thank all those who responded to the survey.

Thank you for this wonderful post, which has called forth what is perhaps the largest smile-to-paragraph ratio of any GLL column in my memory … every single line was well-conceived, thought-provoking, and fun too.

On statistical grounds — and also from innate optimism — I’m entirely confident that there are alive today at least 70 mathematicians alive today who are similarly hard-working and creative as the GLL “Euclid—Turing Seven” … it will be mighty fun to see the wonderful ideas that they produce, and so we are all of us exceedingly lucky to be alive in this time.

Maybe you should have also included Einstein also. I guess he would have continued his search the grand unified theory of everything

Haha….This is excellent, and really funny!

This is really great. I’m glad you wrote it up like this instead of merely showing the resulting numbers. Made it well worth the participation!

Yikes! Looks like ol’ Euclid (111.4%) and Gauss (117.1%) have over 100% of their time taken up. Busy guys.

Euler would be a civil engineer since he worked on the Konigberg bridge problem.

Gauss would work on hardware since he was into magnetism.

Did Euclid deal with straight-edge and compass constructions? If so

he might now work on field theory since that what was used to prove

that you couldn’t square the circle, double the cube, or trisect the angle.

LOL