Your era at the helm of Canada’s national strategy for research and development, has been one of action, proactive leadership in research policy, tight management of federally funded programs, as well as increased and sustained support for certain research areas.

Indeed, we have been hearing a great deal lately about the targeting of Canada’s research effort towards government priorities, such as the Automobile of the 21^{st} century, Bombardier, Pratt & Whitney and others.

Other research areas were also identified by the Council of Canadian Academies (CCA) in its report, *“The State of Science and Technology in Canada”(STIC)*, and eventually earmarked as government priorities in the *“Science and Technology Strategy”.*

We respect and accept unreservedly your right and responsibility as elected officials to determine and select the areas of research that warrant government funding, and we have no doubt that the currently targeted areas were sound choices and are worth supporting.

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It has been said that, “*the CCA report and S&T Strategy selected these targeted areas, after soliciting and receiving a broad input from the Canadian science and technology community.”* Unfortunately the call for input was apparently not broad enough to reach us, and so we missed this golden opportunity to contribute ours. I am therefore appealing directly to you, because I feel that some extremely important research challenges were missed. Their essence and existence, or maybe their relevance, must have slipped by the Tri-Council presidents, their advisors, the CCA, and the authors of STIC, when they were conducting their analysis of what should be our national priorities.

This doesn’t surprise me in the least, because these research areas are simply of a different level of complexity than those we are used to in official reports and communiqués. They are epic challenges that defy the current state of human intellect.

I urge you to please take a look at these 20 research areas and to consider making at least some of them government priorities and therefore targeted for federal funding.

These problems, Hon. Ministers, are nothing short of the holy grail of 21st century science. The solution of any one of them would signal a new threshold of Biblical proportion to the state of our knowledge, but also to our standard of living. It would be as earth shattering as the discovery of “infinitesimal calculus” by Isaac Newton. Not the calculus that kids love to hate in high school and early college, but the one behind almost every major scientific and technological discovery of the last four centuries.

I need to warn you however, that all these problems are firmly anchored in the mathematical sciences, which are not considered so hot lately because Mathematics is by now an old science, as old as Pythagoras, Euclid and Archimedes. On the other hand, if resolved they will have huge ramifications into almost every aspect of human endeavor, from medicine to commerce, and unfortunately warfare.

Another note of caution is that most of these problems may not be solved during your terms in office. Actually, they may take a century or so to settle. But every step on the way towards their resolution would be a giant leap forward for mankind.

You may have guessed by now that in Canada these problems fall under the rubric of “basic research”, which is also sometimes dubbed, “curiosity-driven”. But please take a look and judge by yourselves. This is curiosity of a different kind, the one that transcends time and human limitations, but also the one that one day your successors in public office will put a tax on, just like the great Michael Faraday told British Chancellor Gladstone, when the latter asked him about the use of “this electricity” he was working on.

My plea may seem like a Michael Moore’s slogan:* “Target This! Random challenges from an unempowered Canadian”. *But it is not. I did not make up these problems. They were conceived by true geniuses, and took decades of deep reflective thought to formulate. The only inference from Moore’s movie is that some of our current granting policies may be making us a nation that is addicted to *fast solutions for easy problems.*

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It is also useful to note that these problems were also earmarked by DARPA for targeted funding. Yes, DARPA or Defense Advanced Research Projects Agency.

Here they are. I know you will find them interesting. I also know that you will be pleasantly surprised by how obvious it is that any progress made towards the solution of these basic research problems could have a huge impact on humanity.

**1. The Mathematics of the Brain**

Develop a mathematical theory to build a functional model of the brain that is mathematically consistent and predictive rather than merely biologically inspired.

**2. The Dynamics of Networks**

Develop the high-dimensional mathematics needed to accurately model and predict behavior in large-scale distributed networks that evolve over time occurring in communication, biology, and the social sciences.

**3. Geometric Langlands Program and Quantum Physics**

How does the program of Princeton based Canadian mathematician Robert Langlands, which originated in number theory and representation theory, explain the fundamental symmetries of physics? And vice versa?

**4. Settle the 150-years old Riemann Hypothesis**

The Holy Grail of number theory, which is at the basis of cryptography, coding and digital commerce that your government is rightly keen on promoting and developing.

**5. 21st Century Fluids**

Classical fluid dynamics was extraordinarily successful in obtaining quantitative understanding of shock waves, turbulence, and solutions, but new methods are needed to tackle complex fluids such as foams, suspensions, gels, and liquid crystals.

**6. Computational Complexity**

As data collection increases can we “do more with less” by finding lower bounds for sensing complexity in systems? This is related to questions about entropy maximization algorithms.

7**. What are the Fundamental Mathematical Laws of Biology?**

**8. Biological Quantum Field Theory**

Quantum and statistical methods have had great success modeling virus evolution. Can such techniques be used to model more complex systems such as bacteria? Can these techniques be used to control pathogen evolution?

**9. What are the Physical Consequences of the latest breakthrough in Geometry?**

Can profound theoretical advances in understanding three dimensions be applied to construct and manipulate structures across scales to fabricate novel materials?

**10. Algorithmic Origami and Biology**

Build a stronger mathematical theory for isometric and rigid embedding that can give insight into protein folding.

**11. Optimal Nanostructures**

Develop new mathematics for constructing optimal globally symmetric structures by following simple local rules via the process of nanoscale self-assembly.

**12. The Mathematics of Quantum Computing, Algorithms, and Entanglement**

In the last century we learned how quantum phenomena shape our world. In the coming century we need to develop the mathematics required to control the quantum world.

**13. An Information Theory for Virus Evolution**

Can Shannon’s theory shed light on this fundamental area of biology?

**14. The Geometry of Genome Space**

What notion of distance is needed to incorporate biological utility? i.e. how to measure the similarity or difference between two genomes instances.

**15. What are the Symmetries and Action Principles for Biology?**

Extend our understanding of symmetries and action principles in biology along the lines of classical thermodynamics, to include important biological concepts such as robustness, modularity, evolvability, and variability.

**16. Computation at Scale**

How can we develop asymptotics for a world with massively many degrees of freedom?

**17. The Smooth Poincare Conjecture in Dimension 4**

What are the implications for space-time and cosmology? And might the answer unlock the secret of “dark energy”?

18**. Capture and Harness Stochasticity in Nature**

Develop methods that capture persistence in stochastic environments.

**19. Settle the Hodge Conjecture**

This conjecture in algebraic geometry is a metaphor for transforming transcendental computations into algebraic ones.

**20. Creating a Game Theory that Scales**

Since the work of Nobelist (and beautiful mind) John Nash, Game theory has been fundamental to economics, management and decision-making. What new scalable mathematics is needed to replace the traditional mathematical (i.e., Partial Differential Equations) approach to differential games?

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