# Solve a few math problems and make some extra cash!

Discussion in 'Community Discussion' started by Doctor Q, Oct 6, 2008.

### Staff Member

Joined:
Sep 19, 2002
Location:
Los Angeles
#1
No, I don't need help with my math homework. But I thought you might like to know that the U.S. government, through DARPA, needs some help with its own math homework. All you have to do is get a government contract to solve a few problems!

Unfortunately, some of them might be a bit hard. They span wide-ranging fields, not just pure mathematics, and some have been well-known unsolved problems for a long time.

You've got 23 to choose from, so take your pick and have fun! Be sure to apply by the deadline of next September. See FedBizOpps for details.

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. Capture and Harness Stochasticity in Nature
Address Mumford's call for new mathematics for the 21st century. Develop methods that capture persistence in stochastic environments.​
4. 21st Century Fluids
Classical fluid dynamics and the Navier-Stokes Equation were extraordinarily successful in obtaining quantitative understanding of shock waves, turbulence and solitons, but new methods are needed to tackle complex fluids such as foams, suspensions, gels and liquid crystals.​
5. 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?​
6. Computational Duality
Duality in mathematics has been a profound tool for theoretical understanding. Can it be extended to develop principled computational techniques where duality and geometry are the basis for novel algorithms?​
7. Occam's Razor in Many Dimensions
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.​
8. Beyond Convex Optimization
Can linear algebra be replaced by algebraic geometry in a systematic way?​
9. What are the Physical Consequences of Perelman's Proof of Thurston's Geometrization Theorem?
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. Creating a Game Theory that Scales
What new scalable mathematics is needed to replace the traditional Partial Differential Equations (PDE) approach to differential games?​
14. An Information Theory for Virus Evolution
Can Shannon's theory shed light on this fundamental area of biology?​
15. The Geometry of Genome Space
What notion of distance is needed to incorporate biological utility?​
16. 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.​
17. Geometric Langlands and Quantum Physics
How does the Langlands program, which originated in number theory and representation theory, explain the fundamental symmetries of physics? And vice versa?​
18. Arithmetic Langlands, Topology, and Geometry
What is the role of homotopy theory in the classical, geometric, and quantum Langlands programs?​
19. Settle the Riemann Hypothesis
The Holy Grail of number theory.​
20. Computation at Scale
How can we develop asymptotics for a world with massively many degrees of freedom?​
21. Settle the Hodge Conjecture
This conjecture in algebraic geometry is a metaphor for transforming transcendental computations into algebraic ones.​
22. Settle 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"?​
23. What are the Fundamental Laws of Biology?
This question will remain front and center for the next 100 years. DARPA places this challenge last as finding these laws will undoubtedly require the mathematics developed in answering several of the questions listed above.​

2. ### Jaffa Cake macrumors Core

Joined:
Aug 1, 2004
Location:
The City of Culture, Englandshire
#2
4 looks like it might be a bit of a giggle, so I might put my name down for that one. But hang on  do you need to be a USAian to be awarded one of these Government contract thingys?

3. ### calculus Guest

Joined:
Dec 12, 2005
#3
It would surely be against all the free trade agreements if you had to be a local.

I'm going to go for these three, do you think I have a chance?

2, 7, 11, 19

4. ### JNB macrumors 604

Joined:
Oct 7, 2004
Location:
In a Hell predominately of my own making
#4
1. 42
2. 42
3. 42
4. 42
5. 42
6. 42
7. 42
8. 32
9. 42
10. 42
11. 42
12. 42
13. 42
14. 42
15. 42
16. 42
17. 42
18. 32
19. 42
20. 42
21. 42
22. 42
23. 42

Who do I see about my check? (Thank you, Douglas Adams, wherever you are)

5. ### Jaffa Cake macrumors Core

Joined:
Aug 1, 2004
Location:
The City of Culture, Englandshire
#5
I'd think you'd be well suited for number 7, calculus – on all the occasions I've met you you've always been immaculately clean shaven.

6. ### calculus Guest

Joined:
Dec 12, 2005
#6
I'm clean shaven rounded to the nearest ten...

7. ### FunkyMonkey macrumors 6502

Joined:
Sep 4, 2007
Location:
Right behind you
#7
The Hitchiker's Guide to the Galaxy has answered all of my questions. When I wonder what the meaning of life is, I just think 42!

8. ### Abstract macrumors Penryn

Joined:
Dec 27, 2002
Location:
Location Location Location
9. ### rhsgolfer33 macrumors 6502a

Joined:
Jan 6, 2006
#9
Eww, Calculus shares a razor with Occam?

10. ### gauchogolfer macrumors 603

Joined:
Jan 28, 2005
Location:
American Riviera
#10
That sounds like the simplest answer to me.

Joined:
Nov 27, 2003
12. ### RITZFit macrumors 65816

Joined:
Sep 16, 2007
Location:
In my Corner
#12
I just got done cramming for a chem test...this made my head hurt

### Staff Member

Joined:
Sep 19, 2002
Location:
Los Angeles
#13
22. Settle the Smooth Poincare Conjecture in Dimension 4

Could this one be settled by arm wrestling?

Actually, it was the impressive work of Grisha Perelman that produced a proof of the Smooth Poincare Conjecture in Dimension 3. If you are interested, read an overview and commentary on Perelman's proof written by Terence Tao, the Australia-born Fields Medal winner who is a math professor at UCLA. Or take an entire class that covers "as much as possible" of the proof!

Once I finish solving the 23 problems above, there will be a few Millennium Problems left to keep me busy.

14. ### mickbab macrumors 65816

Joined:
Sep 13, 2008
Location:
Sydney, Australia
#14
I think you should learn to count before you start anything too hard here.

I count four.

15. ### Jaffa Cake macrumors Core

Joined:
Aug 1, 2004
Location:
The City of Culture, Englandshire
#15
Did anyone just hear a whooshing sound, or was that just me?