Overlooking the U.C. Berkeley campus is the world's largest research center for pure mathematics. Top mathematicians meet there to scratch out formulas on a chalk board. We take a look at how some of these complex equations are fueling the drive to discover advancements in everything from science to social issues.

There's math in music, and there's musical talent in many of the world's top mathematicians. That's why there's a grand piano in the lecture hall of the Mathematical Sciences Research Institute perched atop Grizzly Peak in Berkeley.

The University of Waterloo's Professor Henry Wolkowicz specializes in a field called optimization. The optimal placement for 30 modules on a computer chip to communicate with each other had never been accomplished until he helped solve the problem.

Prof. Henry Wolkowicz, University of Waterloo, Ontario: "And so this is why computers keep increasing in speed

Optimal positioning of modules means chips get smaller, faster and generate less heat.

Prof. Henry Wolkowicz: "And interesting enough, the faster the computer is, the better you can do this mathematics to get smaller and smaller chips. So it's a vicious circle going on."

Stanford's Dr. Gunnar Carlson is using topology to understand the patterns in nature. His work is helping scientists understand how the brain encodes visual signals in the primary visual cortex.

Gunnar Carlson, Ph.D., Stanford Mathematics Professor: "You probably cannot develop a good bionic eye without understanding this encoding in the visual cortex."

Professor Don Saari of U.C. Irvine uses symmetry groups and chaotic dynamics to solve social problems like voting.

Don Saari, Ph.D., University of California, Irvine: "The current method which we now know -- a vote for one person turns out to be the worst method possible."

Saari devised a ranking technique based on a points system.

Don Saari, Ph.D.: "This is where I would give two points to my first place candidate."

Sounds simple, but it took Saari 15 years to sort out the variances and all the complexities of the equations.

Don Saari, Ph.D.: "It is the method that most accurately reflects what the voters want."

Now Saari's system is being used by the BCS to rank college football teams.

Prof. Bernd Sturmfels is involved in stem cell research. He's using computational algebra to examine 30,000 genes in a mouse and identify which ones trigger spinal cord development.

Prof. Bernd Sturmfels, Math and Computer Science, U.C. Berkeley: "At a fundamental level we'd like to understand biology."

Mathematical Sciences Research Institute Director, David Eisenbud, says these thinkers are the unrecognized heroes who forge the tools that make the inventions. And this is where much of it happens.

Dr. David Eisenbud, Mathematical Sciences Research Institute Director: "It's the backroom part of science."

And each new discovery builds on those theorems established by past mathematicians. Think of the math equations for electromagnetic waves and circuitry that made your cell phone or iPod work. Yet most of these innovators say they have no desire to pursue intellectual rights for their work.

Dr. David Eisenbud: "It's like discovering a waterfall. It's like discovering something beautiful in nature, and it's just there. It's real. All we're doing is uncovering the truth."