# List of Unsolved Scientific Problems with Large Monetary Prizes

Май 2015

# http://scienceprizes.org/

,000,000

Successfully launch, land, and operate a rover on the lunar surface.

,000,000

Demonstrate a commercially viable design which results in the permanent removal of greenhouse gases out of the Earth's atmosphere to contribute materially in global warming avoidance.

,000,000

Create free Android apps to spread reading, writing, and arithmetic skills, and prove their effectiveness over an 18-month period in African pilot communities.

,000,000

Create a mobile device that can "diagnose patients better than or equal to a panel of board certified physicians."

,000,000

Design, build, and deliver flight-qualified, small satellites capable of advanced operations near and beyond the moon.

,250,000

Accelerate the use of sensors and sensing technology to tackle health care problems.

,000,000

Improve our understanding of ocean acidification.

,500,000

Build an autonomous rough-terrain robot which can find and retrieve geologic samples.

,000,000

Experiment and computer simulations suggest the existence of a "mass gap" in the solution to the quantum versions of the Yang-Mills equations. But no proof of this property is known.

,000,000

The prime number theorem determines the average distribution of the primes. The Riemann hypothesis tells us about the deviation from the average. Formulated in Riemann's 1859 paper, it asserts that all the 'non-obvious' zeros of the zeta function are complex numbers with real part 1/2.

,000,000

If it is easy to check that a solution to a problem is correct, is it also easy to solve the problem? This is the essence of the P vs NP question. Typical of the NP problems is that of the Hamiltonian Path Problem: given N cities to visit, how can one do this without visiting a city twice? If you give me a solution, I can easily check that it is correct. But I cannot so easily find a solution.

,000,000

This is the equation which governs the flow of fluids such as water and air. However, there is no proof for the most basic questions one can ask: do solutions exist, and are they unique? Why ask for a proof? Because a proof gives not only certitude, but also understanding.

,000,000

The answer to this conjecture determines how much of the topology of the solution set of a system of algebraic equations can be defined in terms of further algebraic equations. The Hodge conjecture is known in certain special cases, e.g., when the solution set has dimension less than four. But in dimension four it is unknown.

### Millennium Problems: Birch and Swinnerton-Dyer Conjecture

by Clay Mathematics Institute

2000 - present

,000,000

Supported by much experimental evidence, this conjecture relates the number of points on an elliptic curve mod p to the rank of the group of rational points. Elliptic curves, defined by cubic equations in two variables, are fundamental mathematical objects that arise in many areas: Wiles' proof of the Fermat Conjecture, factorization of numbers into primes, and cryptography, to name three.

,000,000

Create a bioengineered replacement for the native liver of a large mammal, enabling it to recover in the absence of native function and survive three months with a normal lifestyle.

,000,000

Develop a therapy that extends the life of ALS mice by 25%.

,000,000

Develop small hydrogen refueling stations that can generate hydrogen from electricity or natural gas and dispense it to vehicles at least 1 kg at a time.

,000,000

An open competition to build a (much) smaller power inverter.

0,000

Restore homeostatic capacity (using heart rate variability as the surrogate measure) of an aging reference mammal to that of a young adult.

0,000

Extend the mean lifespan of a wild-type mammalian intervention cohort by 50% relative to acceptable published natural history of untreated norms.

0,000

Discover a prime number with at least 1,000,000,000 decimal digits.

0,000

Demonstrate two molecular machines capable of nanoscale positional accuracy and computation

0,000

Discover a prime number with at least 100,000,000 decimal digits.

## Solved Problems

,000,000

Develop a high-quality, high-efficiency solid-state lighting product to replace the common 60W incandescent light bulb.

,000,000

Launch a reusable manned spacecraft into space twice within two weeks.

,000,000

Design, build, and race super-efficient vehicles.

,000,000

Identify patients who will be admitted to a hospital within the next year using historical claims data.

,000,000

Develop systems that help Veterans schedule appointments to receive care from the Veterans Health Administration and to reduce risks in the future procurement and deployment of those systems.

,000,000

Accelerate innovation in space exploration by advancing rocket-powered vehicle technology for repeated space travel.

,000,000

In 1904 the French mathematician Henri Poincar

,000,000

Find the best collaborative filtering algorithm to predict user ratings for films, based on previous ratings without any other information about the users or films.

,000,000

Develop a tool to track the progression of the ALS disease.

,000,000

Complete the best technology demonstration of the removal of test oil in a test environment with salt water and wave conditions.

### Igor I. Sikorsky Human Powered Helicopter Competition

by American Helicopter Society International

1980 - 2013

0,000

Create and fly the first human powered helicopter to meet a particular set of flight requirements.

0,000

Discover a prime number with at least 10,000,000 decimal digits.

€100,000

Find the best plan for a UK exit from the European Union.

,000

Model and predict the maximum compressive loads for 3D printed objects.

,000

Discover a prime number with at least 1,000,000 decimal digits.

,000

Demonstrate technologies that may be relevant to future NASA Science Mission Directorate Mars missions.

,000

Help improve the prediction of disease progression in ALS patients.

,000

Design an unmanned space probe that would take measurements of the asteroid Apophis to determine whether it would impact Earth.

,000

Fly non-stop from New York City to Paris or vice versa. (Won by Charles Lindbergh.)

£20,000

Find simple and practical methods for the precise determination of a ship's longitude. (The present value of these awards would be millions of dollars.)

12,000

Devise a cheap and effective method of preserving large amounts of food. (The solution was to cook food in glass jars and seal them.)

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