1) How to get the world population to stop growing. Fact: over 90% of the global growth in population is occurring in developing nations. In those countries, couples have 4, 5, 6 children, as each child is an extra source of revenue in the couple’s retirement years. The simple solution to stop world population growth is to have a mandated world pension system, bankrolled by the USA’s 12.5 trillion dollars a year of discretionary funding, and administered by the UN. Over a generation, the couples in those countries will cease to have 5 children and start to have 2 children, as they head towards consumerism. The disposable income of those individuals in those countries will grow as the costs of child-rearing are slashed by 60%. The governments of those developing nations will respond by increasing taxes, and the USA will be there to market US security, defence, medical and technology products and services to those nations. This will keep the USA as the global superpower for another fifty or a hundred years. The US is not perfect, but seriously, there is no other contender for world superpower with the moral authority and might the US has.
2) How to remove petroleum burning cars from the roads: Electric vehicles are the answer, but not in their current form. What needs to happen is that the lithium ion batteries of electric vehicles need to be replaced with lithium ferric phosphate batteries. These last from 3-5,000 complete charge and discharge cycles, which you will never normally do in a vehicle; about 3-10 times as long as a lithium ion battery. In this scenario, the car is purchased from the dealer. The battery is, as usual, the most expensive part of the electric vehicle. But, when the car body is exhausted/out of fashion, the battery is still good, so simply a new car body is purchased from the dealer and the battery is swapped from vehicle to vehicle while the customer waits. The batteries last so long that they can be passed down intergenerationally. This makes sense, especially as lithium is a finite resource, and lithium refining is an expensive process. The weight of the battery will be increased, so the vehicle will have to be to some degree larger and heavier than a contemporary electric vehicle. This is good, as larger, heavier vehicles are safer for the occupants.
3) How to cure all cancers: There are molecules known as the Beticolins. They come from a fungus on the sugar beet. These molecules self-assemble into hexadimeric nanopores in the presence of Ca2+ ions, which then go on to insert into cell membranes and allow the free passage of cations into and out of the cell. This destroys the proton gradient across the cell membrane and thus stops H+ ATPase from generating ATP. In the absence of ATP, the cell dies after a few seconds. This remarkable cell-killing utility of the Beticolins would enable cells, such as cancer cells, to be killed instantly. In addition to this, the Beticolin molecules can be put inside vesicles, which can be targeted to particular cell types, say, metatasising lung cancer cells, using peptoid tags which can be used to decorate the vesicle surface. The result is a chemotherapy that could effectively cure every form of cancer that a peptoid can be found for which targets that particular cell type. The result of this research would be a contender for the Nobel Prize in Medicine.