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I was wondering what subjects a freshman in mathematics ought to choose in the future if s/he wanted to help working on energy and environment-related issues we are currently facing, and will very likely be even more profound in the future.

I am currently day-dreaming about using the skills I will acquire as a mathematician to create more efficient solar cells or wind-mills, but I guess a little understanding of the physics involved wouldn't hurt.

Which subjects should I choose to enhance my knowledge on this subject? Could you perhaps suggest a rough pathway by means of which I could deepen my understanding of the subject matter?

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High-school physics and chemistry are a good start. For solar cells - semiconductors and/or plant biology. For wind-mills, some basic electro/mechanical engineering. –  Mike Dunlavey Oct 24 '11 at 14:31
    
Don't know why this wasn't pointed out before: If you want to understand how things actually work, you have to be a scientist, not a mathematician. If you want to build new things, then you have to be an engineer. If you are so dedicated to solving environmental problems, being just a mathematician isn't going to mesh with that life goal. There's nothing wrong with dedicating 80% of your studies to math, but if you want to engineer something, you will also have to devote 80% of your studies to that subject. It will be demanding on your time. –  Chris White Jun 19 '13 at 3:48
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5 Answers

The most important observation I have about your question is that it is, as of yet, technology agnostic.

You need to ask yourself, do you want to research in a specific technology, or do you want to deal with the bigger picture? I know a lot of people who have pursued an engineering career that actually encompasses a broad range of energy technologies. One professional I know, for instance, started out in steam turbines, and wound up in energy efficiency.

If you're interested in a bigger picture, I would strongly point you to smart grid technologies and power systems. You can go pretty far into that education, learning about the promise of different technologies, before deciding on a more specific path. There are several active and growing smart grid and smart grid technology centers where a strong background in math would serve you well. In fact, given no other information about your interests, this would be my #1 suggestion. I'm not sure if it's appropriate for me to link to something so specific, but the FREEDM center is an example of what I talk about.

Smart grid also has the unique distinction of being something that no one credibly disagrees with the imperative for. Let's say, for instance, that you really want to do photovoltaics. Why? Solar thermal has always been cheaper and remains cheaper today. The challenge in both technologies lies in better scaling for manufacturing. Surely, you're not holding your breath for an efficiency revolution. Provided you agree with me in that decreasing price per area in manufacturing is the worthwhile approach, maybe thin film is the way to go? Need I remind you of the fact that Silicon Valley recently failed to make headway with 1,100 employees and a $500 million federal loan backstop? Maybe we'll look elsewhere. The cost of many residential systems is about half in the power conversion systems. Maybe the panels are already cheap enough and we should look to the power system technologies and business model. We're mostly back to the smart grid at this point.

Any technology you choose will have problems. You need to get more specific with your direction, but you also need to realize that you will always be looking back if your direction is "energy and environment" and your background is mathematics. Right now, diversification of energy research is often agreed to be worthwhile. Browse through the ARPA-E catalog if you haven't already.

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I recently learned about Nanoholdings, which I think is good ideological match with the OP, although, we could spend all day listing these. nanoholdings.com –  AlanSE Oct 24 '11 at 17:40
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I suggest you have a look The Azimuth blog, which is John Baez's move to address environmental issues as a Mathematician/Mathematical Physicist. He's had that focus for about a year, and if you read through the posts you'll find a number of possibilities gathered together there. Good luck.

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Environmentalists and ecologists and climatologists all need a reasonably strong background in statistics in order to analyse whether something actually works or not in the field, so do not forget Statistics. This is needed no matter what technology you work with, and is even more needed in order to find out what damage existing technology is doing.

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You should research Pons/Fleischmann cold fusion, which also goes by the name LENR (Low Energy Nuclear Reactions). This field is taboo to all mainstream researchers, but the effect is obviously real, and extremely important.

Unfortunately, there are frauds in this field, like Rossi. Avoid the frauds, and try to find the serious people--- you can see who these are on lenr-canr.org.

You can read more about this here: Why is cold fusion considered bogus?

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Can I recommend hot fusion, instead of cold fusion? It works in the sun and other stars and may yet work here on earth.
If it works well, it will have many advantages.

A standard general physics sequence will be a good start for this. Pay particular attention to electromagnetism.
Eventually you would specialize in nuclear physics.

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-1: Hot fusion is a fraud, cold fusion is not. –  Ron Maimon Aug 27 '12 at 21:15
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