As Nick Boston pointed out (http://www.nickbostrom.com/extraterrestrial.pdf)

this is the worst news the human race has ever received.

The idea is that the Fermi Paradox must be the result of a Great Filter which stymies the creation of long lived intelligent races. The easier it is for life to evolve, the more likely it is that the Filter lies ahead of us, rather than behind.

Therefore microbes on Mars is bad bad news.

I'm not a programmer, I'm a mathematician, but I notice the same thing in my field.

To those who say there is not a tendency toward weirdness in mathematical disciplines, I suggest the following experiment. First go to the weekly math colloquium at a local research university. Then, go to the weekly philosophy colloquium and see if you can discern a difference in the people who come. I believe you will almost certainly find that the mathematicians are less attractive and charismatic. You could argue that philosophy simply selects for attractiveness and charisma, but I believe you will have similar findings if many different subjects are substituted for phil.

To those who say that the strangeness of programmers is somehow reducible to various qualities of "geeks", this is clearly begging the question, as any good geek should know. The topic for this thread is very similar to asking "why are geeks the way they are?" but phrased differently.

I have spent large amounts of time wondering why mathematicians are weird, ugly, uncharismatic and so forth. My answer is that they live largely in their own imaginations, and spend correspondingly less time in the "real world." Therefore, not surprisingly, their real world appearance, manners etc gives evidence of a lack of attention. Conversely people in other fields are not selected for an ability to concentrate deeply, spend more time in the here and now, and reap consequent benefits in hygiene, social skills, etc.

I can think of some very important mathematical works from the last century, but I can't imagine anyone wanting to read them:

1. Principia Mathematica, Russell & Whitehead
2. On Undecidable Propositions, Kurt Goedel
3. Classification Theory, Saharon Shelah
4. Topology from the Differentiable Viewpoint, Milnor

I assume you are interested only in original documents, and not summaries or expositions. Unfortunately the technical and specialized nature of modern science is likely to make "accessible science" and "original science" mutually exclusive.

I very much second paiute's opinion (above).

I'm a mathematics professor. I first became interested in math after reading Excursions in Number Theory during my junior year of college. It is a wonderful introduction to the power of proof, and requires no more background than simple arithmetic. I second someone's earlier suggestion of "e" by Eli Maor. That is truly an outstanding book. Unfortunately what's good for a high school student may not be good for the rest of us. I found Zero: The History of a Dangerous Idea to be completely vapid, but it is full of intrigue and controversy, and is not difficult. A genuinely good book is John Derbyshire's history of algebra, though it is challenging in places. It is worth remembering that Ramanujan (according to myth) was strongly motivated by the book "A synopsis of elementary results in pure and applied mathematics", written by George S. Carr. It shows that a book of facts (such as Excursions) may be as good or better than a popular or historical book. I will go out on a limb and make a strange suggestion: Tractatus Logico Philosophicus, by Wittgenstein is completely fascinating, and no less comprehensible to a high school student than to the rest of us. It may create an appreciation for the mysterious and profound aspects of mathematics that could be powerfully motivational.

I'm a recent graduate with a PhD in mathematical logic; I can totally relate to this problem of having a non-standard background. Before Grad School I went to a liberal arts college, where my math major consisted of something like 9 courses. When my advanced studies began I felt totally lost. But you have to ask yourself: Do I really have the time and energy to commit to a high level exposition of physics at this point? The answer to this question will depend on whether you intend to specialize in PDE's. If the answer is no, then I believe you should buy some good popular explication of the topics you're covering. Unfortunately, I do not know what such a book would be, but having read extremely good expositions of several high level mathematical concepts (Prime Obsession; Unknown Quantity; "e", the Story of a Number, and Incompleteness) I have some confidence that a book of similar quality may exist in this area. Of course, if you are intending to specialize in PDE's, it will be worth the time and effort you will need to invest in reading a serious text. Even so, keep in mind that you can never learn everything, even about a small subdiscipline. My advice is to find a particular area of PDE's, become an expert on that, and get out of graduate school as soon as possible.