The Next Fifty Years: Science in the First Half of the Twenty-first Century

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Book Reviews of The Next Fifty Years: Science in the First Half of the Twenty-first Century

Book Review: A fairly good overview
Summary: 3 Stars

- "The Future of the Nature of the Universe" (Lee Smolin). The author predicts that quantum computing will become a reality in 50 years, as long as quantum mechanics remains true when extrapolated to macroscopic systems. COMMENT: Due to studies in decoherence and more honest interpretations of experiments testing the phenomenon of entanglement, quantum theory will instead be viewed in more "classical" terms in its formalism and foundations. Research into quantum computation, as understood presently, will fade from the scene.

- "Cosmological Challenges: Are We Alone, and Where?" (Martin Rees). The author is optimisitic about the SETI project and other attempts to detect the presence of life external to the Earth. COMMENT: Due to advances in solid state device physics, life on other planets will be detected via the by-products they put into their atmospheres. The information theory behind the SETI searches will become more refined also, increasing the probability of understanding a real message from another civilization.

- "Son of Moore's Law" (Richard Dawkins). The author predicts an exponential increase in DNA sequencing power, which he labels as the "Son of Moore's Law." The author also expresses a fear that there will still be theologians in 2050, this being done in the context of ethical debates on the genetic sequencing of "Lucy" and the possibility of the reintroduction of dinosaurs. COMMENT: The sequencing projects and the number of sequenced organisms will increase hyperexponentially. In addition, tens of thousands of new "transgenic" organisms will appear, all of them optimized to carry out certain biological functions. The field of horticulture will explode, with thousands of new species of ornamental plants appearing before 2050. The university will meet its demise by 2050, but theologians will not disappear. On the contrary, and perhaps unfortunately, the major religions will be with us for many centuries to come, and they will accompany humankind on their voyages to other worlds, for better or worse.

-"The Mathematics of 2050" (Ian Stewart). The author predicts major revolutions in mathematics, due partially to the increasing influence of the computer, bioinformatics, and financial engineering. He also predicts that the current split between "pure" and "applied" mathematics will end, with the result being just "mathematics". He mentions also the "Milennium Problems", one being the Riemann hypothesis, which he predicts will be solved by 2050, its solution being hinted at by considerations in physics. The P/NP problem will be proved undecidable, the Hodge conjecture will be disproved, the Birch/Swinnerton-Dyer conjecture will be proved, the Navier-Stokes equations will turn out not to have solutions in certain circumstances, the Yang-Mills mass gap problem will be settled but will be deemed irrelevant by physicists, and the Poincare conjecture will be "wide-open". Interestingly, the author is one of the few who have mentioned the role of "quantization of mathematics" via quantum algebra, quantum topology, and quantum number theory. COMMENT: The Poincare conjecture will be resolved by 2010 with its resolution being in the context of the "quantization of mathematics" mentioned by the author. In fact, the quantization of mathematics will be the driving force behind whole new areas of mathematics. Pure mathematics will continue to be viewed as disjoint from applied mathematics. In fact, there will be an intense effort, as evident from the last two meetings of the International Congress of Mathematicians, to keep pure and applied mathematics as separate disciplines. Mathematical finance will continue to explode and there will be intense competition between financial firms to develop highly sophisticated algorithms for financial prediction and portfolio manangement. Financial mathematics will also have more overlap with physics and meteorology, as energy and weather derivatives take on even more importance. The next fifty years will see the rise of financial firms, and others, managed, staffed, and run completely by intelligent machines. In addition, due to hardware advances and the development of highly sophisticated algorithms in mathematical biology and bioinformatics, the entire biosphere will be sequenced by 2050. Complete mathematical models of the entire human body will be developed by mathematicians working in the biotechnology industry, and drug discovery will be viewed as essentially mathematical, with the actual physical chemistry and manufacture being essentially automatic. In this same light, combinatorial chemistry will become a branch of mathematics in its own right, attracting the attention of hundreds of mathematicians. Advances in artificial intelligence will bring about, with indications by the year 2040, of intelligent machines able to construct original concepts and theories in pure mathematics. Skepticism as to the possibility of thinking machines will be alleviated because of these developments. "Artificial" mathematicians will begin to become competitive with "natural" ones by the year 2050. Further, cryptography will continue to explode as a field of mathematics, due to the increasing need for online security and individual privacy. Increased computer power will fuel this need, and the competition between encryption and de-encryption algorithms will become very intense. lastly, by 2050 it will be accurate to say that mathematics will enter into every phase of human and machine activity. There will be no process, no business transaction, no entertainment function, no leisurely activity, that will not depend predominantly on mathematical structures or algorithms.

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