Mathematical Perspectives
Progress for the past decade or so has been extraordinary. The solution of Fermat's Last Theorem [11] and of the Poincare Conjecture [1] have resolved two of the most outstanding challenges to mathematics. For both cases, deep and advanced theories and whole subfields of mathematics came into play and were developed further as part of the solutions. And still the future is wide open. Six of the original seven problems from the Clay Foundation challenge remain open, the 23 DARPA challenge problems are open. Entire new branches of mathematics have been developed, including financial mathematics and the connection between geometry and string theory, proposed to solve the problems of quantized gravity. New solutions of the Einstein equations, inspired by shock wave theory, suggest a cosmology model which fits accelerating expansion of the universe possibly eliminating assumptions of 'dark matter'. Intellectual challenges and opportunities for mathematics are greater than ever. The role of mathematics in society continues to grow; with this growth comes new opportunities and some growing pains; each will be analyzed here. We see a broadening of the intellectual and professional opportunities and responsibilities for mathematicians. These trends are also occuring across all of science. The response can be at the level of the professional societies, which can work to deepen their interactions, not only within the mathematical sciences, but also with other scientific societies. At a deeper level, the choices to be made will come from individual mathematicians. Here, of course, the individual choices will be varied, and we argue for respect and support for this diversity of responses. In such a manner, we hope to preserve the best of the present while welcoming the best of the new.
- Research Organization:
- Brookhaven National Lab. (BNL), Upton, NY (United States)
- Sponsoring Organization:
- DOE - OFFICE OF SCIENCE
- DOE Contract Number:
- DE-AC02-98CH10886
- OSTI ID:
- 1020850
- Report Number(s):
- BNL-94543-2011-JA; KJ04030000; TRN: US201116%%876
- Journal Information:
- Bulletin of the American Mathematical Society, Vol. 47, Issue 1; ISSN 0273-0979
- Country of Publication:
- United States
- Language:
- English
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