International Society of Biomechanics
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Here, you will uncover historical information about the society. Enjoy these nuggets curated by John Challis, our Archives Officer.  

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    On August 8th, 1900, at the International Congress of Mathematicians held at the Sorbonne in Paris, David Hilbert presented ten unsolved mathematical problems. Hilbert (1862-1943) was one of the leading mathematicians of the late nineteenth and early twentieth centuries; many may be familiar with his eponymous Hilbert spaces used in linear algebra and calculus. His mission in presenting the problems was to set an agenda for research in mathematics. The publication of his problems actually comprised 23 problems, related to many branches of mathematics (Hilbert, 1902). The first problem solved, number three, asked whether for two polyhedra of equal volume it was always possible for one of them to be sliced into many polyhedral pieces and for the other to be assembled from those pieces. It turns out one polyhedron cannot always be assembled from the slices of the other polyhedron. Some of Hilbert’s problems remain unsolved, including problem nine, the Riemann hypothesis. The Clay Mathematics Institute has, in a similar vein, presented seven problems: the Millennium Prize Problems. The Riemann hypothesis is one of those seven problems. Hilbert thought solving any of his problems would advance mathematics and potentially provide glory to the mathematician solving a problem; the Millennium Prize Problems also have a monetary incentive.

    Biomechanics builds on knowledge from the natural sciences (e.g., biology, chemistry, and physics). In all of these areas, mathematics provides essential tools. Indeed, wonder has been expressed at the effectiveness of mathematics in the natural sciences (Wigner, 1960). Progress in science is, in important ways, different from the way mathematics progresses. Generally, scientific hypotheses are proposed and then tested based on evidence, typically from experiments. The evidence does not provide proof; rather, it can provide support for a hypothesis. In mathematics, the testing of ideas is not based on evidence from the natural world, and it is possible in a single paper to provide a proof (e.g., Wiles, 1995). In mathematics, a paper with a valid proof can be sufficient evidence for acceptance of the proof by the mathematics community.

   Given the differences between science and mathematics, while it is possible to present problems to the biomechanics community, there is less chance of a definitive answer to the problem. In biomechanics, rather than problems to solve, challenges to tackle are perhaps more relevant (e.g., Fregly et al., 2012). Robert (Bob) Norman, a former ISB president (1989-1991) and an honorary member, wrote an article for the ISB Newsletter in 1985: “Biomechanics: Are there substantive issues?”. He presents three challenges to the biomechanics community, which are both thought-provoking and still relevant (Norman, 1985). While Bob acknowledges his list is not exhaustive, the areas of his problems are still enticing and have some of the desirable potential rewards outlined by Hilbert (1902):

 

“Who of us would not be glad to lift the veil behind which the future lies hidden; to cast a glance at the next advances of our science and at the secrets of its development during future centuries?”

 

References

  • Fregly, B. J., Besier, T. F., Lloyd, D. G., Delp, S. L., Banks, S. A., Pandy, M. G., & D'Lima, D. D. (2012). Grand challenge competition to predict in vivo knee loads. Journal of Orthopaedic Research, 30(4), 503-513.
  • Hilbert, D. (1902). Mathematical problems. Bulletin of the American Mathematical Society, 8, 437-479.
  • Norman, R. W. (1985). Biomechanics: Are there substantive issues? International Society of Biomechanics Newsletter, 18, 2-4.
  • Wigner, E. P. (1960). The unreasonable effectiveness of mathematics in the natural sciences. Communications on Pure and Applied Mathematics, 13(1), 1-14.
  • Wiles, A. (1995). Modular elliptic curves and Fermat's last theorem. Annals of Mathematics, 141(3), 443-551.

 

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