Closing Comments of the US-Mexico Workshop on “Nanoscience for Advanced Applications: on Crossroads of Disciplines”

 

“Physics/Science and Mathematics”

 

12 Noon, February 19th, 2005

University of Guanajuato, Mexico

 

 

Da Hsuan Feng

Vice President for Research and Graduate Education and Professor of Physics

The University of Texas at Dallas

http://www.utdallas.edu/research

 

 

This has been an exhilarating and exciting workshop.  Next spring, the second US-Mexico Workshop on Nanoscience for Advanced Applications will be held at The University of Texas at Dallas.  I hope many of you will be able to join us.

 

As a mathematical physicist, I enjoyed being reminded how beautiful mathematics and nanoscience are.   More importantly, I enjoy being reminded that physics in particular and science in general always have deep and intricate relations with mathematics. The talk by my colleague Stephen Levene on knots and DNA showed us the tip of the iceberg of biology and mathematics. In Professor Adolfo Sanchez Valenzuela’s talk, he mentioned the Mobius strip and its topological properties.  Actually, the very first time I heard about the Mobius strip was in 1978 from a great physicist, Professor C. N. Yang, when he talked about the deep connection between the so-called “non-Abelian gauge theory” and fiber bundles in geometry, and Mobius strip emerged from the discussion.

 

Allow me to tell you a story about mathematicians and physicists. 

 

In the early 1920’s, a brilliant young Chinese student named Wu-Zhi Yang entered the University of Chicago to study mathematics under Professor L. E. Dickson.  After Wu-Zhi Yang completed his Ph.D degree, he returned to China and taught in Tsinghua University. Among his many brilliant graduate students was a young man named Shiing-Shen Chern, or S. S. Chern. Chern’s name is well known to all our friends in CIMAT, was one of the greatest geometrist of the 20th century. Very sadly, Chern passed away on 3rd of December 2004 at the age of 93.  To commemorate Chern’s profound impact on the world of mathematics, especially on the Latin American mathematics, CIMAT and UT Dallas will organize a symposium in October or November of this year, right here in Guanajuato.

 

The story would seem out of place if this was the end.  Well, it is not.  Professor Wu-Zhi Yang had several sons and daughters, and the eldest is named Chen-Ning Yang.  As scientists in the world know, Chen-Ning Yang, or C. N. Yang, who also received his Ph.D. from the University of Chicago under the tutelage of the legendary Edward Teller, and Tseng-Dao Lee, or T. D. Lee, showed in 1956 that parity need not be conserved in nuclear weak interactions.  This discovery won Lee and Yang the highest scientific accolade, the Nobel Prize in physics in 1957.

 

In 1975, Yang drove to El Cerito to meet Chern in his house.  Yang told Chern that “what surprised me (Yang) is not that gauge field is the connection of fiber bundles, but more so that mathematicians can create it without touching the world of physics”. “I (Yang) was shocked and puzzled, because you mathematicians can create these ideas from nothing”, added Yang.  Chern responded “no, no, these ideas are not just imagination, they are natural and real.” (I want to thank Professor Paul Chu for providing me with an accurate account of this profound interchange between two maestro!).

 

Indeed, C. N. Yang has profound respect for Chern as a world-class mathematics.  This feeling was revealed totally when he wrote the following poem, and I quote:

 

"A piece of literature is meant for the millennium...Euclid, Gauss, Riemann, Cartan and Chern are all that count"

 

This is still not the end of the story.  After Professor Chern became Professor of Mathematics at UC Berkeley, the Chinese University of Hong Kong awarded him in 1969 an honorary degree.  There he met a brilliant young undergraduate.  Chern immediately recognized that this young man was unusually gifted in mathematics.  So he invited him to Berkeley to immediately begin his doctoral studies.  This young man is none other than Shing Tong Yau, the great Harvard mathematics professor, whose work on Calibi-Yau is world renowned.

 

It turns out that Chern has a daughter and her name is May. After completing an undergraduate degree in physics from Berkeley, May decided to enter UC San Diego as a graduate student.  There she met a young graduate student in physics and eventually married him.  Well, this young man is now world renowned and his name is Paul Ching-Wu Chu.  Paul Chu and collaborators in 1987 made the stunning discovery that certain materials could exhibit high temperature (90 degree Kelvin) superconductivity.  Currently, Paul is both T.L.L. Temple Chair of Science at the University of Houston and President of Hong Kong University of Science and Technology.

 

This interesting story tells us that not only physics and mathematics can be connected intellectually; it can also be connected “biologically”!

 

Finally, it is important to recognize scientists and mathematicians have been talking about the ability to express nature in mathematics terms since the two groups first began speaking.  Indeed, towards the end of his life, Michael Faraday was still wondering how mathematics could describe nature so well. 

 

 “The attention of two very able men and eminent mathematicians (Lord Kelvin and Sir James Clark Maxwell) has fallen upon my proposition to represent the magnetic force; and it is to me a source of great gratification and much encouragement to find that they affirm the truthfulness and generality of the method of representation.”

 

One could conclude here that physicists, or scientists, believe that nature, however mysterious, is what it is and mathematics is a language invented by men, or mathematicians (and in calculus case, invented by a physicist) to portray nature.  The profound comment of Chern seems to imply that mathematics is nature, and therefore it is only “natural” that mathematics can portray, and even predict, the subtleties of nature.

 

Perhaps this discussion between mathematics and nanoscience can and will contribute to the illumination of this deep philosophical point.

 

Thank you and see you in 2006.