Edward Frenkel is a mathematician who wants to introduce us to the "hidden parallel universe of beauty and elegance" that is mathematics. Sounds great! I am totally on board for this project. Unfortunately, Frenkel fails to engage me despite my receptivity to his message.
The problem is that Frenkel doesn't explain why we should care about the discoveries he presents. He excitedly reports that difficult problems in one area of mathematics, such as number theory, can be solved using methods from another area, such as harmonic analysis. But who cares that the study of automorphic functions can shed light on the counting of solutions of equations modulo primes? I understand the satisfaction that comes from making connections, but without knowing the significance of equations modulo primes or automorphic functions (or Riemann surfaces or braid groups or...) it feels like empty puzzle-solving rather than a view into the mind of God.
Frenkel reserves his most ardent enthusiasm for a research project called the Langlands Program, "considered by many as the Grand Unified Theory of mathematics. It's a fascinating theory that weaves a web of tantalizing connections between mathematical fields that at first glance seem to be light years apart: algebra, geometry, number theory, analysis, and quantum physics." In later chapters he finally attempts to bring the abstractions back down to Earth through connections to physics, but alas the "reality" of the quantum world is just as hard to imagine as multidimensional reduction. I got a better sense of the importance and beauty of symmetry from Frank Wilczek's A Beautiful Question, even though I won't claim to have understood Wilczek.
Love & Math includes sections of memoir, which I found more engaging because more relatable. Frenkel's reminiscences give a fine sense of the life of an apprentice mathematician and of growing up in the Soviet Union in the 1980s.
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