Author Archives: John Lee

A Notable Quote on Richard Feynman

From Freeman Dyson, “Disturbing the Universe”, Harper & Row, New York, 1979: “Dick was also a profoundly original scientist. He refused to take anybody’s word for anything. This meant that he was forced to rediscover or reinvent for himself almost … Continue reading

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$\sum_{n=0}^\infty e^{nix}$ is Cesàro Summable

Back when I was a Ph.D. student, a friend of mine (he was a Ph.D. student in physics studying laser optics) asked me if the series $\sum_{n=0}^\infty e^{nix}$ converges. I vaguely remember that his advisor needed to have a finite … Continue reading

Posted in Summability Methods | 4 Comments

$1+2+3+4+\cdots=-\frac{1}{12}$?

No, folks! I am not drunk nor I am pot-headed. Yet, I am about to discuss the crazy identity $$1+2+3+4+\cdots=-\frac{1}{12}.$$ No, I am not joking either. This is actually pretty serious mathematics and is also pretty serious stuff even to … Continue reading

Posted in Foundations of Mathematics, Summability Methods | 3 Comments

Time Travel, Parallel Universes (Alternate Realities) and the Greys

Time Travel in Science Fiction It does not require a physicist to get excited about time travel. Time travel is one of the most popular themes in modern day science fiction genre. “The Time Machine, H. G. Wells, 1895″ is … Continue reading

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Real Structure, Fundamental Symmetry and Quantum Mechanics

In the standard Hermitian quantum mechanics, the space of states of a quantum mechanical system forms a complex Hilbert space in general. But often the space of states becomes a real vector space. When the space of states is a … Continue reading

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