False Beliefs in Mathematics

Test your intuition: For two n by n matrices A and B, is it always the case that tr(ABAB) = tr(ABBA)?

Over Math Overflow Tim Gowers asked about common false beliefs in mathematics. There are many exciting answers on many different levels and I could identify some of my own false beliefs.

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6 thoughts on “False Beliefs in Mathematics

  1. Thinking about this I found out a cool fact (which solves the problem elegantly):

    If M is a matrix permuting the coordinates, then its trace is the number of fixed points of the relative permutation!!

  2. A very common false belief in mathematics, I hold onto firmly: “I will one day prove a really significant mathematical theorem”.

  3. Pingback: Ram Sethu: Proof of Great Science of Ancient Past | World University Information

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