Mathematicians the world over

Mathematics as much as music does bring us together, as evidenced by the fifteen or so responses to the Quora question below, coming I’d like to believe from nearly as many different lands across the globe (but to read their names, I wonder if they don’t all come from just a few countries, India, Russia, China certainly. Also, given that Americans come from probably every country in the world they could all be Americans. Music of course may reach us all, that is billions of us, but mathematics many fewer, millions at the most. Why is that?

I imagine a world where music and mathematics have somehow replaced religion in our lives. Would the people in such a world ever go to war with one another?  Mathematicians, like musicians, speak the same language, and obey the same rules.

Would mathematicians ever fight for the rightness of their equations over those of other mathematicians, even those of other lands and other languages? Would musicians ever have to defend their particular music against someone else’s?

Whereas it does seem that believers in this or that God have always gone to war with believers in another God, or simply with the non-believers barbarians beyond their respective kingdoms and control.

Here is the Quora question put to the world online with a, actually my selection of some of the answers. I’m not enough of a mathematician myself to be able to tell you the best of them, and why. I’m working on it, you know, life-long learning.


One



Solutions by squaring both sides and solving for x

fivesquare5


Srinath Srinivasa, philosophically curious about mathematics


Vincen Mathai, Drinking the wine of life

1 upvote by Bernd Gmelin.

sixK Sylvan



eightsquare4

Since, many of you were demanding me to prove that 0 is not a solution of this sequence of nested roots,

For , X_{0}>0, X _{n} →2
To see this, note that X _{n+1}=y(X _{n}), where the function y:x↦√2x is such that x<y(x)<2 for every x in (0,2), y(2)=2, and 2<y(x)<x if x>2. Thus (X _{n}) is increasing if 0<X_{0}<2and decreasing if X_{0}>2 and converges to 2 in both cases.


The common proof for this is squaring both sides and solving the quadratic, as many have done here. However, when dealing with infinite series or expressions, we have to be very careful with the assumptions we are making. There is a clear assumption in this method, which is that this infinite expression is convergent and has a specific value.To be more rigorous, the proof using limits or even the one with the powers of 2 forming the well known convergent series is probably better.


One thought on “Mathematicians the world over”

  1. a very intriguing question/idea:
    “Would mathematicians ever fight for the rightness of their equations over those of other mathematicians, even those of other lands and other languages? Would musicians ever have to defend their particular music against someone else’s?”
    I’d like to think that people engaged in such demanding, full-filling, creative, all encompassing pursuits that require real thought and feeling, (not just musicians and mathematicians) would have the confidence in themselves and their world, to not ‘worry’ about making everyone else like or agree with them. Real dedication, real art, real passion, that goes a long way for building self-confidence and respect for others.

    Like

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