what he called ’’Dirichlet’s Principle” incorrectly. Hilbert incorrectly thought
that he had proven the Continuum Hypothesis. There are umpteen exam-
ples. These are only for such recorded and well known written cases. But
when an individual scientist/mathematician, during his private moments, in
trying to go beyond known mathematics, keeps on making mistakes. He
struggles through a maze of mistakes and then arrives at whatever he thinks
is consistent mathematics and is ’’publishable”. Only these are what we hear
of and what one talks of. These private mistakes should also be considered
’’mistakes” in mathematics. These are too innumerable and are often well
kept secrets ( as never uttered ) to be recorded here!
Just as a child when speaking a language tries to experiment with sounds
and names, it discovers new sounds ( gibberish ) and in fact enjoys doing it.
That gibberish would be proven to be a ’’mistake” due to social pressures and
ultimately abandoned by the child. But clearly such mistakes are part of the
very process of speech learning. So also are mistakes in mathematics. As na-
ture is very demanding and requires strict adherence to its ” intrinsic” mathe-
matics so even gibberish mathematics would have rules of consistency. Hence
though mistakes would be made these would be subsequently corrected. In
fact mistakes would be an inevitable part of discovering new mathematics.
This analogy too shows that indeed mathematics is a ” language” ( of nature
)■....... , , , ,
A thought, on as to how two different mathematics - pure and applied
arise. In everyday language I am free to visualize objects which are half
man - half woman or part horse - part dog - part snake or part cow - part
human - part bird - part elephant etc. I can visualize groups of these as co-
existing with humans. In such cases my imagination allows me to cook up all
kind of ” realities” and thus think that I am able to visualize that these may
have some kind of existence in a Platonic world of its own. However quite
clearly we should call all these objects and their interactions etc as nothing
but gibberish, in as much as we know that these do not correspond to any
realistic objects. However it may be that in spite of being unaware of geology
and palaentology, that on observing a lizard at close quarters. I may be able
to imagine of a time when earth may have had extremely large and dangerous
lizards living on it. That hypothesis may later on be actually proven to be
correct by Palaentologists as those creatures having been dinosaurs. So there
is a small, though non-zero chance that some of my gibberish imaginings may
turn out to reflect some aspect of reality in future.
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