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<p>Another gem of scepticism from Derek. This time he is due
unambiguous thanks. (There's condescension for you!)</p>
<p>Yet one does not need to turn to complex mathematics to find
examples of potentially perfidious proofs. <br>
</p>
<p><br>
</p>
<p>Consider the equation: ax<sup>3</sup>e<sup>-x</sup> = 1.</p>
<p>With only a little wrangling, it is easy to *see* that this
equation has exactly one root when a = (e/3)<sup>3</sup>. Now,
according to Galculator, this quantity is approximately equal to
0.743908774934. Hence one *expects* that the equation</p>
<p>0.74391x<sup>3</sup>e<sup>-x</sup> has exactly two real roots
very close together - as can be found by numerical solution using
Newton's method. ... But the question now arises as to *what would
constitute a rigorous proof* that this equation has exactly two
real roots?</p>
<p>I'll leave this as a teaser for the more mathematically literate
on this list.</p>
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<p>Olwen</p>
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<br>
<div class="moz-cite-prefix">On 10/12/2020 15:54, Derek M Jones
wrote:<br>
</div>
<blockquote type="cite"
cite="mid:421fd3b1-b3c0-a485-368f-1136a846bd7b@knosof.co.uk">All,
<br>
<br>
"What is Mathematics?"
<br>
<a class="moz-txt-link-freetext" href="https://www.andrew.cmu.edu/user/avigad/meetings/fomm2020/slides/fomm_buzzard.pdf">https://www.andrew.cmu.edu/user/avigad/meetings/fomm2020/slides/fomm_buzzard.pdf</a>
<br>
<br>
A discussion involving recent examples of 'proofs'
<br>
that may or may not be correct, starting at slide 5.
<br>
<br>
There is some discussion of the use of programs to create proofs,
<br>
and the problem that software contains faults, just like
mathematical proofs.
<br>
<br>
</blockquote>
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