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math-knowledge.html
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<HTML>
<!-- Mirrored from lamport.azurewebsites.net/tla/math-knowledge.html by HTTrack Website Copier/3.x [XR&CO'2014], Thu, 26 Mar 2020 22:42:03 GMT -->
<HEAD>
<META HTTP-EQUIV="Content-Type" CONTENT="text/html; charset=iso-8859-1">
<STYLE type="text/css">
H1 {line-height:38px}
H2 {line-height:45px; margin-bottom:0px; text-align: left; font-size:26px;
color:#000000}
H3 {line-height:10px; margin-bottom:8px; text-align: left}
body {background-color:#ffffe4; max-width:750px;
font-family:Calibri,Trebuchet MS,Verdana;
font-size:18px;
line-height:22px;
}
UL {margin-top:-10px}
.smallpar {margin-top: 7px}
</STYLE>
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</HEAD>
<BODY BGCOLOR=#ffffe4>
<font style="font-family:Calibri,Trebuchet MS,Verdana">
<title>Computer Scientists Don't Learn Math
</title>
<H1 style="margin-bottom:-10px">Why Don't Computer Scientists Learn Math?</H1>
<p style="max-width:650px" width>
<I>Last modified 28 March 2017</I>
</p>
<p style="width:600px" width>
I recently attended the <A href="http://www.heidelberg-laureate-forum.org/">
Heidelberg Laureate Forum</A>, in which some older
researchers--mainly Fields Medalists and Turing Award winners--talked
to and with young researchers. The young researchers ranged from
a few students just entering university to young faculty members, most
being graduate students. They came from all over the world and were
about evenly divided between mathematicians and computer scientists.
There was a rigorous selection process, and almost all the young
researchers seemed to be very intelligent.
</p>
<p style="width:600px" width>
In my talk I presented a formula that I said was the definition of
"the set of all permutations from 1 to N" [sic]. I had already
explained that [1..N ⟶ 1..N] is the set of functions
that map the set 1..N of integers from 1
through N into itself, and that I was writing f[x] instead
of f(x) to mean function application. Here's the formula,
about how it appeared on my slide:
</p>
<DL> <DD> <font size=+1> {f ∈ [1..N ⟶ 1..N] :
<BR> ∀ y
∈ 1..N : ∃ x ∈ 1..N : f[x]=y} </font> </DL> </font>
<p style="width:600px" width>
I then asked the audience to raise their hands if they could
look at this formula and understand it. About half the audience
raised their hands. I then asked all the mathematicians to
lower their hands. Almost no hands remained up.
Hardly any of the computer scientists could understand it.
</p>
<p style="width:600px" width>
Remember, these were specially selected, bright young researchers from around
the world.
</p>
<p style="width:600px" width>
This may explain why TLA+ is not more widely used, and
why it should be.
</p>
<p style="width:600px" width>
<A href="https://www.youtube.com/watch?v=FKFH_-QogN0">Click here</A>
to see a video of my talk. The relevant part starts at 15:00 and
lasts about 2.5 minutes; you can go directly to that part by <A href="https://youtu.be/FKFH_-QogN0?t=901">clicking here</a>.
</p>
</BODY>
<!-- Mirrored from lamport.azurewebsites.net/tla/math-knowledge.html by HTTrack Website Copier/3.x [XR&CO'2014], Thu, 26 Mar 2020 22:42:03 GMT -->
</HTML>