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BEGIN:VEVENT
UID:9cfa12767c8b82124495af4dbce319e9
CATEGORIES:Graduate Pizza Seminar
CREATED:20181107T103020
SUMMARY:Analysis without the Analysis
LOCATION:GSL
DESCRIPTION:Abstract: I'd like to share a definitely true story. Once upon a time, the
re lived a logician named Abraham Robinson. Overall, he had a happy life, b
ut there was one problem: the analysts of his department were constantly be
ing friendly and telling him about their research. This led to far too many
conversations involving the letter epsilon for Robinson to live a happy an
d successful life. Then, one day, Robinson had an idea. "What if I reengine
ered all of real analysis so that it required a whole course in model theor
y to understand even the most basic definitions? Surely," he thought, "that
would make the analysts stop trying to talk to me".\nAnd with that, he set
to work. To succeed with his plan, he knew he would first have to learn ho
w to do analysis. For months, he read paper after paper, and filled entire
chalkboards, only to find himself lost in a sea of epsilons and sign errors
. As he chased references backwards, he started reading older and older wor
ks, until eventually, he found himself all the way back at the beginning, i
n Leibniz's first formulations of calculus. Back then, before the idea of e
psilons, people had been making do with just the idea of "infinitesimal num
bers". Most sensible mathematicians of Robinson's day would criticize this
as informal and lacking in rigor; and with good reason. Nevertheless, this
proved to be the one paper Robinson could read, and so here he began his wo
rk.\nSome years later, Robinson had perfected an analyst-proof formulation
of calculus. Unfortunately for him, it turned out better than standard calc
ulus in many ways, and some of the open minded analysts wanted to actually
learn this horrible system he had derived, and they made him spend the rest
of his career explaining it to them.\nThese days, the framework he built i
s called "non-standard analysis". In my talk, I plan to introduce you to th
is wonderful world where definitions make intuitive sense without 5 layers
of quantifiers, and all the proofs feel like you're definitely cheating. My
agenda will be to define the hyperreals properly, then spend the remaining
5 minutes spewing out definitions, and perhaps actually proving a theorem.
\n
X-ALT-DESC;FMTTYPE=text/html:Abstract: I'd like to share a definitely true story. Once upon a t
ime, there lived a logician named Abraham Robinson. Overall, he had a happy
life, but there was one problem: the analysts of his department were const
antly being friendly and telling him about their research. This led to far
too many conversations involving the letter epsilon for Robinson to live a
happy and successful life. Then, one day, Robinson had an idea. "What if I
reengineered all of real analysis so that it required a whole course in mod
el theory to understand even the most basic definitions? Surely," he though
t, "that would make the analysts stop trying to talk to me".

And with
that, he set to work. To succeed with his plan, he knew he would first hav
e to learn how to do analysis. For months, he read paper after paper, and f
illed entire chalkboards, only to find himself lost in a sea of epsilons an
d sign errors. As he chased references backwards, he started reading older
and older works, until eventually, he found himself all the way back at the
beginning, in Leibniz's first formulations of calculus. Back then, before
the idea of epsilons, people had been making do with just the idea of "infi
nitesimal numbers". Most sensible mathematicians of Robinson's day would cr
iticize this as informal and lacking in rigor; and with good reason. Nevert
heless, this proved to be the one paper Robinson could read, and so here he
began his work.

Some years later, Robinson had perfected an analyst-
proof formulation of calculus. Unfortunately for him, it turned out better
than standard calculus in many ways, and some of the open minded analysts w
anted to actually learn this horrible system he had derived, and they made
him spend the rest of his career explaining it to them.

These days, t
he framework he built is called "non-standard analysis". In my talk, I plan
to introduce you to this wonderful world where definitions make intuitive
sense without 5 layers of quantifiers, and all the proofs feel like you're
definitely cheating. My agenda will be to define the hyperreals properly, t
hen spend the remaining 5 minutes spewing out definitions, and perhaps actu
ally proving a theorem.

CONTACT:Brian Pinsky - Rutgers University
DTSTAMP:20230326T053448Z
DTSTART;TZID=America/New_York:20181109T134000
DTEND;TZID=America/New_York:20181109T144000
SEQUENCE:0
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