Rebuild mathematics with (almost) no
Introduce the fundamental theories of physics
(Relativity and quantum physics)
It may be situated in between undergraduate and graduate
levels: by its way of rebuilding everything from the start,
it aims to fill the role of (a subset in progress of) an
undergraduate curriculum (1st university year), but the difficulty
level with the care for powerful methods and deep and complete
explanations, is comparable to graduate level (3rd year). Also, it
takes some of its inspiration and concepts from existing
graduate-level mathematics (in a simplified form).
It is thus mainly targeted at
Clever undergraduate students with genuine interests in
mathematics or physics (rather than focused on preparing for
exams): my precise ambition is to make this the best course of
mathematics for geniuses (much better than Harvard, MIT or whatever);
Teachers of mathematics or physics looking for deeper
understandings of their subject;
Any people trying to learn science outside the academic
It does not aim (nor exclude) to bring new ideas, results or
theories (with few exceptions : the set generation principle;
the page "Time in set theory" - interpretations
of quantum physics), but focuses on developing new optimized paths to
already known fundamental theories of mathematics and physics :
putting things in the right order, to make high concepts look as
clear, simple and fast to learn as possible. It combines the
To be as rigorous as possible (everything is
explained, all what is provable is proven from the beginning)
To give powerful and general concepts and tools, avoiding
any unnecessary lengths. Rigor will not dilute or
obscure the meaning. Proofs are usually very short. Pages are
very dense, with many ideas per page to explain everything. The
right formalism will express the highest concentration of
Original (cleaned up and restructured)
approaches are given to most subjects
Emphasis is placed on intuition, deep and
"philosophical" explanations, the main foundational
concepts and paradoxes, the mathematical world.
The set theory formalism presented here differs from the traditional
ZF system, but aims to more directly fit the common use and
notations of mathematics (without artificial encoding and
abbreviation systems), and be cleaner on foundation and meaning.
I wrote this long introduction to the contents of this site and relations
between logic and physics, for what was first supposed to be the news bulletin of the
Iranian Association for Logic, but finally was a book "Logic around the world".
Why leave the system
I first made an introduction video on youtube (in 3 parts, total is more than 1 hour):
I wrote a draft plan of couses I might make of
initiation to non-euclidean
geometries, special and general relativity, tensors and/or quantum
physics), but usually did not find the context (gathering students) to actually do something
even for free (because everybody is much too busy wasting their time in the f**g system to ever think about doing
something more meaningful). I do not consider going to America nor Africa, but elsewhere if you would be
interested or you know places where such students can be found, you can please write me, so if
a group can be made I might consider to come.
Students might eventually register to this
group but it is always better to write me email anyway.
For a long time I wished to offer such free teaching, but could not find a chance to do it anywhere; even
organizers of non-institutional science teaching are sticked to
old methods; here is an anecdote about it.
Thanks for the link added by the author of this
page, but I have offered to join and present my
approach there and they refused... I wrote the below message in
I see that your program for this summer includes some
introductions to Special and General relativity following the
usual old unclarified approach. I had offered to come and present
my approach to these subjects, but got the organizer's reply that
you prefer to not invite me because of the inconvenience of making
it in English. (...) I doubt that considering all aspects, you
will make things any clearer in your way (...). Indeed the very
title you give for that course, insists that things will appear
paradoxical. That is, things will seem strange and hard to figure
out. Indeed, the usual approach that you follow (because, all
teachers follow each other as I explained in my video),
has the inconvenience of making things appear obscure and more
complicated than necessary, somehow feeling illogical (of course
there is no contradiction but I speak about the impression it
gives). My own view, on the other hand, focuses on the aspects of
how things are simple and coherent according to the physical
world's internal logic, and thus better understandable. (...) I
will be available to independently offer my teaching (for free), I
just do not know how to organize this (time and place). And
without selecting students, so anyone interested can write me
privately and we'll see if how we can organize.
which was deleted, with the reaction that the author did not
consider his approach as an "old and thoughtless repetition".. well,
did I need to specify that I meant "old and thoughtless repetition"
in a relative manner.... that is, lacking the harder work that would
be needed by the teacher to make it more clearly and easily
understandable for students.
The first texts of mathematics are generally intended to be
slowly read, respecting the order.
Writing history and notes
A first version was written in French,
then partially corrected and translated to make the start of this
site, which then continued directly in English on other subjects.
Now over 50 pages ready from the start on mathematics (entirely
self-contained), plus more sections of maths and physics in bulk
or draft; still incomplete (some French pages should be corrected
before translation, and others are in plans to be directly written
I cannot ensure the perfection of the English vocabulary as I'm
not native English speaker. Moreover I need to name some concepts
that have not always a standard name in the mathematical
literature; I know that my use of "functor" differs from (is more
general than) its standard meaning in category theory, and thus
breaks the standard convention, but I do not know any better word
for what I need.
As this site is relatively recent, it is not well-known yet. So if
you see it worth, please help spreading the word about it (look here for how).
About the author
Sylvain Poirier (one of maybe around 200 homonyms worldwide according to facebook search)
From Le Havre, France (and probably the one one from there) PhD in Mathematics
(but I did not like the academic system; I learnt more
mathematics and physics on my own since teenage, including General
Relativity at 16).
(Other sites on the web with the same are from homonyms)
For many years I was upset. Here is why. Now
things seem to be going a little better in the sense that I found a programmer to start
the work but more will be needed.
Email : trustforum at gmail.com
A facebook account I sometimes
losed access to just because of their "security procedures"...
and where I give some news, though I keep the main interesting long-term content in my web sites