This site aims to

**Rebuild mathematics**with (almost) no prerequisites.-
**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);**Teachers**of mathematics or physics looking for deeper understandings of their subject;- Any people trying to learn science outside the academic system.

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 following advantages:

- 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 meaning.
- 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.

I first made an introduction video on youtube (in 3 parts, total is more than 1 hour):

Also available in text version : Why learn physics by yourself

A shorter version (about 15 min) was done more recently at Ukraine Crisis Media Center where I announced my offer of free physics courses in Ukraine for summer 2016. Full text version and video.

Students are invited to register to this group.

The first texts of mathematics are generally **intended to be
slowly read, respecting the order**.

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
here).

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. First by clicking the G+ button on the main page (using your google+ account). Then if you don't know what more, look here.

from Le Havre, France

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).

I have the following other sites :

- First site in French (with a diversity of subjects): spoirier.lautre.net = sylvainpoirier.fr - English entry page. Includes
- Economic theory : infoliberalism
- A free software project for a global revolution : trust-forum.net - web programmers needed !
- Philosophy site: antispirituality.net (and a smaller one)

For many years I was upset. Here is why. Now at last things seem to be going better in the sense that I found some programmers to start the work but more will be needed.

Contact : trustforum at gmail.com (g+ profile)

(a facebook account not much used...)

Back to entry page, or Part 1 : First foundations of mathematics.