His first schooling was at Pallais's school, run by the music master from the cathedral. There Josephstudied Latin and French and showed great promise. He proceeded in 1780 to the École Royale Militaire of Auxerre where at first he showed talents for literature but very soon, by the age of thirteen, mathematics became his real interest. By the age of 14 he had completed a study of the six volumes of Bézout's Cours de mathématiques. In 1783 he received the first prize for his study of Bossut'sMécanique en général.
In 1787 Fourier decided to train for the priesthood and entered the Benedictine abbey of St Benoit-sur-Loire. His interest in mathematics continued, however, and he corresponded with C L Bonard, the professor of mathematics at Auxerre. Fourier was unsure if he was making the right decision in training for the priesthood. He submitted a paper on algebra to Montucla in Paris and hisletters to Bonard suggest that he really wanted to make a major impact in mathematics
Fourier did not take his religious vows. Having left St Benoit in 1789, he visited Paris and read a paper on algebraic equations at the Académie Royale des Sciences. In 1790 he became a teacher at the Benedictine college, École Royale Militaire of Auxerre, where he had studied. Up until this time there had beena conflict inside Fourier about whether he should follow a religious life or one of mathematical research. However in 1793 a third element was added to this conflict when he became involved in politics and joined the local Revolutionary Committee. As he wrote:-
As the natural ideas of equality developed it was possible to conceive the sublime hope of establishing among us a free governmentexempt from kings and priests, and to free from this double yoke the long-usurped soil of Europe. I readily became enamoured of this cause, in my opinion the greatest and most beautiful which any nation has ever undertaken.
Certainly Fourier was unhappy about the Terror which resulted from the French Revolution and he attempted to resign from the committee. However this proved impossible and Fourierwas now firmly entangled with the Revolution and unable to withdraw. The revolution was a complicated affair with many factions, with broadly similar aims, violently opposed to each other. Fourier defended members of one faction while in Orléans. A letter describing events relates:-
Citizen Fourier, a young man full of intelligence, eloquence and zeal, was sent to Loiret. ... It seems thatFourier ... got up on certain popular platforms. He can talk very well and if he put forward the views of the Society of Auxerre he has done nothing blameworthy...
This incident was to have serious consequences but after it Fourier returned to Auxerre and continued to work on the revolutionary committee and continued to teach at the College. In July 1794 he was arrested, the charges relating to theOrléans incident, and he was imprisoned. Fourier feared the he would go to the guillotine but, after Robespierre himself went to the guillotine, political changes resulted in Fourier being freed.
Later in 1794 Fourier was nominated to study at the École Normale in Paris. This institution had been set up for training teachers and it was intended to serve as a model for other teacher-trainingschools. The school opened in January 1795 and Fourier was certainly the most able of the pupils whose abilities ranged widely. He was taught by Lagrange, who Fourier described as
the first among European men of science,
and also by Laplace, who Fourier rated less highly, and by Monge who Fourier described as
having a loud voice and is active, ingenious and very learned.