In 1895, at the age of sixteen, Einstein sat the entrance examinations for the Swiss Federal Polytechnic in Zürich (later the Eidgenössische Technische Hochschule ETH). He obtained the best results in the mathematical and natural science subjects, but in the linguistic and historical subjects his achievements were unsatisfactory. His overall result was rated as insufficient. On the advice of the Principal of the Polytechnic, he attended the Aargau Cantonal School in Aarau, Switzerland, in 1895–96 to complete his secondary schooling.
In September 1896, he passed the Swiss Matura with mostly good grades, including a top grade of 6 in physics and mathematical subjects, on a scale of 1-6, and, though only seventeen, enrolled in the four-year mathematics and physics teaching diploma program at the Zürich Polytechnic. The Swiss A-levels are called “Matur”; it corresponds to the German “Abitur”. Furthermore it has to be noticed that the assessment scale for school performance (school grades) in Germany and in Switzerland differs from each other, i.e. the grade 1 (excellent) in Germany equals grade 6 in Switzerland; the grade 2 (good) equals grade 5, etc.
In 1935, a rabbi in Princeton showed him a clipping of the Ripley’s column with the headline “Greatest living mathematician failed in mathematics”. Einstein laughed. “I never failed in mathematics”, he replied, correctly. “Before I was fifteen I had mastered differential and integral calculus”. In primary school, he was at the top of his class and “far above the school requirements” in math. By age 12, his sister recalled, “he already had a predilection for solving complicated problems in applied arithmetic”, and he decided to see if he could jump ahead by learning geometry and algebra on his own. His parents bought him the textbooks in advance so that he could master them over summer vacation. Not only did he learn the proofs in the books, he also tackled the new theories by trying to prove them on his own. He even came up on his own with a way to prove the Pythagorean theory.
The matriculation certificate translated in English:
The Council of Education of the Canton of Aargau hereby certifies:
Mr. Albert Einstein of Ulm, born 14 March 1879, attended the Cantonal School of Aargau, namely, the IIIrd and IVth class of the Commercial School.
On taking the written and oral exam of maturity on 18, 19 and 21 September, and on 30 September 1896, he received the following grades:
1. German language and literature: 5
2. French language and literature: 3
3. English language and literature: —
4. Italian language and literature: 5
5. History: 6
6. Geography: 4
7. Algebra: 6
8. Geometry (planimetry, trigonometry, stereometry and analytical geometry): 6
9. Descriptive geometry: 6
10. Physics: 6
11. Chemistry: 5
12. Natural history: 5
13. In drawing: 4
14. In technical drawing: 4
Based thereon he is issued the certificate of maturity.
Aarau, 3 October 1896.
(The President / The Secretary)