We just moved house after 57 years, and with a child-like delight I discovered my 1963 copy of the 1960 edition of a seminal 1929 text which I had often grieved over as irretrievably lost:

‘Foundations of Analysis’ by Professor Edmund Landau.

Professor Landau begins his slim monograph with a charming ‘Preface for the student’, where he cautions:

“Please don’t read the preface to the teacher. … Please forget everything you have learned in school; for you haven’t learned it. Please keep in mind at all times the corresponding portions of your school curriculum; for you haven’t actually forgotten them. … my daughters have been studying (chemistry) for several semesters, think they have learnt differential and integral calculus at school, and yet even today don’t know why ‘x.y = y.x’ is true.”

I vividly remember the moment that I read those lines as one of a profound instinctive insight:

I could either commit myself to acquiring understanding of what I think I know, or commit myself to protecting my understanding of what I think I know. I could not do justice to both commitments.

Professor Landau begins his ‘Preface for the teacher’ as charmingly:

“This little book is a concession to those of my colleagues (unfortunately in the majority) who do not share my point of view …”

He apparently held that the teaching of a rigorous and complete explanation of the subject matter, and methods of proof, of elementary mathematics at the entry level in universities was necessary to the laying of a stable foundation for the learning of any scientific discipline that expressed itself mathematically.

For me there is another intriguing titbit in his preface for the teacher, where he notes in passing:

“I do not, to be sure, prove the consistency of the five Peano Axioms (because that can not be done), …”

Intriguing, because that is essentially the proof in a paper that I presented at the AISB/IACAP Turing 2012 Conference in Birmingham last July!

For a more fitting tribute to—and fascinating background perspectives of the life amidst troubled times of—this uncompromising teacher and disciple of logical and mathematical rigour, see:

Edmund Landau: The Master Rigorist

Zionist Internationalism through Number Theory: Edmund Landau at the Opening of the Hebrew University in 1925

Mathematics at Göttingen under the Nazis

Bhupinder Singh Anand

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