In Mathematics There Are No True Controversies.

I Mean The Word Proof Not In The Sense Of The Lawyers, Who Set Two Half Proofs Equal To A Whole One, But In The Sense Of A Mathematician, Where Half Proof = 0, And It Is Demanded For Proof That Every Doubt Becomes Impossible.

To Praise It Would Amount To Praising Myself. For The Entire Content Of The Work... Coincides Almost Exactly With My Own Meditations Which Have Occupied My Mind For The Past Thirty Or Thirty-five Years.

Sin2 φ Is Odious To Me, Even Though Laplace Made Use Of It; Should It Be Feared That Sin2 φ Might Become Ambiguous, Which Would Perhaps Never Occur, Or At Most Very Rarely When Speaking Of Sin(φ2), Well Then, Let Us Write (sin φ)2, But Not Sin2 φ, Which By Analogy Should Signify Sin (sin φ)

With A Thousand Joys I Would Accept A Nonacademic Job For Which Industriousness, Accuracy, Loyalty, And Such Are Sufficient Without Specialized Knowledge, And Which Would Give A Comfortable Living And Sufficient Leisure, In Order To Sacrifice To My Gods [mathematical Research]. For Example, I Hope To Get The Editting Of The Census, The Birth And Death Lists In Local Districts, Not As A Job, But For My Pleasure And Satisfaction.

The Problem Of Distinguishing Prime Numbers From Composite Numbers And Of Resolving The Latter Into Their Prime Factors Is Known To Be One Of The Most Important And Useful In Arithmetic. It Has Engaged The Industry And Wisdom Of Ancient And Modern Geometers To Such An Extent That It Would Be Superfluous To Discuss The Problem At Length. ... Further, The Dignity Of The Science Itself Seems To Require That Every Possible Means Be Explored For The Solution Of A Problem So Elegant And So Celebrated.