Look at the following beginning of a sequence of rational numbers:

The question is: What value receives B₁? This question was answered in 1840 by two grand masters of the Bernoulli numbers, von Staudt and Clausen, independently. The right solution is not difficult to find, try it. And sure, the prime numbers govern the picture. You don't need to be a rocket scientist to see all this. In fact, you must be a rocket scientist to be able not to see it. Or at least a mathematician who only copies from other work, for example from the Handbook of the American National Institute of Standards. Astounding, even unbelievable is what an absurd answer you can find there. Believe it or not they say B₁ = −1 + 1/2. No explanation given.

Hear us, O Mathematicians of the World!

 B₁ = 1 - 1/2

The first chorus, from left: Unbelievable! We never thought this could be true!
The second chorus, from right: Don't believe this. This will only create confusion! ... the greatest confusion of the century!

But we say: Take the Bernoulli function as your advisor!

The Bernoulli numbers are the children of the zeta function ...

And G. H. Hardy adds: "The mathematician's patterns, like the painter's or the poet's must be beautiful; the ideas like the colours or the words, must fit together in a harmonious way."

Jakob Bernoulli says:

The Bernoulli Rebellion
   -- 'Invito patre..'

But No, No, Ten Thousand Times No!

These are the words of D.E. Knuth in his famous paper Two Notes on Notation by which he objects to the opinion that 0⁰ is to be left undefined. And these also shall be our words when we battle the absurd B₁ = -1/2.

Junk the chapter on the Bernoulli numbers in the Handbook of Mathematical Functions. And write an email to Karl Dilcher, the editor of the Bernoulli chapter in the Digital Library of Mathematical Functions in the (probable) case that he will carry on this unhappy tradition in this online library and object! [dlmf_feedback@nist.gov].

Tell him what he is actually supposed to know: That the definition based on the zeta function will win in the long run over the ad-hoc definition of the Handbook and all he can achieve by not using the natural definition is to prolong the pains of confusion.

Invite Karl Dilcher to the Wikipedia article on Bernoullli numbers where he can read, among other things, that:

• The important connection with Stirling polynomials gives B₁=σ_n(1)=1/2.
• The natural connection with the Stirling set numbers gives B₁ = 1/2.
• The beautiful connection with the Worpitzky numbers gives B₁ = 1/2.
• The connection with the Stirling cycle number gives B₁ = 1/2.
• The Akiyama-Tanigawa algorithm gives B₁ = 1/2.
• The important connection with the Eulerian numbers "are valid for n ≥ 0 if B₁ is set to 1/2. If B₁ is set to −1/2 they are valid only for n ≥ 1 and n ≥ 2 respectively."

No, the mathematical community should not allow the authorities and Institutes of Standards to get away with this balderdash to distort the sign of B₁. And π (pi) does not equal 3.2, even if enforced by pi-bill ...

Let us not wait longer!

The Euler-Riemann reflection formula of the zeta function belongs to the crown jewels of mathematics. Let us no longer allow the barbarism to violate this equation by giving B₁ the value -1/2. And also let us honor the great Jakob Bernoulli by simply no longer fasten on him numbers which he has never written. Is it not conceivable that he had recognized the connection with the zeta function, at least on some intuitive level, whereas some of his followers were not in the position to see this?

Join us! We believe in the unity of mathematics!

Sansei Takekazu-Kowa Seki, Jakob Bernoulli, von Staudt and Clausen, Worpitzky, Hasse, Neukirch, Woon, Conway and Guy, ...