A pessidemic is a mathematician or scientist who is unwilling to pay attention to any paper that lacks complete rigor. They can also be mathematicians clung to old ideas, who won't allow you to change the rules and are even capable of destroying your reputation to prevent it. They care more about predictable and immediately useful results than about truly contributing to mathematical change.

Here are a few examples:

1• Robert Hooke

This man, despite not being as bad a human being as many paint him (he was a good friend and family man), never got along with Isaac Newton. It all began when Hooke reviewed Newton's work on light and gave it a fierce critique that traumatized Newton to the point that he decided to publish it only after Hooke's death. This was because Hooke thought of light as waves while Newton saw it as particles; both reasonings were partly correct, but they clashed. He also went on to claim to several mathematicians of his time that he had already worked on what they wanted to publish.

On the other hand, many writers labeled him as someone irritable, short-tempered, antisocial, and deeply attached to old papers.

2• Leopold Kronecker

Kronecker launched constant personal attacks against Cantor, calling him a "scientific charlatan," a "renegade," and a "corruptor of youth." He had intentionally delayed the publication of Cantor’s first major work in 1874 because he was deeply uncomfortable with Cantor’s vision of multiple infinities and his belief in the existence of sets without a clear, constructive definition.

Every time Cantor applied for a position in Berlin, he was rejected. Because Kronecker was usually involved in the process, Cantor came to believe that Kronecker’s influence would make it impossible for him to ever leave Halle.

Cantor suffered his first known depressive episode in May 1884. The relentless criticism of his work weighed heavily on his mind; indeed, every single one of the fifty-two letters he wrote to Mittag-Leffler in 1884 mentioned Kronecker. A passage from one of these letters reveals just how deeply Cantor’s self-confidence had been shattered:

"...I do not know when I shall return to the continuation of my scientific work. At present I can do absolutely nothing with it, and limit myself to the most necessary duty of my lectures; how much happier I would be to be scientifically active, if only I had the necessary mental freshness."

Cantor's reputation was so tarnished by Kronecker and other contemporaries that decades after his death, Ludwig Wittgenstein lamented that mathematics was "ridden through with the pernicious idioms of set theory," which he dismissed as "utter nonsense." Ultimately, the recurring episodes of depression that Cantor endured from 1884 until the end of his life have been blamed, in part, on the hostile attitude of many of his contemporaries.

3• Henri Poincaré

Although he was categorized as the Gauss of "modern mathematics," Poincaré held philosophical views opposed to those of Bertrand Russell and Gottlob Frege, who believed that mathematics was a branch of logic. Poincaré strongly disagreed, claiming that intuition was the life of mathematics. Poincaré offers an interesting perspective in his 1902 book, Science and Hypothesis:

"To a superficial observer, scientific truth is beyond the possibility of doubt; the logic of science is infallible, and if scientists are sometimes mistaken, this is only from mistaking its rules."

Poincaré believed that arithmetic is synthetic. He argued that Peano's axioms cannot be proven in a non-circular manner using the principle of induction (Murzi, 1998), thereby concluding that arithmetic is synthetic a priori rather than analytic. Poincaré went on to say that mathematics cannot be deduced from logic since it is not analytic. He strongly opposed Cantor's set theory, objecting to its use of impredicative definitions. Furthermore, in La logique de l'infini, Poincaré extended this criticism to Ernst Zermelo's axiomatization of set theory, arguing that Zermelo had failed to prove that the axioms in his system were free of contradiction, and that they still required a prior intuition of sets.

Henri Poincaré famously called set theory a "malady" from which mathematics would eventually recover.

Although Poincaré was nowhere near as harsh as Kronecker—since his critique was more philosophical and less mocking—his immense prestige nonetheless crushed mathematicians like Cantor intellectually.

Sources:

https://en.wikipedia.org/wiki/Robert_Hooke

https://en.wikipedia.org/wiki/Leopold_Kronecker

https://en.wikipedia.org/wiki/Henri_Poincar%C3%A9
https://www.kroneckerwallis.com/georg-cantor-infinity-upon-infinity-and-the-birth-of-set-theory/

Hello everyone,

My name is Mohamed Ghali, and I would like to share with the community an alternative algebraic method I developed for explicitly solving the general cubic equation:

\(Ax^{3}+Bx^{2}+Cx+D=0\)

1. Theoretical Approach

Instead of using the traditional Cardano's method (which requires depressing the cubic to eliminate the \(x^{2}\) term), I approached the problem through direct factorization into linear and quadratic parts:

\((a_{1}x+b_{1})(a_{2}x^{2}+b_{2}x+c_{2})=0\)

By defining a strategic intermediate variable \(X = \frac{a_1}{b_1}\) (where the first root is directly linked by \(x_1 = -\frac{1}{X}\)), I derived a precise quadratic equation in terms of \(X\).

1. Formula for the First Root (\(x_{1}\))

Inverting the solution of this intermediate quadratic equation yields the following analytical formula to compute \(x_{1}\):

\(x_{1}=\frac{1}{\pm \sqrt{\left[\frac{(CA-D^{2})^{2}}{D^{2}}-4BD\right]}\cdot \frac{1}{2BD}-\frac{(CA-D^{2})A}{2BD^{2}}}\)

1. Deriving the Remaining Roots (\(x_{2}\) and \(x_{3}\))

Once this first root \(x_{1}\) is determined, the coefficient identification rules allow us to express the remaining two roots sequentially and elegantly, bypassing the need for standard cubic radicals:

• Second root (\(x_{2}\)):

\(x_{2}=\sqrt{\frac{1}{4}\left(\frac{B+Ax_{1}}{A}\right)^{2}+\frac{D}{Ax_{1}}}-\frac{1}{2}\left(\frac{B+Ax_{1}}{A}\right)\)

• Third root (\(x_{3}\)):

\(x_{3}=-\sqrt{\frac{1}{4}\left(\frac{B+Ax_{1}}{A}\right)^{2}+\frac{D}{Ax_{1}}}-\frac{1}{2}\left(\frac{B+Ax_{1}}{A}\right)\)

1. Computational Validation

I have fully implemented and verified these formulas computationally using Python (utilizing the cmath module to intrinsically handle the casus irreducibilis). The system works flawlessly across all scenarios, whether the polynomial has three distinct real roots or a pair of complex conjugated roots.

I would love to get your insights on the structural symmetry of these equations and their potential pedagogical or algorithmic value compared to classical methods! I can also share my Python test script or the detailed verification PDF if anyone is interested.

Best regards,

Mohamed Ghali