Notes

Recapitulation theory

The theory of recapitulation, also called the biogenetic law or embryological parallelism—often expressed using Ernst Haeckel‘s phrase “ontogeny recapitulates phylogeny“—is a historical hypothesis that the development of the embryo of an animal, from fertilization to gestation or hatching (ontogeny), goes through stages resembling or representing successive adult stages in the evolution of the animal’s remote ancestors (phylogeny). It was formulated in the 1820s by Étienne Serres based on the work of Johann Friedrich Meckel, after whom it is also known as Meckel–Serres law.

Since embryos also evolve in different ways, the shortcomings of the theory had been recognized by the early 20th century, and it had been relegated to “biological mythology” by the mid-20th century.

Analogies to recapitulation theory have been formulated in other fields, including cognitive development and music criticism.

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

Recapitulation theory was last modified: January 30th, 2022 by Jovan Stosic

Genius (mathematics software)

Genius (also known as the Genius Math Tool) is a free open-source numerical computingenvironment and programming language, similar in some aspects to MATLAB, GNU Octave, Mathematica and Maple. Genius is aimed at mathematical experimentation rather than computationally intensive tasks. It is also very useful as just a calculator. The programming language is called GEL and aims to have a mathematically friendly syntax. The software comes with a command-line interface and a GUI, which uses the GTK+ libraries. The graphical version supports both 2D and 3D plotting. The graphical version includes a set of tutorials originally aimed at in class demonstrations.

https://en.wikipedia.org/wiki/Genius_(mathematics_software)

Genius (mathematics software) was last modified: October 24th, 2020 by Jovan Stosic

Évariste Galois

Évariste Galois (/ɡælˈwɑː/; French: [evaʁist ɡalwa]; 25 October 1811 – 31 May 1832) was a French mathematician and political activist. While still in his teens, he was able to determine a necessary and sufficient condition for a polynomial to be solvable by radicals, thereby solving a problem standing for 350 years. His work laid the foundations for Galois theory and group theory, two major branches of abstract algebra, and the subfield of Galois connections. He died at age 20 from wounds suffered in a duel.

https://en.wikipedia.org/wiki/%C3%89variste_Galois

Évariste Galois was last modified: February 4th, 2020 by Jovan Stosic

Russell’s paradox

In the foundations of mathematics, Russell’s paradox (also known as Russell’s antinomy), discovered by Bertrand Russell in 1901, showed that some attempted formalizations of the naïve set theory created by Georg Cantor led to a contradiction. The same paradox had been discovered in 1899 by Ernst Zermelo but he did not publish the idea, which remained known only to David Hilbert, Edmund Husserl, and other members of the University of Göttingen. At the end of the 1890s Cantor himself had already realized that his definition would lead to a contradiction, which he told Hilbert and Richard Dedekind by letter.

According to naive set theory, any definable collection is a set. Let R be the set of all sets that are not members of themselves. If R is not a member of itself, then its definition dictates that it must contain itself, and if it contains itself, then it contradicts its own definition as the set of all sets that are not members of themselves.

https://en.wikipedia.org/wiki/Russell%27s_paradox

Russell’s paradox was last modified: February 4th, 2020 by Jovan Stosic

Principia Mathematica

The Principia Mathematica (often abbreviated PM) is a three-volume work on the foundations of mathematics written by Alfred North Whitehead and Bertrand Russell and published in 1910, 1912, and 1913. In 1925–27, it appeared in a second edition with an important Introduction to the Second Edition, an Appendix A that replaced ✸9 and all-new Appendix B and Appendix C. PM is not to be confused with Russell’s 1903 The Principles of Mathematics. PM was originally conceived as a sequel volume to Russell’s 1903 Principles, but as PM states, this became an unworkable suggestion for practical and philosophical reasons: “The present work was originally intended by us to be comprised in a second volume of Principles of Mathematics… But as we advanced, it became increasingly evident that the subject is a very much larger one than we had supposed; moreover on many fundamental questions which had been left obscure and doubtful in the former work, we have now arrived at what we believe to be satisfactory solutions.”

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

Principia Mathematica was last modified: February 4th, 2020 by Jovan Stosic