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Plants cannot continue the natural ripening or aging process.

ⵓⵔ ⵢⴰⴷ ⵏⵏⵉⵏ ⵉⵎⵖⴰⵢⵏ ⴰⴷ ⵙⵙⵓⴷⵓⵏ ⴳ ⵜⵉⵅⵅⵉⵜⵔⵜ ⵜⴰⵖⴰⵔⴰⵏⵜ ⵏⵙⵏ ⵓⵍⴰ ⴳ ⵜⴰⵡⵙⵔⵜ ⵏⵙⵏ.

The specialty of processing food by ionizing radiation is the fact, that the energy density per atomic transition is very high, it can cleave molecules and induce ionization (hence the name) which cannot be achieved by mere heating.

ⵜⴰⵥⵍⴰⵢⵜ ⵏ ⵓⵙⵎⴽⵍ ⵏ ⵡⵓⵜⵛⵉ ⵙ ⵜⵖⴰⵔⴰⵙⵜ ⵏ ⵓⵥⵏⵥⵕ ⴰⵢⵢⵓⵏ, ⵉⴳⴰ ⵙ ⵜⵉⴷⵜ ⵜⴰⵏⵥⵥⵉ ⵏ ⵜⵣⵎⵔⵜ ⵉ ⴽⴰ ⵉⴳⴰⵜ ⴰⵎⵓⵜⵜⵢ ⴰⴱⵍⴽⵉⵎ ⵢⴰⵜⵜⵓⵢⵏ ⴽⵉⴳⴰⵏ, ⴷ ⵉⵖⵢ ⴰⴷ ⵜⴱⴱⵉ ⵜⵉⴼⵓⵍⵉⵏ ⴷ ⵓⵏⵣⴰⵍ ⵏ ⴰⵢⵢⵓⵏ ( ⵙⴳ ⴷⴰ ⵉⵙⵎ ), ⵏⵏⴰ ⵓⵔ ⵉⵏⵏⵉⵏ ⴰⴷ ⵢⵉⵍⵉ ⵙ ⵓⵏⵏⵔⵖⵉ.

However, the use of the term, cold pasteurization, to describe irradiated foods is controversial, because pasteurization and irradiation are fundamentally different processes, although the intended end results can in some cases be similar.

ⵡⴰⵅⵅⴰ ⵀⴰⴽⴽⴰⴽ, ⴰⵙⵙⵎⵔⵙ ⵏ ⵜⴳⵓⵔⵉ “ ⴰⵙⵙⵃⵎⵓ ⴰⵏⴽⵔⴰⵎ “ ⵎⴰⵔ ⴰⴷ ⵏⵙⵏⵓⵎⵎⵍ ⵏ ⵡⵓⵜⵛⵉⵜⵏ ⵉⵜⵜⵓⵙⵏⵥⵕⵏ ⵖⵉⴼⵙ ⵜⴰⵇⵇⵓⵔⵜ, ⴰⵛⴽⵓ ⴰⵙⵙⵃⵎⵓ ⵓⵙⵙⵏⵥⵕ ⴳⴰⵏ ⵙⵏⴰⵜ ⵜⵎⴳⴳⵉⵜⵉⵏ ⵉⵎⵣⴰⵔⴰⵢⵏ ⴳ ⵓⴳⵏⵙ, ⵡⴰⵅⵅⴰ ⵜⵉⵢⴰⴼⵓⵜⵉⵏ ⵜⵉⵎⴳⴳⵓⵔⴰ ⵖⵉⵏⵜ ⴰⴷ ⵉⴽⵙⵉⵍⵏⵜ ⴳ ⵉⵜⵙⵏ ⵡⴰⴷⴷⴰⴷⵏ.

Marie Curie died from aplastic anemia which resulted from her high levels of exposure.

ⵜⵎⵎⵓⵜ ⵎⴰⵔⵉ ⴽⵓⵕⵉ ⵙ ⵥⵥⵍⴹ ⵏ ⵉⴷⴰⵎⵎⵏ ⴰⵙ ⵜⴳⴰ ⵍⵎⵉⴽⴰ, ⴰⵛⴽⵓ ⵉⴳⵓⵍⴰⵏ ⴷⵉⴽⵙ ⵜⵉⵙⴽⴼⴰⵍ ⵎⵇⵇⵓⵕⵏ.

Approximately half of the deaths from Hiroshima and Nagasaki died two to five years afterward from radiation exposure.

ⵉⵎⵎⵓⵜ ⵓⵣⴳⵏ ⵏ ⵡⵉⵏⵏⴰ ⵉⵎⵎⵓⵜⵏ ⴳ ⵀⵉⵔⵓⵛⵉⵎⴰ ⴷ ⵏⴰⴳⴰⵣⴰⴽⵉ ⴹⴰⵕⵜ ⵙⵉⵏ ⵉⵙⴳⴳⵯⴰⵙⵏ ⴰⵔ ⵙⵎⵎⵓⵙ ⴰⵢⴷⵜⵏ ⵉⵏⵏⴰⵍ ⵓⵎⵥⵏⵥⵕ.

A nuclear meltdown refers to the more serious hazard of releasing nuclear material into the surrounding environment.

ⵉⵎⵎⴰⵍ ⵓⵔⴷⴰⵍ ⵏ ⵓⵖⵢⴰⵢ ⵉⵎⵉⵣⵉ ⵉⵅⵅⴰⵏ ⴽⵉⴳⴰⵏ ⵉⴳⴰⵏ ⴷ ⴰⵏⵏⴼⵛⵓ ⵏ ⵜⴰⵏⴳⴰⵡⵉⵏ ⵏ ⵓⵖⵢⴰⵢ ⴳ ⵜⵡⵏⵏⴰⴹⵜ ⵉⵏⵎⴰⵍⴰⵏ.

Military reactors that experienced similar accidents were Windscale in the United Kingdom and SL-1 in the United States.

ⴰⵏⵎⴰⴳⴳⵓ ⴰⵙⵔⴷⴰⵙ ⵏⵏⴰ ⵖⴼ ⴽⴽⴰⵏ ⵉⵏⴳⴰⵙⵏ ⴰⵎ ⵡⵉ; ⵡⵉⵏⴷⵙⴽⴰⵍ ⴳ ⵜⴳⵍⴷⵉⵜ ⵜⴰⵎⴰⵙⵙⴰⵖⵜ,ⴷ ⵙⵍ-1 ⴳ ⵜⵎⴰⵥⵍⴰⵢⵜ ⵜⴰⵎⴰⵙⵙⴰⵖⵜ.

Another topic of transhumanist research is how to protect humanity against existential risks, such as nuclear war or asteroid collision.

ⵢⴰⵏ ⵓⵔⵣⵣⵓ ⵏⵏⵉⴷⵏ ⴹⴰⵕⵜ ⵜⴼⵓⴳⵏⴰ, ⵎⴰⵎⴽ ⵙ ⵏⵔⴰ ⴰⴷ ⵏⴳ ⴰⴼⵔⴰⴳ ⵉ ⵜⴼⵓⴳⵏⴰ ⴳ ⵉⵎⵉⵣⵉⵜⵏ ⴰⴷ ⵉⵍⵍⴰⵏ,ⵣⵓⵏⴷ ⵉⵎⵏⵖⵉ ⴰⵖⵢⴰⵢ ⴷ ⵓⵏⴳⴰⵙ ⵏ ⵜⵣⵡⵉⵏⵏⵉⵜⵉⵏ.

The assertion would lay the intellectual groundwork for the British philosopher Max More to begin articulating the principles of transhumanism as a futurist philosophy in 1990, and organizing in California a school of thought that has since grown into the worldwide transhumanist movement.

ⵇⴰⴷ ⵉⵙⵔⵙ ⵓⵙⴷⴷⵉ ⴰⴷ ⵜⴰⵙⵉⵍⴰ ⵏ ⵓⵙⵡⵉⵏⴳⵎ ⵏ ⵓⴼⴰⵢⵍⴰⵙⵓⴼ ⴰⴱⵔⵉⵟⴰⵏⵉ ⵎⴰⴽⵙ ⵎⵓⵔ, ⵎⴰⵔ ⴰⴷ ⵉⵙⵙⵏⵜⵉ ⴰⵙⵙⴼⵔⵓ ⵏ ⵉⵎⵏⵣⴰⵢⵏ ⵏ ⴹⴰⵕⵜ ⵜⴼⵓⴳⵏⴰ ⵉⴳⴰⵏ ⵜⴰⴼⵍⵙⴰⴼⵜ ⵏ ⵉⵎⴰⵍ 1990, ⴷ ⵓⵙⵙⵓⴷⵙ ⵏ ⵜⵉⵏⵎⵍ ⵏ ⵓⵙⵡⵉⵏⴳⵎ ⴳ ⴽⴰⵍⵉⴼⵓⵕⵏⵢⴰ, ⵜⵜⵓⵎⵔⵏⴰⵡ ⵙⴳ ⵜⵉⵣⵉ ⵏⵏⴰⵖ ⴰⴳ ⵜⴳⴰ ⴰⵎⵓⵙⵙⵓ ⵏ ⴹⴰⵕⵜ ⵜⴼⵓⴳⵏⴰ ⵜⴰⴳⵔⴰⵖⵍⴰⵏⵜ.

In the Discourse, Descartes envisioned a new kind of medicine that could grant both physical immortality and stronger minds.

ⴳ ⵓⵡⵏⵏⵉ, ⵉⴽⴰ ⴷⵉⴽⴰⵔⵜ ⵢⴰⵜ ⵜⵡⴰⵍⵉⵜ ⵜⴰⵎⴰⵢⵏⵓⵜ ⵏ ⵓⵙⴳⵏⴰⴼ ⵜⵖⵢ ⴰⴷ ⵜⴽ ⵜⴼⴽⴽⴰ ⵜⴰⵎⵖⵍⴰⵍⵜ ⴷ ⵡⴰⵏⵍⵍⵉ ⵉⴷⵓⵙⵏ.

St. Leon may have provided inspiration for his daughter Mary Shelley's novel Frankenstein.

ⵄⵏⵉⵖ ⵉⵙⵙⵏⴽⴷ ⵓⵎⵙⴼⵓⵥⵥⵔ ⵍⵢⵓⵏ ⴰⵙⴰⴳⵯⵎ ⵉⵙⵜⴰⵡⵀⵎⵎⴰⵏ ⵉ ⵡⴰⵍⵍⵙ ⵏ ⴼⵔⴰⵏⴽⵉⵏⵛⵜⴰⵢⵏ ⵉ ⵉⵍⵍⵉⵙ ⵎⴰⵔⵉ ⵛⵉⵍⵉ.

In particular, he was interested in the development of the science of eugenics, ectogenesis (creating and sustaining life in an artificial environment), and the application of genetics to improve human characteristics, such as health and intelligence.

ⵙ ⵓⵥⵍⴰⵢ ⵉⵖⴹⴼ ⵙ ⵓⵣⵣⵉⴳⵣ ⵏ ⵜⵎⴰⵙⵙⴰⵏⵜ ⵏ ⵓⵙⵖⵓⴷⵓ ⵏ ⵡⴰⵔⵔⴰⵡ, ⴷ ⵓⵙⵎⵓⵜⵜⴳ ⴰⴱⵕⵕⴰⵏⵉⵢ ( ⵜⵉⴳⵉ ⵏ ⵜⵓⴷⵔⵜ ⴷ ⵓⵃⵟⵟⵓ ⵏⵏⵙ ⴳ ⵜⵡⵏⵏⴰⴹⵜ ⵜⴰⵎⴳⵓⵔⴰⵏⵜ), ⴷ ⵓⵙⵙⵎⵔⵙ ⵏ ⵜⵎⴰⵙⵙⴰⵏⵜ ⵜⴰⵜⵔⵔⴰⵡⵜ ⵉⵙⵖⵓⴷⵓⵏ ⵎⴰⵢⵥⵍⵉⵏ ⵙ ⴰⴼⴳⴰⵏ, ⵣⵓⵏⴷ ⴰⴷⵡⴰⵙ ⴷ ⵓⴼⵓⵍⵍⵙ.

These ideas have been common transhumanist themes ever since.

ⵜⵉⴷⵖ ⴳⴰⵏⵜ ⵜⵉⵡⵏⴳⵉⵎⵉⵏ ⵏ ⵉⵙⵏⵜⵉⵍⵏ ⵏ ⴹⴰⵕⵜ ⵜⴼⵓⴳⵏⴰ ⵍⵍⴰⵏⵜ ⵙⴳ ⵡⴰⴽⵓⴷ ⵏⵏⴰⵖ.

"In the Material and Man section of the manifesto, Noboru Kawazoe suggests that:After several decades, with the rapid progress of communication technology, every one will have a ""brain wave receiver"" in his ear, which conveys directly and exactly what other people think about him and vice versa."

ⴳ ⵜⴷⴰⵍⴰ ⵏ ⵜⴰⵏⴳⵉⵡⵉⵏ ⴷ ⵓⴼⴳⴰⵏ ⴳ ⵓⵍⵖⵓ, ⵉⵙⵙⵓⵎⵔ ⵏⵓⴱⵓⵔⵓ ⴽⵡⴰⵣⵓ: ⵏ ⵡⵉⵙⵙ ⴷⴰⴷⵖ ⵙ ⵎⵏⵏⴰⵡⵜ ⵏⵉⴳⵍⵍⴰⵢⵏ , ⵙ ⵓⵣⵣⵉⴳⵣ ⵉⵙⵔⴱⵉⵏ ⵏ ⵜⵉⴽⵏⵓⵍⵉⵊⵉⵜ ⵜⴰⵎⵢⴰⵡⴰⴹⵜ, ⴽⵓ ⵉⵊⵊ ⵓⴼⴳⴰⵏ ⵇⴰⴷ ⴷⴰⵔⵙ ⵢⵉⵍⵉ ⵓⵏⵔⵎⴰⵙ ⵏ ⵓⵎⵣⴰⵣ ⵏ ⵓⵏⵍⵍⵉ ⴳ ⵜⵎⵥⵥⵓⵖⵜ ⵏⵏⵙ,ⴰⵙⴷ ⵉⵜⵜⴰⵡⵉⵏ ⵙ ⵡⵓⵙⵔⵉⴷ ⵎⴰⴳ ⵙⵡⵉⵏⴳⵉⵎⵏ ⵡⵉⵢⵢⴰⴹ, ⵢⴰⵡⵢ ⴰⵙⵏ ⵓⵍⴰ ⵏⵉⵜⵏⵉ ⵎⴰⴳ ⵉⵙⵡⵉⵏⴳⵉⵎ.

"In 1966, FM-2030 (formerly F. M. Esfandiary), a futurist who taught ""new concepts of the human"" at The New School, in New York City, began to identify people who adopt technologies, lifestyles and world views transitional to posthumanity as ""transhuman""."

ⴳ ⵓⵙⴳⴳⵯⴰⵙ ⵏ 1966, ⴼⵎ-2030(ⴼⵔⵉⴷⵓⵏ ⵉⵙⴼⴰⵏⴷⵉⵢⴰⵔⵉ) ⵉⴳⴰⵏ ⴰⵎⵓⵙⵏⴰⵡ ⵏ ⵉⵎⴰⵍ “ⵉⵙⵙⵖⵔⴰ ⵉⵔⵎⵎⵓⵙⵏ ⵉⵎⴰⵢⵏⵓⵜⵏ ⵉ ⵓⴼⴳⴰⵏ”, ⴳ ⵜⵉⵏⵎⵍ ⵜⴰⵎⴰⵢⵏⵓⵜ ⴳ ⵏⵢⵓⵢⵓⵔⴽ, ⵉⵙⵜⵉ ⵉⵡⴷⴰⵏ ⵉⵙⴳⵎⴰⵏ ⵜⵉⵇⵏⵉⵢⴰⵜ ⴷ ⵢⵉⴳⴳⵉⵜⵏ ⵏ ⵜⵓⴷⵔⵜ ⴷ ⵜⴰⵏⵏⴰⵢⵉⵏ ⴳ ⵓⵎⴰⴹⴰⵍ ⵉⵜⵎⴰⵜⵜⴰⵢⵏ ⵙ ⴹⴰⵕⵜ ⵜⵉⴼⴼⵓⴳⵏⴰ, ⵏⵏⴰ ⵉⵏⵏⴰⵏ ⴰⴷ ⵉⴳ ⵉⵣⵔⵔⵓⵢⵏ ⵖⴼ ⵎⴷⴷⵏ.

FM-2030 and Vita-More soon began holding gatherings for transhumanists in Los Angeles, which included students from FM-2030's courses and audiences from Vita-More's artistic productions.

ⵉⵙⵙⵏⵜⵉ ⴼⵎ-2030 ⴷ ⴼⵉⵜⴰ ⵎⵓⵔ ⵉⴳⵔⴰⵡⵏ ⵏ ⵉⵎⵓⵙⵏⴰⵡⵏ ⵏ ⴹⴰⵕⵜ ⵜⵉⴼⴼⵓⴳⵏⴰ ⴳ ⵍⵓⵙ ⴰⵏⵊⵍⵓⵙ, ⴳ ⵍⵍⴰⵏ ⵉⵎⵣⵔⴰⵡⵏ ⵙⴳ ⵜⵙⵓⵜⴰⵍ ⵏ ⴼⵎ-2030,ⴷ ⵓⴳⴷⵓⴷ ⵙ ⵓⵙⵏⴼⵍ ⵏ ⴼⵉⵜⴰ ⵎⵓⵔ ⵜⴰⵏⴰⵥⵓⵕⵜ.

A particular concern is the equal access to human enhancement technologies across classes and borders.

ⴰⵙⴰⴳⵯⵎ ⴰⵎⵥⵍⴰⵢ ⵏ ⵓⵏⵣⴳⵓⵎ ⵉⴳⴰⵜ ⵢⵉⵡⴹ ⵏ ⵉⵎⵙⴰⵙⴰⵜⵏ ⵖⵔ ⵜⵉⵇⵏⵉⵢⵜ ⵏ ⵓⵙⴷⵓⵙ ⴰⵏⴰⴼⴳⴰⵏ ⵙ ⵜⴰⴳⴳⴰⵢⵉⵏ ⴷ ⵉⵡⵜⵜⴰ.

This left the World Transhumanist Association as the leading international transhumanist organization.

ⴰⴼⴼⴰⵍ ⵏ ⵜⵣⵍⵖⴰ ⴰⴷ ⵜⴰⵎⴰⴹⵍⴰⵏⵜ ⵙ ⴹⴰⵕⵜ ⵜⵉⴼⴼⵓⴳⵏⴰ ⵣⵓⵏⴷ ⵜⴰⵎⴰⴷⴷⴰⵙⵜ ⵜⴰⴳⵔⴰⵖⵍⴰⵏⵜ ⵉⵎⵎⵓⵔⵙⵏ ⴳ ⵢⵉⴳⵔ ⵏ ⴹⴰⵕⵜ ⵜⵉⴼⴼⵓⴳⵏⴰ.

The Mormon Transhumanist Association was founded in 2006.

ⵜⴱⴷⴷⴰ “ⵜⵎⵙⵎⵓⵏⵜ ⵏ ⵎⵓⵔⵎⵓ ⴹⴰⵕⵜ ⵜⵉⴼⴼⵓⴳⵏⴰ” ⴳ ⵓⵙⴳⴳⵯⴰⵙ ⵏ 2006.

"Transhumanism stresses the evolutionary perspective, including sometimes the creation of a highly intelligent animal species by way of cognitive enhancement (i.e. biological uplift), but clings to a ""posthuman future"" as the final goal of participant evolution."

ⵜⵙⵙⵍⴽⴰⵏ ⴹⴰⵕⵜ ⵜⵉⴼⴼⵓⴳⵏⴰ ⵖⴼ ⵓⵎⵏⴰⴷ ⵏ ⵓⵙⴱⵓⵖⵍⵓ, ⴳ ⵢⴰⵎⵓ ⵓⵙⴽⴰⵔ ⵏ ⵡⴰⵏⴰⵡ ⵏ ⵉⵎⵓⴷⴰⵔ ⵉⵛⵡⴰⵏ ⴽⵉⴳⴰⵏ ⵙ ⵜⴱⵔⵉⴷⵜ ⵏ ⵓⵙⴷⵓⵙ ⴰⵎⴰⵙⵙⴰⵏ (ⵙ ⵡⴰⵍⴰⵢ ⴰⴱⵢⵓⵍⵓⵊⵉ), ⵎⴰⵛⴰ ⵜⵓⵎⵣ ⴳ “ⵉⵎⴰⵍ ⵏ ⴹⴰⵕⵜ ⵜⵉⴼⴼⵓⴳⵏⴰ”, ⴰⵛⴽⵓ ⵏⵜⵜⴰ ⴰⵢⴷ ⵉⴳⴰⵏ ⴰⵙⵓⵖⴷ ⵏ ⵜⵎⵔⵏⵉⵡⵜ ⵏ ⵉⵎⴷⵔⴰⵡⵏ.

"While such a ""cultural posthumanism"" would offer resources for rethinking the relationships between humans and increasingly sophisticated machines, transhumanism and similar posthumanisms are, in this view, not abandoning obsolete concepts of the ""autonomous liberal subject"", but are expanding its ""prerogatives"" into the realm of the posthuman."

ⴷ ⵣⵓⵏⴷ “ⴹⴰⵕⵜ ⵜⴼⵓⴳⵏⴰ ⵜⴰⴷⵍⵙⴰⵏⵜ” ⵜⵖⵢ ⴰⴷ ⵜⵙⴽⵔ ⵉⵙⵓⴳⴰⵎ ⵏ ⵡⵓⵍ ⵏ ⵓⵙⵡⵉⴳⵎ ⴳⵔ ⵉⵡⴷⴰⵏ ⴷ ⵉⵎⴰⵙⵙⵏ ⵉⵜⵜⵓⵙⴱⵓⵖⵍⵍⴰⵏ ⴽⵉⴳⴰⵏ, ⵉⵡⴰ ⴹⴰⵕⵜ ⵜⴼⵓⴳⵏⴰ ⴷ ⴹⴰⵕⵜ ⵜⴼⵓⴳⵏⴰ ⵜⴰⵏⴰⵡⴰⵢⵜ, ⴳ ⵜⴰⵏⵏⴰⵢⵜ ⴰⴷ, ⵓⵔ ⴷⴰ ⵜⵎⵣⴰⵔⴰⵢ ⴷ ⵉⵙⵉⵙⵙⵏ ⵉⵣⴰⵢⴽⵓⵜⵏ “ⴰⵏⴽⴽⵉⵏ ⴰⵍⵉⴱⵉⵔⴰⵍⵉ ⵉⵥⵍⵉⵏ”, ⵎⴰⴽⴰ ⴰⵙⵙⵉⵔⵡ ⵏ ⵜⴱⵖⵓⵔⵉⵏ ⵖⵔ “ ⵓⵎⴰⴹⴰⵍ ⵏ ⴹⴰⵕⵟ ⵓⴼⴳⴰⵏ”.

However, other progressives have argued that posthumanism, whether it be its philosophical or activist forms, amounts to a shift away from concerns about social justice, from the reform of human institutions and from other Enlightenment preoccupations, toward narcissistic longings for a transcendence of the human body in quest of more exquisite ways of being.

ⵡⴰⵅⵅⴰ ⵀⴰⴽⴽⴰⴽ , ⵎⵏⵣⴰⵖⵏ ⵉⵙⴰⵜⵜⵓⵢⵏ ⵢⴰⴹⵏ ⵏ ⵡⵉⵙ ⴷ ⴹⴰⵕⵜ ⵜⴼⵓⴳⵏⴰ, ⵙⵡⴰ ⴳⴰⵏⵜ ⵜⴰⵍⵖⵉⵡⵉⵏ ⵏⵏⵙ ⵜⵉⴼⵍⵙⴰⴼⵉⵏ ⵓⵍⴰ ⵜⵉⵍⴰⵍⵉⵏ, ⵜⵓⵡⴹ ⴰⵙⵎⵓⵜⵜⵢ ⵏ ⵜⵉⵡⵉⵜⵉⵏ ⵉⵣⴷⵉⵏ ⴰⴽⴷ ⵜⴰⵣⵔⴼⵉ ⵜⴰⴳⴷⵓⴷⴰⵏⵜ, ⵙⴳ ⵓⵎⵓⴽⵏ ⵜⵉⵎⵔⵙⴰⵍ ⵏ ⵜⵉⴼⴼⵓⴳⵏⴰ ⴷ ⵙⴳ ⵉⵙⵡⵓⵔⵉⵜⵏ ⵏ ⵓⵙⵙⵉⵙⴼⵉⵡ ⵢⴰⴹⵏ, ⵖⵔ ⵢⵉⵔⵉ ⴰⵏⴰⵔⵊⵉⵙ ⵏ ⵓⵙⵙⵓⵔⴼ ⵉ ⵓⴼⴳⴰⵏ ⵉ ⵜⴼⴽⴽⴰ, ⵅⴼ ⵓⵔⵣⵣⵓ ⵏ ⵜⴱⵔⵉⴷⵉⵏ ⵏ ⵜⵉⵍⵉⵜ ⵡⴰⵍⴰ ⵉⵥⵉⵍⵏ.

Many transhumanists actively assess the potential for future technologies and innovative social systems to improve the quality of all life, while seeking to make the material reality of the human condition fulfill the promise of legal and political equality by eliminating congenital mental and physical barriers.

ⴷⴰ ⵉⵙⴽⴰⵔ ⵡⴰⵀⵍⵉ ⵏ ⵉⵎⵓⵙⵏⴰⵡⵏ ⵏ ⴹⴰⵕⵜ ⵜⴼⴼⵓⴳⵏⴰ ⴰⵣⵣⵔⴰⵢ ⵖⴼ ⵉⵎⴰⵎⴽⵏ ⵏ ⵜⵉⵇⵏⵉⵜⵉⵏ ⵏ ⵉⵎⴰⵍ, ⴷ ⵉⴳⵔⵔⴰⵜⵏ ⵉⵏⴰⵎⵓⵏⴻⵏ ⵉⵜⵜⵓⴳⴰⵏ ⵉⵜⵀⵢⵢⵓⵜ ⵏ ⵡⴰⵏⴰⵡⵏ ⵏ ⵜⵓⴷⵔⵜ ⵎⴰⵕⵕⴰ, ⴷ ⵜⵓⵜⵜⵔⴰ ⵏ ⵓⵀⵢⵢⵓ ⵏ ⵜⵉⵏⴰⵡⵜ ⵜⴰⴳⵎⴰⵎⵜ ⵏ ⵡⴰⴷⴷⴰⴷ ⴰⴼⴳⴰⵏ, ⴰⵔ ⵢⴰⴽⴽⴰ ⴰⵙⵉⵙⴽⵍ ⴰⵣⵔⴼⴰⵏ ⴷ ⵓⵙⵔⵜⴰⵏ ⵙⴳ ⵡⵓⴽⵓⵙ ⵏ ⵉⴼⵔⴰⴳⵏ ⵉⵏⵍⵍⵉⵜⵏ ⴷ ⵉⴳⵎⴰⵎⵏ ⵏ ⵜⵓⴳⵉⵜ.

Some theorists such as Ray Kurzweil think that the pace of technological innovation is accelerating and that the next 50 years may yield not only radical technological advances, but possibly a technological singularity, which may fundamentally change the nature of human beings.

ⴷⴰ ⵜⵜⵉⵖⵉⵍⵏ ⴽⵉⴳⴰⵏ ⵏ ⵉⵎⵙⵙⵉⵥⵉⵕⵏ ⵣⵓⵏⴷ ⴽⵓⵍⵣⵡⵉⵕ ⵎⴰⵙⴷ ⵜⴰⵏⴰⵡⵜ ⵜⴰⵙⵏⴼⵍⵓⵍⵜ ⵜⴰⵜⵉⴽⵏⵓⵍⵓⵊⵉⵜ ⵜⵜⴰⵣⵍⴰ, ⴷ ⵎⴰⵙⴷ 50 ⴷ ⵉⴷⴷⴰⵏ ⵇⴰⴷ ⵜⴰⵡⵢ ⵓⵔ ⵉⴷ ⵖⴰⵙ ⵉⵙⴱⵓⵖⵍⵓⵜⵏ ⵉⵜⵓⴽⵏⵓⵍⵓⵊⵉⵜⵏ ⵉⵥⵓⵕⴰⵏ, ⵎⴰⴽⴰ ⵉⵖⵢ ⴰⴷ ⵜⴰⵡⵢ ⴰⵥⵍⴰⵢ ⴰⵜⵉⴽⵏⵓⵍⵓⵊⵉ ⵏⵏⴰ ⵉⵏⵏⴰⵏ ⴰⴷ ⵉⵙⵏⴼⴻⵍ ⴰⵖⴰⵔⴰⵏ ⵏ ⵓⴼⴳⴰⵏ ⵙ ⵜⴰⵍⵖⴰ ⵜⴰⵙⵉⵍⴰⵏⵜ.

For example, Bostrom has written extensively on existential risks to humanity's future welfare, including ones that could be created by emerging technologies.

ⵙ ⵓⵎⴷⵢⴰ, ⵢⴰⵔⴰ ⴱⵓⵙⵜⵕⵓⵎ ⴳ ⵓⴼⵓⵖⴰⵍ ⴰⴱⴰⵔⴰⵡ ⵏ ⵉⵎⵉⵣⵉⵜⵏ ⵏ ⵜⵉⵍⵍⴰⵡⵜ ⵖⴼ ⵓⵟⵕⵕⵃ ⵏ ⵓⴳⴷⵓⴷ ⵙ ⵉⵎⴰⵍ, ⴳ ⵜⴰⵎⵓⵏ ⵜⵏⵏⴰ ⵉⵖⵉⵏ ⴰⴷ ⵉⵜⵜⵓⵙⴽⵔ ⵙ ⵜⵖⴰⵔⴰⵙⵜ ⵜⴰⵜⵉⵇⵏⵉⵜ ⵜⴰⵏⴳⵎⴰⵏⵜ.

To counter this, Hawking emphasizes either self-design of the human genome or mechanical enhancement (e.g., brain-computer interface) to enhance human intelligence and reduce aggression, without which he implies human civilization may be too stupid collectively to survive an increasingly unstable system, resulting in societal collapse.

ⵉ ⵓⵎⵏⴰⵍⴰ ⵏ ⵖⴰⵢⴰⵏ, ⵉⵙⵍⴽⴰⵏ ⵀⵓⴽⵉⵏⴳ ⵙⵡⴰ ⵙ ⵓⵎⴰⵎⴽ ⴰⵢⵎⴰⵏ ⵏ ⵍⵊⵉⵏⵓⵎ ⴰⵏⴰⴼⴳⴰⵏ ⵏⵖⴷ ⴰⵙⴷⵓⵙ ⴰⵎⵉⴽⴰⵏⵉⴽ ( ⵙ ⵓⵎⴷⵢⴰ ⴰⵇⵎⵓ ⵏ ⵓⵏⵍⵍⵉ, ⴷ ⵓⵎⵙⵙⵓⴷⵙ), ⵉ ⵓⵙⴷⵓⵙ ⵏ ⵛⵛⵡⵉⵢⵜ ⵏ ⵓⴼⴳⴰⵏ ⴷ ⵓⵙⵙⴷⵔⵙ ⵏ ⵉⵛⵏⴳⵯⴰ, ⵏⵏⴰ ⵉⵜⵜⵉⵏⵉ ⴱⵍⴰ ⵜ; ⵜⴰⵖⵔⵎⴰ ⵜⴰⵏⴰⴼⴳⴰⵏⵜ ⵉⵖⵢ ⴰⴷ ⵜⴱⴱⵓⵀⵍⵍⵓ ⴽⵉⴳⴰⵏ ⵙ ⵓⵎⴰⵜⴰ, ⵎⴰⵔ ⴰⴷ ⵜⵇⵉⵎ ⵜⴷⴷⵔ ⴳ ⵓⵏⴳⵔⴰⵡ ⵓⵔ ⵉⵣⵣⴳⴰⵏ ⵙ ⵜⴰⵍⵖⴰ ⵜⴰⵎⵔⵏⵉⵡⵜ, ⴰⵢⴷ ⵢⵓⵡⵉⵏ ⵖⵔ ⵜⴹⵓⵕⵉ ⵏ ⵓⴳⴷⵓⴷ.

These thinkers argue that the ability to discuss in a falsification-based way constitutes a threshold that is not arbitrary at which it becomes possible for an individual to speak for themselves in a way that is not dependent on exterior assumptions.

ⵜⵎⵏⵣⴰⵖⵜ ⵉⵎⵙⵡⴰⵏⴳⴰⵎ ⵖⴼ ⵜⵉⵖⵉⵢⵜ ⵏ ⵓⵎⴷⴰⴽⴰⵕ ⵙ ⵜⴱⵔⵉⴷⵜ ⵉⴱⴷⴷⴰⵏ ⵖⴼ ⵓⵎⵔⵊⵓⵏ, ⵜⴳⴳⴰ ⵢⴰⵜ ⵍⵄⴷⴼⵜ ⵓⵔ ⵉⴳⵉⵏ ⵜⴰⵙⵇⴷⴷⵛⵜ, ⴰⵔⴷ ⵢⵉⵖⵉⵢ ⵓⴼⴳⴰⵏ ⴰⴷ ⵉⵙⵉⵡⵍ ⵖⴼ ⵉⵖⴼ ⵏⵏⵙ ⵙ ⵜⴱⵔⵉⴷⵜ ⵓⵔ ⵉⵙⴽⵓⵜⵜⵓⵏ ⵖⴼ ⵢⵉⵏⵉⵜ ⵏ ⴱⵕⵕⴰ.

"In keeping with this, many prominent transhumanist advocates, such as Dan Agin, refer to transhumanism's critics, on the political right and left jointly, as ""bioconservatives"" or ""bioluddites"", the latter term alluding to the 19th century anti-industrialisation social movement that opposed the replacement of human manual labourers by machines."

“ⴰⵙⵙⵓⴷⵓ ⴷ ⵎⴰⵢⴰ, ⴷⴰ ⵙⵏⵄⴰⵜⵏ ⴽⵉⴳⴰⵏ ⵏ ⵡⵉⵏⵏⴰ ⵉⵇⵇⴰⵔⵏ ⵖⵔ ⴹⴰⵕⵜ ⵜⴼⴼⵓⴳⵏⴰ ⵣⵓⵏⴷ: ⴷⴰⵏ ⴰⵊⵉⵏ, ⵙ ⵉⵙⵎⵜⴰⵍⵏ ⵏ ⴹⴰⵕⵜ ⵜⴼⴼⵓⴳⵏⴰ, ⵅⴼ ⵓⵢⴼⴼⴰⵙ ⴷ ⵓⵥⵍⵎⴰⴹ ⵉⵙⵔⵜⴰⵏⴻⵏ ⵙ ⵜⵓⵛⵓⵔⵜ ⵙ ⵢⵉⵙⵎ ⵏ “ ⵉⵎⵃⴷⴰⵢ ⵉⴱⵢⵓⵍⵓⵊⵉⵜⵏ”, ⵏⵖⴷ “bioluddites” ⵜⴰⴳⵓⵔⵉ ⴰⴷ ⵙⴳ ⵓⵙⴰⵜⵓ ⵡⵉⵙⵙ 19, ⴰⵎⵓⵙⵙⵓ ⴰⵏⴰⵎⵓⵏ ⵢⵓⴳⵉⵏ ⵜⴰⵎⴳⵓⵔⵉ, ⵢⵓⴳⵢ ⴰⵙⵏⴼⴻⵍ ⵏ ⵉⵏⴰⵡⵓⵔⵏ ⵏ ⵓⴼⵓⵙ ⵖⵔ ⵉⵎⴰⵙⵙⵏ.”

The same scenario happens when people have certain neural implants that give them an advantage in the work place and in educational aspects.

ⴷⴰ ⵉⵜⵜⴰⵍⵙ ⵙⵙⵉⵏⴰⵕⵢⵓ ⴰⴷⴷⴰⵢ ⵢⵉⵍⵉ ⵖⵓⵔ ⵉⵡⴷⴰⵏ ⵜⵓⵥⵥⵓⵜⵉⵏ ⵏ ⵜⴰⴹⴰ ⴰⵙⵏ ⵢⴰⴽⴽⴰⵏ ⵜⴰⴱⵖⵓⵔⵜ ⴳ ⵡⴰⵏⵙⴰ ⵏ ⵜⵡⵓⵔⵉ ⵓⵍⴰ ⵜⵉⵙⴳⴳⵯⵉⵏ ⵏ ⵓⵙⵙⵍⵎⴷ.

Immortalism, a moral ideology based upon the belief that radical life extension and technological immortality is possible and desirable, and advocating research and development to ensure its realization.

ⵜⴰⵙⵓⵍⵜ, ⵜⴰⴷⵢⵓⵍⵓⵊⵉⵜ ⵜⴰⵖⴰⵔⴰⵏⵜ ⵜⴱⴷⴷⴰ ⵖⴼ ⵢⵉⵖⵉⵍ ⵏ ⵓⵣⴷⴰⵢ ⵏ ⵜⵓⴷⵔⵜ ⵜⴰⵔⴰⴷⵉⴽⴰⵍⵉⵢⵜ ⴷ ⵜⴰⵙⵓⵍⵜ ⵜⴰⵜⵉⴽⵏⵓⵍⵓⵊⵉⵜ ⵜⴰⵖⴰⵡⵙⴰ ⵉⵖⵉⵏ ⴰⴷ ⵢⵉⵍⵉ ⴷ ⵔⴰⵏⵜ ⵉⵡⴷⴰⵏ, ⴰⵔ ⵜⵇⵇⴰⵕ ⵙ ⵓⵔⵣⵣⵓ ⴷ ⵓⵙⴱⵓⵖⵍⵓ ⵎⴰⵔ ⴰⴷ ⵢⵉⵍⵉ ⵓⵙⵓⴳⵔ ⵏ ⵜⵉⵍⵉⵜ ⵏⵏⵙ.

Mathematics (from Greek: ) includes the study of such topics as quantity (number theory), structure (algebra), space (geometry), and change (analysis).

ⵉⵍⵍⴰ ⴳ ⵜⵓⵙⵏⴰⴽⵜ (ⵙⴳ ⵍⵢⵓⵏⴰⵏⵢⴰ) ⵜⴰⵣⵔⴰⵡⵜ ⵜⴰⵙⴳⵓⵎⴰⵏⵜ ⵣⵓⵏⴷ ⵜⴰⵎⴰⴽⵜⴰ (ⵜⴰⵎⴰⴳⵓⵏⵜ ⵏ ⵉⵎⴹⴰⵏ), ⵜⵓⵚⴽⵉⵡⵜ (ⵍⵊⵉⴱⵔ), ⴰⵙⴰⵢⵔⴰⵔ (ⵜⴰⵏⵣⴳⵉⵜ), ⴰⵙⵏⴼⵍ (ⴰⵙⴼⵙⵉ).

When mathematical structures are good models of real phenomena, mathematical reasoning can be used to provide insight or predictions about nature.

ⴰⴷⴷⴰⵢ ⵜⴳ ⵜⴰⵏⵖⴰ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵉⵎⴷⵢⴰⵜⵏ ⵉⵖⵓⴷⴰⵏ ⵉ ⵜⵓⵎⴰⵏⵉⵏ ⵏ ⵜⵉⴷⵜ, ⵉⵖⵢ ⴰⴷ ⵏⵙⵡⵓⵔⵉ ⵙ ⵓⵙⵡⵉⵏⴳⵎ ⴰⵎⵙⵏⴰⴽⵉⵢ ⵎⴰⵔ ⴰⴷ ⵏⴽ ⵜⴰⵏⵏⴰⵢⵜ ⵉⵏⵎⵏ ⴷ ⵉⵙⵏⵉⵎⴰⵍⵏ ⵖⴼ ⵜⵖⴰⵔⴰ.

The research required to solve mathematical problems can take years or even centuries of sustained inquiry.

ⵉⵖ ⴰⴷ ⵉⴽ ⵓⵔⵣⵣⵓ ⵉⵔⴰⵏ ⴰⴷ ⵉⴽ ⴰⴼⵙⵙⴰⵢ ⵉ ⵜⵎⵓⴽⵔⵉⵙⵉⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵉⵙⴳⴳⵯⴰⵙ ⵏⵖⴷ ⵜⵉⵙⵓⵜⵉⵡⵉⵏ ⵏ ⵓⵔⵣⵣⵓ ⴰⵙⵓⵍⴰⵏ.

Mathematics developed at a relatively slow pace until the Renaissance, when mathematical innovations interacting with new scientific discoveries led to a rapid increase in the rate of mathematical discovery that has continued to the present day.

ⵜⵜⵓⵙⴱⵓⵖⵍⵍⴰ ⵜⵓⵙⵏⴰⴽⵜ ⵙ ⵜⴰⵍⵖⴰ ⵜⴰⵎⴷⵔⵓⵙⵜ ⴰⵔ ⴰⵣⵎⵣ ⵏ ⵜⵏⴽⵔⴰ, ⴷⴷⴰⴳ ⴷ ⵓⵡⵉⵏ ⵉⵙⵏⴼⵍⵓⵍⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵏⵏⴰ ⵉⵜⵎⵔⴰⵔⴰⵏ ⴰⴽⴷ ⵢⵉⴼⵉⵜⵏ ⵏ ⵜⵓⵙⵙⵏⴰ ⵉⵎⴰⵢⵏⵓⵜⵏ, ⵖⵔ ⵜⵔⵏⴰⵡⵜ ⵉⵙⵔⴱⵉⵏ ⴳ ⵜⵢⴰⴼⵓⵜ ⵏ ⵢⵉⴼⵉⵜⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵏⵏⴰ ⵉⵙⵙⴰⴷⴰⵏ ⴰⵔ ⴰⵙⵙⴰ.

As evidenced by tallies found on bone, in addition to recognizing how to count physical objects, prehistoric peoples may have also recognized how to count abstract quantities, like time—days, seasons, or years.

ⵉⵎⴽ ⵉⵜⵢⴰⴽⵣ ⴳ ⵉⵙⵙⵉⵟⵏ ⵉⵍⵍⴰⵏ ⵖⴼ ⵉⵖⵚⴰⵏ, ⵓⵍⴰ ⵎⴰⵎⴽ ⵙ ⵉⵜⵜⵓⵙⵙⵉⵜⵏ ⵜⵖⴰⵡⵙⵉⵡⵉⵏ ⵜⴰⵏⴳⴰⵎⵉⵏ,ⵉⵖⵢ ⵉⵙ ⴳⴰⵏ ⵉⴳⴷⵓⴷⵏ ⵏ ⴷⴰⵜ ⵓⵎⵣⵔⵓⵢ ⵎⴰⵎⴽ ⵙⵙⵉⵜⵉⵏ ⴰⵏⵛⵜ ⵡⴰⵔⴰⵜⵉⴳ, ⵣⵓⵏⴷ ⵜⵉⵣⵉ- ⵓⵙⵙⴰⵏ ⴷ ⵉⵎⵉⵔⵏ ⵏⵖⴷ ⵉⵙⴳⴳⵯⴰⵙⵏ.

Beginning in the 6th century BC with the Pythagoreans, with Greek mathematics the Ancient Greeks began a systematic study of mathematics as a subject in its own right.

ⵙⴳ ⵜⴰⵙⵓⵜ ⵜⵉⵙⵙ 6 ⴷⴰⵜ ⵜⵍⴰⵍⵉⵜ ⵏ ⵍⵎⴰⵙⵉⵃ ⴰⴽⴷ ⴼⵉⵜⴰⵖⵓⵔⵙ, ⴷ ⵜⵓⵙⵏⴰⴽⵜ ⵜⴰⵢⵓⵏⴰⵏⵉⵢⵜ, ⵙⵙⵏⵜⵉⵏ ⵍⵉⵖⵔⵉⵇ ⵉⵇⴱⵓⵔⵏ ⴰⵙⵏⵜⵍ ⵏ ⵜⴰⴱⵔⵉⴷⵜ ⵜⵓⵙⵏⴰⴽⵜ.

The greatest mathematician of antiquity is often held to be Archimedes (c. 287–212 BC) of Syracuse.

ⴽⵉⴳⴰⵏ ⴰⵢⴷ ⵉⵜⵜⵉⵏⵉⵏ ⵏ ⵡⵉⵙⴷ ⴰⵔⵅⵎⵉⵙⴷ (287-212 ⴷⴰⵜ ⵜⵍⴰⵍⵉⵜ ⵏ ⵍⵎⴰⵙⵉⵃ) ⴰⵢⴷ ⵉⴳⴰⵏ ⴰⵎⵓⵙⵏⴰⵡ ⴰⵅⴰⵜⴰⵔ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⴳ ⵉⵣⵎⴰⵣ ⵉⵇⴱⵓⵔⵏ.

The Hindu–Arabic numeral system and the rules for the use of its operations, in use throughout the world today, evolved over the course of the first millennium AD in India and were transmitted to the Western world via Islamic mathematics.

ⴰⵣⵣⵉⴳⵣ ⵏ ⵓⵏⴳⵔⴰⵡ ⵏ ⵉⵎⴹⴰⵏ ⴰⵀⵉⵏⴷⵉ-ⴰⵄⵕⴰⴱ; ⴷ ⵉⵍⴳⴰⵎⵏ ⵏ ⵓⵙⵎⵔⵙ ⵏ ⵜⵎⴳⴳⵉⵜⵉⵏ ⵏⵏⵙ, ⵉⵜⵜⵓⵙⵎⵔⴰⵙⵏ ⴰⵙⵙⴰ ⴳ ⵓⵎⴰⴹⴰⵍ ⴽⵓⵍⵍⵓⵜ, ⵢⵓⵎⵥ ⵉⴼⴹ ⴰⵎⵣⵡⴰⵔⵓ ⵏ ⵜⵍⴰⵍⵉⵜ ⵏ ⵍⵎⴰⵙⵉⵃ ⴳ ⵍⵀⵉⵏⴷ , ⴰⴳ ⵜⵜⵓⵙⵎⴰⵜⵜⵢ ⵙ ⴰⵎⴰⴹⴰⵍ ⴰⵜⴰⵔⴰⵎ ⵜ ⵜⴱⵔⵉⴷⵜ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵜⴰⵏⵙⵍⵎⵜ.

The most notable achievement of Islamic mathematics was the development of algebra.

ⴰⵙⵙⴹⵔⵓ ⴰⵎⵇⵔⴰⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵜⴰⵏⵙⵍⵎⵜ ⵉⴳⴰⵜ ⵓⵙⴱⵓⵖⵍⵓ ⵏ ⵜⵎⴰⵙⵙⴰⵏⵜ ⵏ ⵍⵊⵉⴱⵔ.

During the early modern period, mathematics began to develop at an accelerating pace in Western Europe.

ⴳ ⵜⴰⵙⵓⵜ ⵜⴰⵜⵔⴰⵔⵜ ⵏ ⵣⵉⴽ, ⵜⵙⵙⵏⵜⵉ ⵜⵓⵙⵏⴰⴽⵜ ⴰⴱⵓⵖⵍⵓ ⵙ ⵢⴰⵜ ⵜⴱⵔⵉⴷⵜ ⵉⵙⵔⴱⵉⵏ ⴳ ⵓⵔⵓⴱⴱⴰ ⵏ ⵓⵜⴰⵔⴰⵎ.

Perhaps the foremost mathematician of the 19th century was the German mathematician Carl Friedrich Gauss, who made numerous contributions to fields such as algebra, analysis, differential geometry, matrix theory, number theory, and statistics.

ⵉⵖ ⵉⵙ ⵜⵜ ⵉⴽⴽⴰ ⵓⵎⵓⵙⵏⴰⵡ ⴰⵍⵎⴰⵏⵉⵢ “ⴽⴰⵕⵍ ⴼⵔⵉⴷⵔⵉⵜⵛ ⴷⵊⴰⵡⵙ” ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⴳ ⵓⵙⴰⵜⵓ ⵡⵉⵙⵙ 19, ⵢⵓⵡⵙ ⴽⵉⴳⴰⵏ ⴳ ⵢⵉⴳⵔⴰⵏ ⵣⵓⵏⴷ ⵍⵊⵉⴱⵔ, ⴰⴼⴰⵔⵙ, ⵜⴰⵏⵣⴳⵉⵜ ⵜⴰⴼⴷⴰⵡⵉⵜ, ⵜⴰⵎⴰⴳⵓⵏⵜ ⵜⴰⴷⵔⴰⵙⵜ ⴷ ⵜⵎⴰⴳⵓⵏⵜ ⵏ ⵉⵎⴹⴰⵏ ⴷ ⵓⵙⵉⴹⵏ.

Mathematical discoveries continue to be made today.

ⵜⵙⵙⴰⴷⴰ ⵜⵡⴰⴼⵉⵜ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⴰⵙⵙ.

"In particular, mathēmatikḗ tékhnē meant ""the mathematical art."""

“ⵙ ⵓⵥⵍⴰⵢ ⵎⴰⵜⵉⵎⴰⵜⵉⴽ ⵜⵉⵅⵏ ⴰⵢⴷ ⵉⴳⴰⵏ “ⵜⴰⵥⵓⵕⵉ ⵏ ⵜⵓⵙⵏⴰⴽⵜ.””

In English, the noun mathematics takes a singular verb.

ⴳ ⵜⵓⵜⵍⴰⵢⵜ ⵜⴰⵏⴳⵍⵉⵣⵜ, ⵜⵍⴰ ⵜⵓⵙⵏⴰⴽⵜ ⵜⴰⵙⵎⴰⵡⴰⵏⵜ ⴰⵎⵢⴰⴳ ⴰⵎⵢⵓⵡⵏ.

"However, Aristotle also noted a focus on quantity alone may not distinguish mathematics from sciences like physics; in his view, abstraction and studying quantity as a property ""separable in thought"" from real instances set mathematics apart."

ⵡⴰⵅⵅⴰ ⵀⴰⴽⴽⴰⴽ, ⵢⵓⴽⵣ ⴰⵔⵉⵙⵟⵓ ⴰⵔⴰⵔ ⵏ ⵜⵢⵏⵏⵉⵜ ⵖⴼ ⵜⵎⴰⴽⵜⴰ ⴷⴰⵢ, ⵉⵖ ⴰⴷ ⵓⵙⵜⵉ ⵜⵓⵙⵏⴰⴽⵜ ⵖⴼ ⵜⵎⴰⵙⵙⴰⵏⵉⵏ ⵣⵓⵏⴷ ⴰⴼⵉⵣⵉⴽ, ⴳ ⵜⴰⵏⵏⴰⵢⵜ ⵏⵏⵙ ⵉⴳⴰ ⵓⴽⵓⵙ ⴷ ⵜⵣⵔⴰⵡⵜ ⵏ ⵜⵎⴰⴽⵜⴰ ⵉⴳⵏ ⵜⴰⵏⴰⵎⴰⵥⵜ, “ⵜⴳⴰ ⵜⵉⵏ ⵓⵎⵣⵉⵔⴰⵢ ⴳ ⵓⵙⵡⵉⵏⴳ”, ⴳ ⵉⵎⴷⵢⴰⵜⵏ ⵏ ⵜⵉⴷⵜ ⴷⴰ ⵜⵜⵓⵎⵣⴰⵔⴰⵢ ⵜⵓⵙⵏⴰⴽⵜ ⴳⵔⴰⵙ.

A peculiarity of intuitionism is that it rejects some mathematical ideas considered valid according to other definitions.

ⵜⴰⵥⵍⴰⵢⵜ ⵏ ⵜⵡⵏⴳⵉⵎⵜ; ⵉⴳⴰⵜ ⴰⴷ ⵢⴰⴳⵢ ⵉⵜⵙⵏⵜ ⵜⵡⵏⴳⵉⵎⵉⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵏⵏⴰ ⵉⵎⵙⴰⵙⴰⵏ ⴷ ⵉⵙⵓⵙⵙⵏ ⵏⵏⵉⴹⵏ.

"Haskell Curry defined mathematics simply as ""the science of formal systems""."

“ⵉⵙⵏⵎⵍ ⵀⴰⵙⴽⴰⵔ ⴽⴰⵔⵉ ⵜⵓⵙⵏⴰⴽⵜ ⵙ ⵓⴼⵔⴰⵔⵉ ⵉⴷ ⵏⵜⵜⴰⵜ ⴰⵢⴷ ⵉⴳⴰⵏ “ⵜⵓⵙⵙⵏⵉⵎⴰⴳⴰⵡⵏ ⵜⵓⵏⵚⵉⴱⵜ””.

"Popper also noted that ""I shall certainly admit a system as empirical or scientific only if it is capable of being tested by experience."""

“ⵉⵙⵙⵎⵜⵔ ⴱⵓⴱⴱⵔ ⵓⵍⴰ ⵏⵜⵜⴰ “ ⵙⵙⵏⵖ ⵉⴷ ⵉⵏⴳⵔⴰⵡⵏ ⴳⴰⵏ ⵖⴰⵙ ⴰⵏⴰⵔⴰⵎ ⵏⵖ ⴰⵎⴰⵙⵙⴰⵏ ⵉⴳ ⵉⴳⴰ ⵡⵉⵏ ⵢⵉⵔⵉⵎ ⵙ ⵜⵉⵔⵎⵉⵜ””.

Intuition and experimentation also play a role in the formulation of conjectures in both mathematics and the (other) sciences.

ⵜⴰⵡⵏⴳⵉⵎⵜ ⴷ ⵢⵉⵔⵉⵎ ⵖⴰⵔⵙⵏ ⴰⵡⵜⵜⴰⵙ ⴳ ⵢⵉⴳⴳⵉ ⵏ ⵢⵉⴽⵉⵣⵏ ⴳ ⵜⵓⵙⵏⴰⴽⵜ ⴷ ⵜⵎⴰⵙⵙⴰⵏⵉⵏ ⵢⴰⴹⵏ.

For example, the physicist Richard Feynman invented the path integral formulation of quantum mechanics using a combination of mathematical reasoning and physical insight, and today's string theory, a still-developing scientific theory which attempts to unify the four fundamental forces of nature, continues to inspire new mathematics.

ⵙ ⵓⵎⴷⵢⴰ, ⵉⵙⴽⵔ ⵓⴼⵉⵣⵉⴽ ⵔⵉⵜⵛⴰⵕⴷ ⴼⴰⵢⵏⵎⴰⵏ ⵢⴰⵏ ⵓⵙⴰⵔⴰ ⵉⵜⵜⵙⵎⴰⴷⵏ ⵎⵉⴽⴰⵏⵉⴽ ⴰⵙⵎⴽⵜⴰ ⵙ ⵜⵓⵛⵓⵔⵜ ⵏ ⵓⵙⵡⵉⵏⴳ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⴷ ⵡⴰⵏⵏⴰⵢ ⴰⴼⵉⴽⵉⴽ, ⵜⵙⵓⵍ ⵜⵎⴰⴳⵓⵏⵜ ⵏ ⵉⴼⵉⵍⴰⵏ, ⵉⴳⴰⵏ ⵜⴰⵎⴰⴳⵓⵏⵜ ⵜⴰⵎⴰⵙⵙⴰⵏⵜ ⴷⴰ ⵜⵜⵓⵙⴱⵓⵖⵍⵓ ⵉⵙ ⵓⵔ ⵜⵙⵎⵓⵏ ⵜⵉⵣⵎⵎⴰⵔ ⵜⵉⴷⵙⵍⴰⵏⵉⵏ ⵏ ⵜⴰⵎⵓⵙⵜ ⵙ ⴽⴽⵓⵥⵜ, ⴰⵙⴰⴳⵯⵎ ⴰⵏⴼⵔⴰⵔ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵜⴰⵎⴰⵢⵏⵓⵜ.

A distinction is often made between pure mathematics and applied mathematics.

ⵉⵜⵙⵏⵜ ⵜⵉⴽⴽⴰⵍ ⴷⴰ ⵉⵜⵜⵉⵍⵉ ⵓⵙⵏⵓⵃⵢⵓ ⵉⵏⴳⵔ ⵜⵓⵙⵏⴰⴽⵜ ⵜⴰⵔⵣⵣⵓⵜ ⴷ ⵜⵓⵙⵏⴰⴽⵜ ⵜⵓⵙⴽⵉⵔⵜ.

As in most areas of study, the explosion of knowledge in the scientific age has led to specialization: there are now hundreds of specialized areas in mathematics and the latest Mathematics Subject Classification runs to 46 pages.

ⵉⵎⴽⵉⵏⵏⴰ ⵉⴳⴰ ⵡⴰⴷⴷⴰⴷ ⴳ ⴽⵉⴳⴰⵏ ⵏ ⵢⵉⴳⵔⴰⵏ ⵏ ⵜⵖⵓⵔⵉ, ⵢⵓⵡⵢ ⵓⵏⵢⵓⴷⴷⵓ ⵏ ⵜⵓⵙⵙⵏⴰ ⴳ ⵓⵣⵎⵣ ⴰⵎⴰⵙⵙⴰⵏ ⵖⵔ ⵜⴰⵥⵍⴰⵢⵜ, ⵖⵉⵍⴰ ⵍⵍⴰⵏⵜ ⵜⵎⵉⴹⵉⵡⵉⵏ ⵏ ⵢⵉⴳⵔⴰⵏ ⵉⵥⵍⵉⵏ ⵙ ⵜⵓⵙⵏⴰⴽⵜ, ⴰⵏⵡⴰⵢⴰ ⴰⵎⴰⵢⴱⵓ ⵉ ⵓⵙⵏⵜⵍ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵉⴳⵓⵍⴰⵏ 46 ⵏ ⵜⵙⵏⴰ.

Many mathematicians talk about the elegance of mathematics, its intrinsic aesthetics and inner beauty.

ⴽⵉⴳⴰⵏ ⴳ ⵉⵎⵓⵙⵏⴰⵡⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⴷⴰ ⵙⴰⵡⴰⵍⵏ ⵖⴼ ⵜⴰⴷⴳⵉ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⴷ ⵜⵉⵃⵍⵉ ⵏⵏⵙ ⵏ ⵓⴳⵏⵙⵓ ⴷ ⵓⵖⵓⴷⵓ ⵏⵏⵙ ⴰⴳⵯⵏⵙⴰⵏ.

G. H. Hardy in A Mathematician's Apology expressed the belief that these aesthetic considerations are, in themselves, sufficient to justify the study of pure mathematics.

ⵉⵙⵙⵓⵔⴼ ⵓⵎⵓⵙⵏⴰⵡ ⵏ ⵜⵓⵙⵏⴰⴽ “ⴳⵓⴷⴼⵔⵉ ⵀⴰⵕⵓⵍⴷ ⵀⴰⵔⴷⵉ “, ⵖⴼ ⵓⴼⴼⵓⵍⵙ ⵏⵏⵙ ⵙ ⵉⵙⴰⵜⵉⴳⵏ ⴰⴷ ⴷⴰⵢ ; ⵖⴼ ⵜⵣⵔⴰⵡⵜ ⵜⵓⵙⵏⴰⴽⵜ ⵜⴰⵔⵣⵣⵓⵜ.

A theorem expressed as a characterization of the object by these features is the prize.

ⵜⴰⵎⴰⴳⵓⵏⵜ ⵖⴼ ⵉⵍⵍⴰ ⵡⴰⵡⴰⵍ ⵣⵓⵏⴷ ⴰⴼⴰⵔⵙ ⵏ ⵓⵎⵖⵏⴰⵡ ⵉⵍⴰⵏ ⵜⵉⵎⵉⵜⴰⵔ ⴰⵎ ⵜⵉ, ⵉⴳⴰⵜ ⵓⴱⵖⵓⵔ.

Euler (1707–1783) was responsible for many of the notations in use today.

ⵉⴽⴽⴰⵜ “ⵓⵡⵉⵍⵔ (1707-1783)”, ⵉⴳⴰ ⴰⵎⵙⵍⴰⵢ ⵖⴼ ⴽⵉⴳⴰⵏ ⵏ ⵜⵎⵉⵜⴰⵔ ⵉⵜⵜⵓⵙⵎⵔⴰⵙⵏ ⴰⵙⵙⴰ.

Unlike natural language, where people can often equate a word (such as cow) with the physical object it corresponds to, mathematical symbols are abstract, lacking any physical analog.

ⵜⵓⵜⵍⴰⵢⵜ ⵏ ⵜⴰⵖⴰⵔⴰⵏⵜ ⴳ ⵖⵉⵏ ⵉⵡⴷⴰⵏ ⴰⴷ ⵙⵙⵉⴽⵙⵍⵏ ⵜⵉⴳⵓⵔⵉⵡⵉⵏ (ⵣⵓⵏⴷ ⵜⴰⴼⵓⵏⴰⵙⵜ) ⴷ ⵓⵎⵏⵉⵡⴰⵢ ⴰⴽⵎⴰⵎ ⵏⵏⵙ, ⵓⵔ ⵉⴷ ⴰⵎ ⵜⵎⵉⵜⴰⵔ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵜⴰⵔⴰⵜⵉⴳ, ⴷ ⵓⵔ ⵜⵍⵉ ⴰⵎⵏⵉⵡⴰⵢ ⴰⴼⵉⴽⵉⵣ.

Mathematical language also includes many technical terms such as homeomorphism and integrable that have no meaning outside of mathematics.

ⵉⵍⵍⴰ ⴰⵡⴷ ⴳ ⵜⵓⵜⵍⴰⵢⵜ ⵜⵓⵙⵏⴰⴽⵜ ⴽⵉⴳⴰⵏ ⵏ ⵜⴳⵓⵔⵉⵡⵉⵏ ⵜⵉⵏⴰⵥⵓⵕⵉⵏ ⵣⵓⵏⴷ ⴰⵎⵎⵔⵡⵙ ⴷ ⵓⵙⵎⴷⴰⵏ, ⵓⵔ ⵉⵍⵉⵏ ⴰⵏⴰⵎⴽ ⴱⵕⵕⴰ ⵏ ⵜⵓⵙⵏⴰⴽⵜ.

"Mathematicians refer to this precision of language and logic as ""rigor""."

“ⴷⴰ ⵙⵏⵄⴰⵜⵏ ⵉⵎⵓⵙⵏⴰⵡⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵙ ⴰⵙⵙⴼⵔⵓ ⴷⵖ ⵏ ⵜⵓⵜⵍⴰⵢⵜ ⴷ ⵓⵎⴳⵏ “”ⵜⴰⵎⵎⴰⵣⵜ””.

"This is to avoid mistaken ""theorems"", based on fallible intuitions, of which many instances have occurred in the history of the subject."

“ⴰⵢⴰ ⵎⴰⵔ ⴰⴷ ⵏⴽⴽ ⵜⴰⵙⴳⴰ ⵉ “”ⵜⵎⴰⴳⵓⵏⵉⵏ“”, ⵉⵣⴳⵍⵏ ⵉⵜⵡⴰⴳⴰⵏ ⵖⴼ ⵓⵙⵡⵉⵏⴳ ⵓⵔ ⵉⵎⵎⵓⵥⵍⵏ, ⵏⵏⴰ ⴷ ⵢⵓⵡⵉⵏ ⴽⵉⴳⴰⵏ ⵏ ⵉⵎⴷⵢⴰⵜⵏ ⵖⴼ ⵓⵙⵏⵜⵍ.”

Misunderstanding the rigor is a cause for some of the common misconceptions of mathematics.

ⴳⴰⵔ ⴰⵔⵎⴰⵙ ⵏ ⵓⵇⵊⴰⵕ ⴰⵢⴷ ⵢⵓⵡⵉⵏ ⵉⵜⵙⵏ ⵉⵔⵎⵎⵓⵙⵏ ⵉⵣⴳⵍⵏ ⵉⵍⵍⴰⵏ ⴳ ⵜⵓⵙⵏⴰⴽⵜ.

On the other hand, proof assistants allow verifying all details that cannot be given in a hand-written proof, and provide certainty of the correctness of long proofs such as that of the Feit–Thompson theorem.

ⴳ ⵜⵙⴳⴰ ⵢⴰⴹⵏ, ⴷⴰ ⵉⵜⵜⴰⴷⵊⴰ ⵓⵎⴰⵡⴰⵙ ⵏ ⵜⵉⵍⵉⵜ ⴰⵙⴰⴳⴳⵯ ⵏ ⵉⴼⵔⵓⵔⵉⵜⵏ ⴽⵓⵍⵍ ⵏⵏⴰ ⵓⵔ ⵉⴳⵉⵏ ⵡⵉⵏ ⵓⵙⵙⵏⴽⴷ ⴳ ⵜⵉⵍⵉⵜ ⵉⵜⵢⴰⵔⴰⵏ ⵙ ⵓⴼⵓⵙ, ⴰⵔ ⴰⴽⴽⴰⵏ ⴰⵙⵍⴽⵏ ⵙ ⵡⴰⵏⵥⴰⵜⵏ ⵉⵎⴷⴷⴰⴷⵏ ⵉⵖⵣⵣⴰⴼⵏ, ⴰⵎⵎ ⵡⵉⵏⵏⴰ ⵉⵍⵍⴰⵏ ⴳ ⵜⵎⴰⴳⵓⵏⵜ ⵏ ⴼⴰⵢⵜ ⵜⴰⵎⵙⵓⵏ.

In addition to these main concerns, there are also subdivisions dedicated to exploring links from the heart of mathematics to other fields: to logic, to set theory (foundations), to the empirical mathematics of the various sciences (applied mathematics), and more recently to the rigorous study of uncertainty.

ⵙ ⵜⵎⵔⵏⵓⵜ ⵉ ⵜⵡⵏⵏⵉⵜⵉⵏ ⴰⴷ ⵜⵉⴷⵙⵍⴰⵏⵉⵏ, ⵍⵍⴰⵏⵜ ⴰⵡⴷ ⵜⴷⴰⵍⵉⵡⵉⵏ ⵜⴰⵢⵢⴰⵡⵉⵏ ⵜⵓⵙⵍⵉⴳⵉⵏ ⵉⵜⵜⴰⴼⴰⵏ ⵜⴰⵣⵍⵖⵉⵡⵉⵏ ⴳ ⵡⵓⵍ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵙ ⵉⴳⵔⴰⵏ ⵢⴰⴹⵏ: ⵙ ⵓⵎⴳⵉⵏ, ⴷ ⵓⵙⵔⵔⵓⵙ ⵏ ⵜⵎⴰⴳⵓⵏⵜ (ⵉⵙⵔⴰⵙⵏ), ⵜⵓⵙⵏⴰⴽⵜ ⵏ ⵜⵉⵔⵎⵉ ⵖⵔ ⵜⵎⴰⵙⵙⴰⵏⵉⵏ ⵢⴰⴹⵏ (ⵜⵓⵙⵏⴰⴽⵜ ⵜⴰⵙⴽⵔⴰⵏⵜ), ⵜⵉⵢⵉⵔⴰ ⵖⵔ ⵜⵣⵔⴰⵡⵜ ⵉⵏⵖⴷⵏ ⵓⵔ ⵉⵟⵟⵉⴼⵏ ⴰⵙⵍⴽⵏ.

Some disagreement about the foundations of mathematics continues to the present day.

ⴰⵔ ⴰⵙⵙⴰ ⵉⵙⵓⵍ ⴽⴰ ⵏ ⵓⵎⵣⵉⵔⴰⵢ ⵖⴼ ⵉⵙⵔⴰⵙⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ.

As such, it is home to Gödel's incompleteness theorems which (informally) imply that any effective formal system that contains basic arithmetic, if sound (meaning that all theorems that can be proved are true), is necessarily incomplete (meaning that there are true theorems which cannot be proved in that system).

ⴳ ⵓⵙⴰⵔⴰ ⴰⴷ, ⵜⴳⴰ ⵜⵉⴳⵎⵎⵉ ⵏ “ⵜⵎⴰⴳⵓⵏⵉⵏ ⵉⵏⵏⴳⵣⴰⵏ” ⵏ ⵊⵓⴷⵍ ( ⵙ ⵜⴰⵍⵖⴰ ⵓⵔ ⵉⴳⵉⵏ ⵜⵉⵏⵚⵉⴱⵜ), ⴰⵔ ⴰⵖ ⵜⵎⵎⴰⵍ ⴽⴰ ⵉⴳⴰⵜ ⴰⴳⵔⵔⴰ ⴰⵎⵙⵡⵓⵔⵉ ⵓⵏⵙⵉⴱ ⴷⴰⵔⵙ ⴰⵙⵙⵉⴹⵏ ⴰⴷⵙⵍⴰⵏ, ⵉⴳ ⵉⴳⴰ ⵉⵎⵙⵍⵉ ( ⵜⵉⵎⴰⴳⵓⵏⵉⵏ ⴽⵓⵍⵍⵓⵜⵏⵜ ⵙ ⵏⵖⵉ ⴰⴷ ⵜⵏⵜ ⵏⵜⵍⴰⵡ ⴷ ⵜⵉⵎⴷⴷⴰⴷⵉⵏ), ⵎⵇⵇⴰⵔ ⵓⵔ ⵜⵙⵎⵉⴷ ( ⵍⵍⴰⵏⵜ ⵜⵎⴰⴳⵓⵏⵉⵏ ⵜⵉⵎⴷⴷⴰⴷⵉⵏ), ⵏⵏⴰ ⵙ ⵓⵔ ⵏⵖⵉⵢ ⴰⴷ ⵜⵏⵜ ⵏⵜⵍⴰⵡ ⴷ ⵜⵉⵎⴷⴷⴰⴷⵉⵏ.

Modern logic is divided into recursion theory, model theory, and proof theory, and is closely linked to theoretical computer science, as well as to category theory.

ⵉⴱⴹⴰ ⵓⵎⴳⵉⵏ ⴰⵎⴰⵢⵏⵓ ⵅⴼ ⵜⵎⴰⴳⵓⵏⵜ ⵜⴰⴷⵡⴰⵍⴰⵏⵜ, ⴷ ⵜⵎⴰⴳⵓⵏⵜ ⵏ ⵓⵎⴷⵢⴰ, ⴷ ⵜⵎⴰⴳⵓⵏⵜ ⵏ ⵜⵉⵍⴰⵡⵜ, ⵉⵍⴰⵏ ⴰⵣⴷⴰⵢ ⴰⴽⴷ ⵎⵇⵇⵓⵔⵏ ⴷ ⵓⵎⵙⵙⵓⴷⵙ ⴰⵎⴰⴳⵓⵏ, ⵓⵍⴰ ⵜⴰⵎⴰⴳⵓⵏⵜ ⵏ ⵜⴳⵔⵔⵓⵎⴰ.

Computability theory examines the limitations of various theoretical models of the computer, including the most well-known model—the Turing machine.

ⴷⴰ ⵜⵙⴽⴰⵔ ⵜⵎⴰⴳⵓⵏⵜ ⵏ ⵓⵙⵙⵉⵟⵏ ⴰⵣⵣⵔⴰⵢ ⵉ ⵉⴽⴰⵔⵉⴼⵏ ⵏ ⵉⵎⴷⵢⴰⵜⵏ ⵏ ⵜⵎⴰⴳⵓⵏⵜ ⵜⴰⵎⵣⵉⵔⴰⵢⵜ ⵉ ⵓⵎⵙⵙⵓⴷⵙ, ⴳ ⵉⵍⵍⴰ ⵓⵎⴷⵢⴰ ⵉⵜⵢⴰⵙⵙⴰⵏ ⴽⵉⴳⴰⵏ; “ⵉⵎⵉⵙ ⵜⵓⵔⵉⵏ”.

"Consideration of the natural numbers also leads to the transfinite numbers, which formalize the concept of ""infinity""."

“ⴰⵙⴽⵙⵡ ⴳ ⵉⵎⴹⴰⵏ ⵉⴳⴰⵎⴰⵢⵏ ⴷⴰ ⵉⵜⵜⴰⵡⵢ ⴰⵡⴷ ⵙ ⵉⵎⴹⴰⵏ ⵉⵣⵔⵉⵏ ⵉⵡⵜⵜⴰ, ⵏⵉⵜⵏⵜⵉ ⴰⵢⴷ ⵉⵜⴳⴳⴰⵏ ⴰⵔⵎⵎⵓⵙ ⵏ “ⵡⴰⵔⵜⵎⵉ” ⴷ ⵓⵏⵚⵉⴱ.”

Thus one can study groups, rings, fields and other abstract systems; together such studies (for structures defined by algebraic operations) constitute the domain of abstract algebra.

ⵉⵎⴽⵉ ⴰⵙ ⵏⵖⵢ ⴰⴷ ⵏⴳ ⵜⴰⵣⵔⴰⵡⵜ ⵖⴼ ⵜⵔⵓⴱⴱⴰ ⴷ ⵜⵎⵜⴻⵜⵜⴰⵢⵉⵏ ⴷ ⵢⵉⴳⵔⴰⵏ ⴷ ⵉⵎⴰⴳⴰⵡⵏ ⵉⵡⵏⴳⵉⵎⵏ ⵢⴰⴹⵏ, ⴷⴰ ⵙⴽⴰⵔⵏⵜ ⵜⵣⵔⴰⵡⵉⵏ ⴰⴷ ( ⵜⴰⵏⵖⵉⵡⵉⵏ ⵉⵜⵜⵓⵥⵍⴰⵢⵏ ⵙ ⵜⵎⵀⵉⵏ ⵜⵉⵊⵉⴱⵔⵉⵢⵉⵏ), ⵉⴳⵔ ⵏ ⵍⵊⵉⴱⵔ ⴰⵡⵏⴳⵉⵎ.

Trigonometry is the branch of mathematics that deals with relationships between the sides and the angles of triangles and with the trigonometric functions.

ⵜⴰⵎⴰⵙⵙⴰⵏⵜ ⵏ ⵜⵎⴽⵕⴰⴹ ⵉⴳⴰ ⴰⵢⵢⴰⵡ ⵏ ⵜⴰⵡⵙⵏⴰⴽⵜ ⵉⵙⵡⵓⵔⵉⵏ ⴰⴽⴷ ⵜⵣⴷⴰⵢⵉⵏ ⵉⵖⵣⴷⵉⵙⵏ ⴷ ⵜⵖⵎⵔⵉⵏ ⵏ ⵜⵎⴽⵕⴰⴹ ⴷ ⵜⵡⵓⵔⵉⵡⵉⵏ ⵜⵉⵎⴽⵕⴰⴹ.

Convex and discrete geometry were developed to solve problems in number theory and functional analysis but now are pursued with an eye on applications in optimization and computer science.

ⵜⵜⵓⵙⴱⵓⵖⵍⵍⴰ ⵜⴳⵣⵉⵜ ⵢⴰⵜⵜⵓⵢⵏ ⵜⴱⴹⵓ ⵎⴰⵔ ⴰⴷ ⵜⴼⵙⵉ ⵜⵉⵎⵓⴽⵔⵉⵙⵉⵏ ⴳ ⵜⵎⴰⴳⵓⵏⵜ ⵏ ⵉⵎⴹⴰⵏ ⴷ ⵓⴼⴰⵔⵙ ⴰⵙⵖⵏⴰⵏ, ⵎⴰⴽⴰ ⴷⴰ ⵜⵜⵓⴹⴼⵓⵕ ⵖⵉⵍⴰ ⵙ ⵓⵙⵎⵙⵙⵉ ⵖⴼ ⵜⵙⵏⵙⵉⵜⵉⵏ ⴳ ⵓⵙⴼⵓⵍⴽⵓ ⴷ ⵜⵎⴰⵙⵙⴰⵏⵉⵏ ⵏ ⵓⵎⵙⵙⵓⴷⵙ.

Lie groups are used to study space, structure, and change.

ⴷⴰ ⵜⵜⵓⵙⵎⵔⴰⵙⵏⵜ ⵜⵔⵓⴱⴱⴰ ⵏ ⵉⵅⴷⴰⴷⵏ ⵎⴰⵔ ⴰⴷ ⵉⵜⵜⵓⵖⵔ ⵓⵙⴰⵢⵔⴰⵔ ⴷ ⵜⵓⵙⴽⵉⵡⵜ ⴷ ⵓⵙⵏⴼⵍ.

Functions arise here as a central concept describing a changing quantity.

ⵜⴳⴰ ⵜⵙⵖⵏⵜ ⵖⵉⴷ ⵣⵓⵏⴷ ⴰⵔⵎⵎⵓⵙ ⴰⵏⴰⵎⵎⴰⵙ ⵉⵙⵏⵓⵎⵎⴰⵍⵏ ⴰⴳⵓⴷⵉ ⵉⵜⵜⵓⵙⵏⴼⴰⵍⵏ.

One of many applications of functional analysis is quantum mechanics.

ⵜⴳⴰ ⵜⵎⵉⴽⴰⵏⵉⴽⵉⵜ ⵏ ⵜⵙⵎⴽⵜⴰ ⵢⴰⵜ ⴳ ⴽⵉⴳⴰⵏ ⵜⵙⵏⵙⵉⵡⵉⵏ ⵏ ⵓⵙⴼⵙⵉ ⴰⵙⵖⵏⴰⵏ.

"Statisticians (working as part of a research project) ""create data that makes sense"" with random sampling and with randomized experiments; the design of a statistical sample or experiment specifies the analysis of the data (before the data becomes available)."

ⵉⵎⵙⵏⵎⴽⵜⵉⵜⵏ (ⵙⵡⵓⵔⵉⵏ ⵖⴼ ⵜⴳⵣⵣⵓⵎⵜ ⴰⵎⵎ ⵓⵙⵏⴼⴰⵔ ⴰⵔⵣⵣⵓ), ⵙⴽⴰⵔⵏ ⵉⵏⵎⵎⴰⵍⵏ ⵓⵎⴳⵉⵏⴻⵏ, ⵙ ⵢⵉⵙⵢ ⵏ ⵉⵜⵙⵏ ⵜⵓⵙⵙⵉⴼⵉⵏ ⵙ ⵉⵜⵙⵏ ⵜⵉⵔⵎⵉⵜⵉⵏ, ⵉⵙⵜⵜⵉ ⴰⵎⴰⵎⴽ ⵏ ⵜⵓⵙⵙⵉⴼⵜ ⵜⴰⵙⵏⵎⴽⵜⵉⵜ ⵏⵖⴷ ⵜⵉⵔⵎⵉ ⵏ ⵓⴼⴰⵔⵙ ⵏ ⵉⵏⵎⵎⴰⵍⵏ ( ⴷⴰⵜ ⵏ ⴰⴷ ⵉⵍⵉⵏ ⵉⵏⵎⵎⴰⵍⵏ).

Numerical analysis studies methods for problems in analysis using functional analysis and approximation theory; numerical analysis includes the study of approximation and discretisation broadly with special concern for rounding errors.

ⴷⴰ ⵉⵙⵙⵖⵔⴰ ⵓⴼⴰⵔⵙ ⴰⵎⵉⴹⴰⵏ ⵜⵉⴱⵔⵉⴷⵉⵏ ⵏ ⵉⵎⵓⴽⵔⵉⵙⵏ ⴳ ⵓⴼⴰⵔⵙ, ⵙ ⵓⵙⵙⵎⵔⵙ ⵏ ⵓⴼⴰⵔⵙ ⵉⵎⴳⴳⵉ ⴷ ⵜⵎⴰⴳⵓⵏⵜ ⵏ ⵓⵙⵏⵎⵉⵍⴰ, ⵉⵍⵍⴰ ⴳ ⵓⴼⴰⵔⵙ ⴰⵎⵉⴹⴰⵏ ⵜⴰⵣⵔⴰⵡⵜ ⵏ ⵓⵙⵏⵎⴰⵍⴰ ⴷ ⵢⵉⵖⵉⵍ ⴳ ⵓⴼⵓⵖⴰⵍ ⵉⵎⵉⵔⴰⵡ, ⴷ ⵜⴰⵡⵉⵜ ⵉⵥⵍⵉⵏ ⵙ ⵓⵙⵏⵎⵉⵍⴰ ⵏ ⵉⵣⴳⴳⴰⵍⵏ.

The Chern Medal was introduced in 2010 to recognize lifetime achievement.

ⵜⵜⵓⴼⴽⴰ ⵜⵙⵎⵖⵓⵔⵜ ⵏ “ⵜⵛⵉⵔⵏ” ⴳ ⵓⵙⴳⴳⵯⴰⵙ ⵏ 2010, ⴰⴷ ⵜⴳ ⵉⵙⵉⵏ ⵙ ⵜⵡⵓⵔⵉⵡⵉⵏ ⵏ ⵓⵙⵎⵎⵓⴷ.

This list achieved great celebrity among mathematicians, and at least nine of the problems have now been solved.

ⵜⴰⵍⴳⴰⵎⵜ ⴰⴷ ⵜⴳⵓⵍⴰⵏ ⵢⴰⵏ ⵓⵎⵙⵓⵙⵙⵏ ⴰⵅⴰⵜⴰⵔ ⴳⵔ ⵉⵎⵓⵙⵏⴰⵡⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ, ⴰⵔ ⴷⵖⵉ ⵜⵜⵓⴼⵓⴽⴽⴰⵏ ⵜⵥⴰ ⵏ ⵉⵎⵓⴽⵔⵉⵙⵏ.

The value of Pi was first calculated by him.

ⵏⵜⵜⴰ ⴰⵢⴷ ⵉⴽⴰⵏ ⴰⵜⵉⴳ ⵉ “ⴱⵉ” ⵜⵉⴽⵍⵜ ⵜⴰⵎⵣⵡⴰⵔⵓⵜ.

"It was the Pythagoreans who coined the term ""mathematics"", and with whom the study of mathematics for its own sake begins."

“ⴽⵔⵏ ⵍⴼⵉⵜⴰⵖⵓⵔⵢⵢⵓⵏ ⵜⴰⴳⵓⵔⵉ ⵏ “ ⵜⵓⵙⵏⴰⴽⵜ” ⵏⵉⵜⵏⵉ ⴰⵖⵓⵔ ⵜⵜⵓⵙⵏⵜⴰⵢ ⵜⵣⵔⴰⵡⵜ ⵜⵓⵙⵏⴰⴽⵜ ⵉ ⵡⴰⴷⵓⵏⵙ.”

Because of a political dispute, the Christian community in Alexandria punished her, presuming she was involved, by stripping her naked and scraping off her skin with clamshells (some say roofing tiles).

ⵙ ⵓⵎⵣⵉⵔⴰⵢ ⴰⵙⵔⵜⴰⵏ, ⵜⵎⵔⵔⵜ ⵜⴰⴳⴳⴰⵢⵜ ⵏ ⵍⵎⴰⵙⵉⵃ ⴳ ⵍⵉⵙⴽⴰⵏⴷⴰⵔⵢⵢⴰ, ⵏ ⵡⵉⵙ ⵜⴰⵎⵓ, ⵜⵢⴰⴽⵙⵏ ⴰⵙ ⵉⵃⵔⵓⵢⵏ, ⵉⵜⵜⵓⴽⵕⴰⴹ ⵓⴱⴹⴹⴰⵏ ⵏⵏⵙ ⵙ ⵉⵍⵎ (ⵍⵍⴰⵏ ⵡⵉⵏⵏⴰ ⵉⵏⵏⴰⵏ ⵉⵏⴱⴷⴰⴷ ⵏ ⵜⵎⴰⵙⵉⵃⵉⵢⵜ).

Funding for translation of scientific texts in other languages was ongoing throughout the reign of certain caliphs, and it turned out that certain scholars became experts in the works they translated and in turn received further support for continuing to develop certain sciences.

ⵉⵙⵙⴰⴷⴰ ⵓⵙⵙⵥⵕⴼ ⵏ ⵓⵙⵓⵖⵍ ⵏ ⵉⴹⵕⵉⵚⵏ ⵉⵎⴰⵙⵙⴰⵏ ⴳ ⵜⵉⵣⵉ ⵏ ⵓⵏⴱⴰⴹ ⵏ ⵉⵎⴽⴽⵓⵙⴰ, ⵉⵎⴽ ⵉⴼⴰⵡ ⵏ ⵡⵉⵙ ⴳⴰⵏ ⴽⴰⵏ ⵉⵜⵙⵏ ⵉⵎⴰⵙⵙⴰⵏ ⵉⵎⵓⵣⴰⵢⵏ ⴳ ⵜⵡⵓⵔⵉⵡⵉⵏ ⵙⵙⵓⵖⵍⵏ, ⴰⵢⴰ ⴰⵖⴼ ⵓⵎⵥⵏ ⴰⵎⵢⵉⵡⴰⵙ ⵏⵏⵉⴹⵏ ⴰⴷ ⵙⵙⵓⴷⵓⵏ ⴳ ⵓⵙⴱⵓⵖⵍⵓ ⵏ ⵉⵜⵙⵏⵜ ⵜⵎⴰⵙⵙⴰⵏⵉⵏ.

A notable feature of many scholars working under Muslim rule in medieval times is that they were often polymaths.

ⵓⴷⴷⵓⵔ ⴰⵏⵥⵍⴰⵢ ⵏ ⵉⵎⵓⵙⵏⴰⵡⵏ ⵉⵙⵡⵓⵔⵉⵏ ⴷⴷⴰⵡ ⵜⵏⴱⴰⴹⵜ ⵜⴰⵏⵙⵍⵎⵜ ⴳ ⵉⵣⵎⴰⵣ ⵉⵏⴰⵎⵎⴰⵙⵏ; ⴽⵉⴳⴰⵏ ⴷⵉⴽⵙⵏ ⵖⴰⵔⵙ ⴰⵎⵢⴰⵏⴰⵡ ⵏ ⵜⴷⵍⵙⴰⵏⵉⵏ.

During this period of transition from a mainly feudal and ecclesiastical culture to a predominantly secular one, many notable mathematicians had other occupations: Luca Pacioli (founder of accounting); Niccolò Fontana Tartaglia (notable engineer and bookkeeper); Gerolamo Cardano (earliest founder of probability and binomial expansion); Robert Recorde (physician) and François Viète (lawyer).

ⴳ ⵜⵉⵣⵉ ⴰⴷ ⵏ ⵓⵎⵎⵓⵜⵢ ⵙⴳ ⵜⴷⵍⵙⴰ ⵏ ⵓⵙⵎⵎⵖⴷ ⴷ ⵜⵎⴰⵙⵉⵃⵜ ⵖⵔ ⵜⴷⵍⵙⴰ ⵜⴰⵍⴰⵙⵙⵏⵜ, ⵉⵙⵡⵓⵔⵉ ⴽⵉⴳⴰⵏ ⴳ ⵉⵎⵓⵙⵏⴰⵡⵏ ⵉⴽⵙⵡⴰⵜⵏ ⴳ ⵜⵖⵍⵉⴼⵉⵏ ⵏⵏⵉⴹⵏ, ⵍⵓⴽⴰ ⴱⴰⵙⵢⵓⵍⵉ (ⴱⴰⴱ ⵏ ⵓⵙⵙⵉⴹⵏ), ⵏⵉⴽⵓⵍⵓ ⴼⵓⵏⵜⴰⵏⴰ ⵜⴰⵔⵜⴰⴳⵍⵉⵢⴰ (ⴰⵎⵏⵣⴰⴳ ⴷ ⵓⵎⵙⵉⴹⵏ ⵎⵇⵇⵓⵕⵏ), ⵊⵉⵔⵓⵍⴰⵎⵓ ⴽⴰⵔⴷⴰⵏⵓ ( ⵏⵜⵜⴰ ⴷ ⴰⵎⵣⵡⴰⵔⵓ ⵉⵙⴽⵔⵏ ⵉⵖⵉⵢ ⴷ ⵓⵙⵙⵉⵔⵡ ⵉⵍⴰⵏ ⵙⵉⵏ ⵉⵡⵜⵜⴰ), ⵔⵓⴱⵉⵔⵜ ⵔⵉⴽⵓⵔⴷ (ⴰⵎⵙⴳⵏⴰⴼ), ⴷ ⴼⵔⴰⵏⵙⵡⴰ ⴼⵢⵉⵜ (ⴰⵎⵙⵜⴰⵏ).

British universities of this period adopted some approaches familiar to the Italian and German universities, but as they already enjoyed substantial freedoms and autonomy the changes there had begun with the Age of Enlightenment, the same influences that inspired Humboldt.

ⵙⵙⴳⵎⴰⵏⵜ ⵜⵙⴷⴰⵡⵉⵜⵉⵏ ⵏ ⴱⵕⵉⵟⴰⵏⵢⴰ ⴳ ⵜⵉⵣⵉ ⴰⴷ, ⵉⵜⵙⵏ ⵡⴰⵎⵎⴰⴽⵏ ⵉⵍⵍⴰⵏ ⴳ ⵜⵙⴷⴰⵡⵉⵜⵉⵏ ⵏ ⵟⴰⵍⵢⴰⵏ ⴷ ⵍⴰⵍⵎⴰⵏ, ⵎⴰⴽⴰ ⵉⴷ ⵖⵓⵔⵙ ⵏⵏⵉⴽ ⵜⵉⵍⴻⵍⵍⵉ ⵎⵇⵇⵓⵕⵏ ⴷ ⵜⴳⴰ ⵜⴰⵙⵉⵎⴰⵏⵜ, ⵙⵙⵏⵜⵉⵏ ⵉⵙⵏⴼⴰⵍⵏ ⴳ ⵓⵙⴰⵜⵓ ⵏ ⵜⵉⴼⴰⵡⵜ, ⵉⴹⵉⵚⵏ ⴰⴷ ⴰⵢⴷ ⵉⵍⵍⴰⵏ ⴰⵡⴷ ⵖⴼ ⵀⵎⴱⵓⵍⵜ.

Students could conduct research in seminars or laboratories and began to produce doctoral theses with more scientific content.

ⵖⵉⵏ ⵉⵎⵣⵔⴰⵡⵏ ⴰⴷ ⴳⵉⵏ ⵉⵔⵣⵣⵓⵜⵏ ⴳ ⵜⵉⵏⴰⵡ ⴷ ⵉⵙⴰⵔⴰⵎⵏ, ⵙⵙⵏⵜⵉⵏ ⴰⴼⴰⵔⵙ ⴰⵙⵏⵓⴱⴱⵛ ⵏ ⵜⴷⵓⴽⵜⵓⵔⵜ ⵙ ⴽⵉⴳⴰⵏ ⵏ ⵜⵓⵎⴰⵢⵜ ⵜⴰⵎⴰⵙⵙⴰⵏⵜ.

Mathematicians and applied mathematicians are considered to be two of the STEM (science, technology, engineering, and mathematics) careers.

ⵉⵎⵓⵙⵏⴰⵡⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⴷ ⵉⵎⵓⵙⵏⴰⵡⵏ ⵏ ⵜⵓⵙⵏⴰⴽⵜ ⵜⴰⵎⵙⴽⴰⵔⵜ ⴷ ⵜⵉⵡⵓⵔⵉⵡⵉⵏ ⵏ ( ⵜⵉⵎⴰⵙⵙⴰⵏⵉⵏ, ⵜⴰⵜⵉⴽⵏⵓⵍⵓⵊⵉⵜ, ⵜⴰⵎⵙⴷⴰⴳⵜ, ⵜⵓⵙⵏⴰⴽⵜ).

Actuaries also address financial questions, including those involving the level of pension contributions required to produce a certain retirement income and the way in which a company should invest resources to maximize its return on investments in light of potential risk.

ⴰⵡⴷ ⵉⴽⵜⵉⵡⴰⵔⵉⵢⵏ ⵓⵡⵉⵏⴷ ⵉⵙⵇⵙⵉⵜⵏ ⵏ ⵜⵉⵥⵔⴰⴼ, ⴳ ⴰⵎⵓⵏⵜ ⵜⵉⵏⵏⴰ ⵉⵍⴰⵏ ⵜⴰⵣⵍⵖⴰ ⵙ ⴰⵙⵡⵉⵔ ⵏ ⵉⵎⵢⵉⵡⴰⵙⵏ ⵏ ⵜⴰⵡⵙⵓⴷⵔⵉⵏ ⵜⵉⵏⴰⴼⴰⵏⵉⵏ ⵉⵜⵢⴰⵜⵜⴰⵔⵏ ⴳ ⵓⵙⵏⴼⵍⴻⵍ ⵏ ⴽⴰⵏ ⵜⴰⵙⵜⴰⵖⵜ, ⴷ ⵜⵖⴰⵔⴰⵙⵜ ⵙ ⵔⴰⴷ ⵜⵙⵢⴰⴼⴰ ⵜⵎⵙⵙⵓⵔⵜ ⵉⵙⵓⴳⴰⵎ, ⵎⴰⵔ ⴰⴷ ⵜⵙⵙⵎⵖⵓⵔ ⵉⵎⴰⵖⵓⵍⵏ ⵏⵏⵙ ⴳ ⵉⵙⵢⴰⴼⴰⵜⵏ ⴰⴳⵏⵙ ⵏ ⵉⵎⵉⵣⵏ ⵉⵖⵉⵏ ⴰⴷ ⵢⵉⵍⵉ.

The hieroglyphic system for Egyptian numerals, like the later Roman numerals, descended from tally marks used for counting.

ⴰⵏⴳⵔⴰⵡ ⴰⵀⵉⴷⵔⵓⵖⵍⴰⴼⵉ ⵉ ⵉⵎⴹⴰⵏ ⵉⵎⵉⵚⵕⵉⵢⵏ, ⵣⵓⵏⴷ ⵉⵎⴹⴰⵏ ⵉⵕⵓⵎⴰⵏⵉⵢⵏ ⵉⴽⴽⴰⵏ, ⵜⵢⴰⵙⴰⵢⵏⴷ ⴳ ⵜⵎⵉⵜⴰⵔ ⵏ ⵓⵙⵙⵉⴹⵏ ⵉⵙⵡⵓⵔⵉⵏ ⵖⴼ ⵓⵙⵉⴹⵏ.

Early number systems that included positional notation were not decimal, including the sexagesimal (base 60) system for Babylonian numerals, and the vigesimal (base 20) system that defined Maya numerals.

ⵓⵔ ⴳⵉⵏ ⵉⴳⵔⵔⴰⵢⵏ ⵏ ⵡⵓⵟⵟⵓⵏⴻⵏ ⵉⵎⵏⵣⵓⵜⵏ ⵏⵏⴰ ⴳ ⵍⵍⴰⵏ ⵉⵣⵎⵎⴻⵎⵏ ⵉⵙⵓⵔⵙⵏ ⵉⵎⵔⴰⵡⵏ, ⴳ ⵢⴰⵎⵓ ⵓⵏⴳⵔⴰⵡ ⴰⵎⵚⴹⵉⵚ-ⵎⵔⴰⵡ (ⴰⵙⵉⵍⴰ 60), ⵏ ⵉⵎⴹⴰⵏ ⵉⴱⴰⴱⵉⵍⵉⵜⵉⵏ, ⴷ ⵓⵏⴳⵔⴰⵡ vigesimal ( ⴰⵙⵉⵍⴰ 20), ⵏⵏⴰ ⵉⵥⵍⵉⵏ ⵓⵟⵟⵓⵏ ⵏ ⵎⴰⵢⴰ.

Prior to the works of Euclid around 300 BC, Greek studies in mathematics overlapped with philosophical and mystical beliefs.

ⴷⴰⵜ ⵏ ⵜⵡⵓⵔⵉⵡⵉⵏ ⵏ ⵓⴽⵍⵉⴷ ⵣⵓⵏⴷ 300 ⵏ ⵓⵙⴳⴳⵯⴰⵙ ⴷⴰⵜ ⵜⵍⴰⵍⵉⵜ ⵏ ⵍⵎⴰⵙⵉⵃ, ⵎⵎⴽⵛⴰⵎⵏⵜ ⵜⵣⵔⴰⵡⵉⵏ ⵜⵉⵢⵓⵏⴰⵏⵉⵢⵉⵏ ⴳ ⵜⵓⵙⵏⴰⴽⵜ ⴰⴽⴷ ⵜⵓⵔⴷⴰ ⵜⴰⴼⵍⵙⴰⴼⵜ ⴷ ⵉⴳⵔⵔⴰⵎⵏ.

The ancient Greeks lacked a symbol for zero until the Hellenistic period, and they used three separate sets of symbols as digits: one set for the units place, one for the tens place, and one for the hundreds.

ⵉⵖⵔⵉⵇ ⵉⵇⴱⵓⵔⵏ ⵓⵔ ⴷⴰⵔⵙⵏ ⵜⴰⵏⴳⴰⵍⵜ ⵏ ⵓⵎⵢⴰ, ⴰⵔ ⴰⵣⵎⵣ ⴰⵀⵉⵍⵉⵏⵉⵙⵜⵉⴽ, ⵙⵡⵓⵔⵉⵏ ⵙ ⴽⵕⴰⴹ ⵜⵔⵓⴱⴱⴰ ⵏ ⵜⵏⴳⴰⵍⵉⵏ ⴰⵢⴷ ⵖⵓⵔⵙⵏ ⵉⴳⴰⵏ ⵉⵎⴹⴰⵏ, ⵜⴰⵔⴰⴱⴱⵓⵜ ⵉ ⵡⴰⵏⵙⴰ ⵏ ⵉⵎⵢⵉⵡⵏ, ⵢⴰⵜ ⵉ ⵡⴰⵏⵙⴰ ⵏ ⵉⴷ ⵎⵔⴰⵡ, ⵜⴰⵢⴹ ⵉ ⵜⵉⵎⵎⴰⴹ.

Their long division algorithm was the same, and the digit-by-digit square root algorithm, popularly used as recently as the 20th century, was known to Archimedes (who may have invented it).

ⵜⴽⴽⴰⵜ ⴰⵍⴳⵓⵔⵉⵜⵎ ⵜⵉⵎⴱⴹⵉⵜ ⵉⵖⵣⵣⵉⴼⵏ ⵣⴰⵔⵚⵏ ⵉⵥⵍⵉⵏ ⵏⵜⵜⴰⵜ ⵏⵉⵜ, ⴷ ⴰⵍⴳⵓⵔⵉⵜⵎ ⵏ ⵓⵥⵓⵕ ⴰⵎⴽⴽⵓⵥ ⴳ ⵉⵍⵍⴰ ⵡⵓⵟⵟⵓⵏ ⵙ ⵓⵟⵟⵓⵏ, ⵏⵏⴰ ⵉⵜⵜⵓⵙⵎⵔⵙⵏ ⵡⴰⵍⴰ ⵜⵉⵢⵉⵔⴰ ⴷⵖ ⴳ ⵓⵙⴰⵜⵓ ⵡⵉⵙⵙ 20, ⵜⵢⴰⵙⵙⵏ ⵙ ⴰⵔⵅⵎⵉⴷⵙ (ⵉⵖⵢ ⵉⴷ ⵏⵜⵜⴰ ⴰⵢⴷ ⵜⵜ ⵉⵙⴽⵔⵏ).

The ancient Chinese had advanced arithmetic studies dating from the Shang Dynasty and continuing through the Tang Dynasty, from basic numbers to advanced algebra.

ⵉⴽⴽⴰ ⵜⵜ ⵖⵓⵔ ⵉⵚⵉⵏⵉⵢⵏ ⵉⵣⴰⵢⴽⵓⵜⵏ ⵜⵉⵣⵔⴰⵡⴰⵏ ⵏ ⵓⵙⵙⵉⵟⵏ ⵢⴰⵜⵜⵓⵢⵏ, ⵍⵍⴰⵏⵜ ⵙⴳ ⵓⵙⴰⵜⵓ ⵏ ⵜⴰⵡⵊⴰ ⵏ ⵛⴰⵏⴳ, ⵜⵙⵙⵓⴷⵓ ⴰⵔ ⴰⵙⴰⵜⵓ ⵏ ⵜⴰⵡⵊⴰ ⵏ ⵜⴰⵏⴳ, ⵙⴳ ⵉⵎⴹⴰⵏ ⵉⴷⵙⵍⴰⵏ ⵖⵔ ⵍⵊⵉⴱⵔ ⵢⴰⵜⵜⵓⵢⵏ.

For the hundreds place, they then reused the symbols for the units place, and so on.

ⴳ ⵜⵓⵣⵓⵏⵜ ⵏ ⵜⵉⵎⵎⴰⴹ, ⵙⵡⵓⵔⵉⵏ ⴷⵉⵖ ⵙ ⵜⵎⴰⵜⴰⵔⵜ ⵉⵥⵍⵉⵏ ⵙ ⴰⵎⵢⵉⵡⵏ, ⵙⵙⵓⴷⵓⵏ.

The ancient Chinese were the first to meaningfully discover, understand, and apply negative numbers.

ⵉⵚⵉⵏⵉⵢⵏ ⵉⵇⴱⵓⵔⵏ ⴰⵢⴷ ⵢⵓⴼⴰⵏ, ⵔⵎⵙⵏ ⵙⵙⵎⵔⵙⵏ ⵉⵎⴹⴰⵏ ⵉⵏⴰⴱⴰⵡⵏ.

"His contemporary, the Syriac bishop Severus Sebokht (650 AD) said, ""Indians possess a method of calculation that no word can praise enough."

ⵉⵏⵏⴰ ⵓⵅⴰⵜⴰⵔ ⵏ ⵙⵙⵉⵔⵢⴰⵏ ⵙⵉⴼⵉⵔⵓⵙ ⵙⵉⴱⵓⵅⵜ (650 ⵙ ⵜⴰⵍⴰⵍⵉⵜ ⵏ ⵍⵎⴰⵙⵉⵃ): ⵜⵍⵍⴰ ⵖⵓⵔ ⵉⵀⵉⵏⴷⵉⵢⵏ ⵜⴱⵔⵉⴷⵜ ⵏ ⵓⵙⵙⵉⴹⵏ ⵏⵏⴰ ⵙ ⵓⵔ ⵏⵖⵉⵢ ⴰⴷ ⵜ ⵏⴰⵍⵖ ⵙ ⴰⵡⴷ ⵢⴰⵜ ⵜⴳⵓⵔⵉ.

The Arabs also learned this new method and called it hesab.

ⵉⵎⴽⵉⵏⵏⴰ ⵍⵎⴷⵏ ⵡⴰⵄⵕⴰⴱⵏ ⵜⴰⴱⵔⵉⴷⵜ ⴰⴷ ⵜⴰⵎⴰⵢⵏⵓⵜ, ⴰⵔ ⴰⵙ ⵇⵇⴰⵔⵏ ⵙ ⵢⵉⵙⵎ ⵏ “ⵃⵉⵙⴰⴱ”.

The flourishing of algebra in the medieval Islamic world, and also in Renaissance Europe, was an outgrowth of the enormous simplification of computation through decimal notation.

ⵉⴽⴽⴰⵜ ⵓⵙⴱⵓⵖⵍⵓ ⵏ ⵜⵓⵙⵏⴰⵊⵉⴱⵔⵜ ⴳ ⵓⵎⴰⴹⴰⵍ ⴰⵏⵙⵍⵎ ⴳ ⵉⵣⵎⴰⵣ ⵉⵏⴰⵎⵎⴰⵙⵏ, ⵓⵍⴰ ⴳ ⵓⵣⵎⵣ ⵏ ⵜⵏⴽⵔⴰ ⴳ ⵓⵔⵓⴱⴱⴰ, ⵜⴰⵢⴰⴼⵓⵜ ⵏ ⵓⴼⵔⴰⵔⵉ ⵎⵇⵇⵓⵔⵏ ⵏ ⵓⵙⵙⵉⴹⵏ ⴳ ⵓⵣⵎⵎⴻⵎ ⴰⵎⵔⴰⵡ.

Arithmetic expressions must be evaluated according to the intended sequence of operations.

ⵉⵇⵏⴻⵏ ⵓⵙⵜⴰⵍ ⵏ ⵓⵡⵏⵏⵉ ⵏ ⵓⵙⵙⵉⴹⵏ ⵖⴼ ⵓⵣⴷⴷⵓⵢ ⵏ ⵜⵎⵀⵍⵜ ⵏⵏⴰ ⵏⵔⴰ.