Mathematics Atlas
Claims this atlas currently marks as unsettled or as tested and found false. A debated fact is one scholars hold competing positions on; a debunked one has been checked against the record and found not to hold. Both are kept in view rather than quietly smoothed over, with the reasoning that put each one where it stands.
24 statements.
Archimedes, Birth Year287 BCE
Central Limit Theorem, Proof Year1810
Central Limit Theorem, Theorems
Standing
Concerns Proof Year
Currently States 1810
The theorem has no single proof date. Abraham de Moivre proved a special case, the normal approximation to the binomial distribution, in 1733. Pierre-Simon Laplace substantially generalized it in 1810, the year given here as the theorem's general form. Aleksandr Lyapunov supplied the first fully rigorous general conditions in 1901.
Source MacTutor History of Mathematics Archive
Euclid, Birth Year325 BCE
Euclid, Death Year265 BCE
Euler's Identity, Proof Year1748
Euler's Identity, Theorems
Standing
Concerns Proof Year
Currently States 1748
The identity follows from Euler's formula, published in his 1748 Introductio in analysin infinitorum, though historical records suggest Euler may never have explicitly written down this exact identity in this form himself.
Source Euler's Identity (Wikipedia)
Fundamental Theorem of Calculus, Proof Year1666
Infinitude of Primes, Proof Year300 BCE
John Napier, Defining ContributionDiscovered logarithms and published the first account of them in 1614 as Mirifici Logarithmorum Canonis Descriptio, replacing laborious multiplication and division in astronomical and navigational calculation with addition and subtraction.
John Napier, Mathematicians
Standing
Concerns Defining Contribution
Currently States Discovered logarithms and published the first account of them in 1614 as Mirifici Logarithmorum Canonis Descriptio, replacing laborious multiplication and division in astronomical and navigational calculation with addition and subtraction.
Napier's 1614 publication is conventionally credited as the origin of logarithms; see the dissent recorded against this fact for Jost Burgi's independent, later-published claim.
Source John Napier (Wikipedia)
Joseph-Louis Lagrange, Defining ContributionLagrange stated, for permutations of polynomial variables, that the number of distinct polynomials obtained is always a factor of n!, the special case later generalized into the theorem bearing his name.
Joseph-Louis Lagrange, Mathematicians
Standing
Concerns Defining Contribution
Currently States Lagrange stated, for permutations of polynomial variables, that the number of distinct polynomials obtained is always a factor of n!, the special case later generalized into the theorem bearing his name.
Lagrange's name is attached to the theorem that a finite group's subgroup order divides the group's order, but he stated only a special case about permutations of polynomial variables; the general statement for all groups was proved later, by Camille Jordan in 1861.
Source Lagrange's Theorem, Group Theory (Wikipedia)
Lagrange's Theorem (Group Theory), Proof Year1861
Lagrange's Theorem (Group Theory), Theorems
Standing
Concerns Proof Year
Currently States 1861
Lagrange himself stated only a special case, about permutations of polynomial variables, in his 1771 paper. The theorem was generalized to all groups later, through the work of Gauss in 1801 and Cauchy in 1844, and finally proved for all permutation groups by Camille Jordan in 1861.
Source Lagrange's Theorem, Group Theory (Wikipedia)
Leonardo of Pisa, Birth Year1170 CE
Leonardo of Pisa, Death Year1240 CE
Muhammad ibn Musa al-Khwarizmi, Birth Year780 CE
Muhammad ibn Musa al-Khwarizmi, Death Year850 CE
Pi, Origin Year250 BCE
Pi, Concepts
Standing
Concerns Origin Year
Currently States 250 BCE
Dates Archimedes' rigorous bounding method; numerical approximations of the ratio itself are considerably older (Babylonian and Egyptian sources, second millennium BCE) and less precisely datable.
Source MacTutor History of Mathematics Archive
Pierre de Fermat, Birth Date1607-10-31
Pierre de Fermat, Mathematicians
Standing
Concerns Birth Date
Currently States 1607-10-31
Some sources give 1601; the discrepancy traces to confusion between Fermat and an older half-brother of the same name who died in infancy. 1607 is MacTutor's and most modern scholarship's preferred date.
Source MacTutor History of Mathematics Archive
Pierre de Fermat, Birth Year1607
Pythagoras, Birth Year570 BCE
Pythagoras, Death Year495 BCE
Pythagoras, BirthplaceSamos, an Ionian Greek island