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.
28 statements.
Hirsch Conjecture, Progress Toward ResolutionThe conjecture was disproved in May 2010, when Francisco Santos Leal of the University of Cantabria announced a 43-dimensional counterexample polytope of 86 facets with a diameter of more than 43.
Hirsch Conjecture, Conjectures
Standing
Concerns Progress Toward Resolution
Currently States The conjecture was disproved in May 2010, when Francisco Santos Leal of the University of Cantabria announced a 43-dimensional counterexample polytope of 86 facets with a diameter of more than 43.
Source Hirsch Conjecture (Wikipedia)
Archimedes, Birth Year287 BCE
Archimedes, Mathematicians
Standing
Concerns Birth Year
Currently States 287 BCE
Calculated from the Byzantine writer John Tzetzes' claim, centuries later, that Archimedes lived 75 years; not independently confirmed.
Source MacTutor History of Mathematics Archive
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, Mathematicians
Standing
Concerns Birth Year
Currently States 325 BCE
No birth record survives; 325 BCE is a commonly cited scholarly estimate derived from his known activity under Ptolemy I (reigned from 305 BCE), not a firm date.
Source MacTutor History of Mathematics Archive
Euclid, Death Year265 BCE
Euclid, Mathematicians
Standing
Concerns Death Year
Currently States 265 BCE
No death record survives; this is a commonly cited estimate, not a firm date.
Source MacTutor History of Mathematics Archive
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
Fundamental Theorem of Calculus, Theorems
Standing
Concerns Proof Year
Currently States 1666
Newton's own working dates to 1665-1666; he published only decades later. Leibniz developed an independent version in the 1670s and published first, in 1684. Priority between them was never settled to both sides' satisfaction.
Source Encyclopaedia Britannica, Mathematics
H-Cobordism Theorem, Proof Year1961
H-Cobordism Theorem, Theorems
Standing
Concerns Proof Year
Currently States 1961
MathWorld gives 1961 for Smale's proof; search-result summaries also report 1962 for the theorem, so the year is not uniform across sources.
Source h-Cobordism Theorem (Wolfram MathWorld)
Infinitude of Primes, Proof Year300 BCE
Infinitude of Primes, Theorems
Standing
Concerns Proof Year
Currently States 300 BCE
Dated to the compilation of Euclid's Elements; no more precise date for the individual proposition survives.
Source MacTutor History of Mathematics Archive
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)
Jordan Curve Theorem, Proof Year1887
Jordan Curve Theorem, Theorems
Standing
Concerns Proof Year
Currently States 1887
Jordan published a claimed proof in 1887; for decades many mathematicians considered that proof flawed and credited Oswald Veblen with the first rigorous proof, but this assessment has since been challenged by Thomas Hales and others, so which proof was genuinely first and correct is not settled among historians of mathematics.
Source Jordan Curve Theorem (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, Mathematicians
Standing
Concerns Birth Year
Currently States 1170 CE
No firm birth record survives; c. 1170 is the commonly cited scholarly estimate.
Source MacTutor History of Mathematics Archive
Leonardo of Pisa, Death Year1240 CE
Leonardo of Pisa, Mathematicians
Standing
Concerns Death Year
Currently States 1240 CE
No firm death record survives; estimates commonly range from 1240 to 1250.
Source MacTutor History of Mathematics Archive
Muhammad ibn Musa al-Khwarizmi, Birth Year780 CE
Muhammad ibn Musa al-Khwarizmi, Mathematicians
Standing
Concerns Birth Year
Currently States 780 CE
No firm birth record survives; c. 780 CE is the commonly cited scholarly estimate.
Source MacTutor History of Mathematics Archive
Muhammad ibn Musa al-Khwarizmi, Death Year850 CE
Muhammad ibn Musa al-Khwarizmi, Mathematicians
Standing
Concerns Death Year
Currently States 850 CE
No firm death record survives; c. 850 CE is the commonly cited scholarly estimate.
Source MacTutor History of Mathematics Archive
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
Pierre de Fermat, Mathematicians
Standing
Concerns Birth Year
Currently States 1607
Some sources give 1601; see the birth-date note.
Source MacTutor History of Mathematics Archive