History of Mathematics |

**In General**

* __And history of science__: Up until the 1950s,
the history of mathematics was an integral part of the history of science; Mathematics was
considered the rational skeleton that organized science and held it together, and its history
was a fundamental component of the broader history of science; When historians began focusing
on the cultural roots of science rather than its rational structure, the study of mathematics was
marginalized and ultimately excluded from the history of science, to the detriment of both.

* __1600s__: 1631, The first fully symbolic, recognizably
modern algebra textbook (Thomas Harriot's *Artis Analyticae Praxis*); 1637, René
Descartes' *La Géometrie* took symbolic algebra further (and introduced the *x*,
*y* notation); The +, −, = and × signs came into widespread use; 1660s and 1670s,
Isaac Newton and Gottfried Leibniz independently developed calculus (Newton used the notation
\(\dot y\), while Leibniz introduced the notation d*x* for a 'differential' and
d*y*/d*x* –or d*y*:d*x*–, but the concept of infinitesimal
was only made precise in the 1800s)s; The great French mathematicians were P de Fermat,
R Descartes and B Pascal.

* __1900s__: Andrew Wiles' proof of Fermat's last theorem.

**Specific Areas**
> s.a. algebraic topology; calculus of
variations; differential equations; knot theory;
series.

@ __Mathematical physics__: Netz PT(00)jun [Archimedes];
Warwick 03 [Cambridge];
Knox & Noakes ed-03 [Lucasian Professors].

@ __Other areas__: McLarty BJPS(90) [topos theory].

> __Geometry__: see differential
geometry; geometry; symplectic geometry.

**References**

@ __General__: Alexander Isis(11),
Gray Isis(11),
Mann Isis(11) [and history of science];
Wolpert & Kinney a2012-FQXi [mathematics as a fundamentally stochastic process];
Guicciardini et al 21 [anachronisms].

@ __Books__: Van Heijenoort 67 [logic];
Struik 67;
Kline 80;
Burton 85;
Newman ed-88;
Motz & Weaver 93 [science-motivated];
Rudman 07
[popularization, r PT(08)jul];
Robson & Stedall 09 [handbook];
Grant & Kleiner 15 [turning points].

@ __Books, special emphasis__: Coolidge 90 [amateurs];
Anglin 94 [and philosophy];
Corry 04 [algebra and abstract structures,
r Isis(09)#2].

@ __And culture__:
Ascher 91;
Ascher 02 [other cultures].

@ __Mathematicians__: Halmos 87 [pictures];
Peterson 98;
Monastyrsky 99 [Riemann];
Sinai ed-03 [Russian, XX century];
Albers & Alexanderson 08 [interviews and profiles];
Tent 08 [Gauss];
Chang 10 [academic genealogy];
Brown 12 [Leibniz and the calculus];
Mauldin 15 [discussions and problems from the Scottish Café].

@ __Personal accounts__: Ulam 76;
Halmos 85;
Quine 85;
Kac 87;
Bollobás 06.

@ __Specific topics__: Rothman a1308 [the cubic equation and the Cardano-Tartaglia Great Feud];
Mazur 14 [mathematical notation];
Rothman et al MI(15);
blog cosmos(20)jan [symbolic notation].

@ __Specific places__:
Fiske BAMS(1905) [in America];
Parshall BAMS(00) [in America];
Christianidis ed-04 [Greek mathematics];
Friberg 05 [Egyptian and Babylonian];
Graham & Kantor Isis(06) [approaches, France and Russia];
in Padmanabhan & Padmanabhan 19 [calculus in India before Leibniz and Newton].

@ __Specific periods__:
Pierpont BAMS(1904) [XIX century];
Milka EJC(10)
[geometry theorems proved by ancient civilizations].

@ __Selected writings__: Hawking ed-05.

# __Mathematicians__: Brauer,
Cantor, Chevalley, Courant, Gauss, Hilbert, Klein, Lie, Noether, Riemann.

**Online Resources** > see St-Andrews MacTutor History of
Mathematics archive;
Internet Encyclopedia of Science pages.

main page
– abbreviations
– journals – comments
– other sites – acknowledgements

send feedback and suggestions to bombelli at olemiss.edu – modified 22 apr 2021