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*from greek* –>
μάθημα
(máthēma)
(“‘knowledge’ / ‘study’ / ‘learning'”)
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*NICKNAMES* –>
‘maths’
‘math’
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[‘mathematix’ is the study of topics such as…]
‘quantity’
(aka ‘numbers’)
‘structure’
‘space’
‘change’
(aka ‘time’?)
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(there is a range of views among mathematicians and philosophers as to the exact scope and definition of ‘mathematics’)
(mathematicians seek out patterns and use them to formulate new ‘conjectures’)
(mathematicians resolve the ‘truth’ or ‘falsity’ of conjectures by ‘mathematical proof’)
(when ‘mathematical structures’ are good ‘models’ of ‘real phenomena’, then mathematical reasoning can provide insight or predictions about ‘nature’)
(“aubry has an utterly MATHEMATICAL BODY!”)
(it just MAKES SENSE!)
(“she’s utterly incredible!”)
(through the use of ‘abstraction’ + ‘logic’, ‘mathematics’ developed from ‘counting’, ‘calculation’, ‘measurement’, and the ‘systematic study of the shapes and motions of physical objects’)
(‘practical mathematics’ has been a human activity from as far back as written records exist)
(the research required to solve mathematical problems can take years or even centuries of ‘sustained inquiry’)
(rigorous arguments first appeared in ‘greek mathematics’, most notably in euclid’s “elements”)
(since the pioneering work of ‘giuseppe peano’ (1858–1932), ‘david hilbert’ (1862–1943), and others on ‘axiomatic systems’ in the ‘late 19th century’, it has become ‘customary’ to view ‘mathematical research’ as ‘establishing truth’ by ‘rigorous deduction’ from appropriately chosen ‘axioms’ + ‘definitions’)
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(‘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’)
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“the universe cannot be read until we have learned the language and become familiar with the characters in which it is written. It is written in mathematical language, and the letters are triangles, circles and other geometrical figures, without which means it is humanly impossible to comprehend a single word. without these, one is wandering about in a dark labyrinth”)
‘galileo galilei’
(1564 – 1642)
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(‘carl friedrich gauss’ (1777 – 1855) referred to ‘mathematics’ as “the queen of the sciences”)
(‘benjamin peirce’ (1809 – 1880) called mathematics “the science that draws necessary conclusions”)
(‘david hilbert’ said of ‘mathematics’ –>)
“we are not speaking here of ‘arbitrariness’ in any sense”
“‘mathematics’ is not like a ‘game’ whose tasks are determined by arbitrarily stipulated rules”
“rather, it is a ‘conceptual system’ possessing internal necessity that can only be so and by no means otherwise”
(‘albert einstein’ (1879–1955) stated that “as far as the laws of ‘mathematics’ refer to ‘reality’, they are not ‘certain’; and as far as they are ‘certain’, they do not refer to ‘reality'”)
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(‘mathematics’ is ‘essential’ in many ‘fields’, including…)
‘natural science’
‘engineering’
‘medicine’
‘finance’
*the ‘social sciences’*
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(‘applied mathematics’ has led to entirely new mathematical disciplines, such as ‘statistics’ and ‘game theory’)
(mathematicians also engage in ‘pure mathematics’, or ‘mathematics for its own sake’, without having any application in mind)
(there is no clear line separating ‘pure’ and (/or) ‘applied’ mathematics)
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(‘practical applications’ for what began as ‘pure mathematics’ are often discovered)
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💕💝💖💓🖤💙🖤💙🖤💙🖤❤️💚💛🧡❣️💞💔💘❣️🧡💛💚❤️🖤💜🖤💙🖤💙🖤💗💖💝💘
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*🌈✨ *TABLE OF CONTENTS* ✨🌷*
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🔥🔥🔥🔥🔥🔥*we won the war* 🔥🔥🔥🔥🔥🔥