From: mk_thisisit
The discussion explores the multifaceted role and perception of mathematics in comprehending the cosmos, delving into whether mathematical concepts are discovered or invented and their relationship to objective truth.
Mathematics as a Descriptive Tool
Mathematics is utilized to describe the properties of the external world [00:20:15]. Concepts like general relativity or quantum mechanics are considered mathematical approaches designed to capture the truth about physical processes occurring in the universe [00:20:22]. For instance, mathematical equations are employed to predict the distant future of the universe [00:07:31].
Inventing vs. Discovering Mathematical Concepts
A central debate revolves around whether mathematical concepts are discovered or invented. While most mathematicians believe that mathematical concepts exist independently and are waiting to be found [00:22:11], an opposing view suggests that humans invent mathematical concepts [00:22:31]. This perspective argues that there is no possibility of mathematics existing outside of us [00:22:43].
From this viewpoint, mathematics is a language developed by humans to grasp observations in the world quantitatively and precisely [00:22:48]. Mathematical theorems and proofs are seen as truths that emerge within this invented language [00:23:32]. They would be meaningless without the language of mathematics, which is itself invented [00:23:42].
Consider the Pythagorean theorem () [00:23:51]. The concepts of a triangle, a line, or a right angle are human inventions; there is no perfect right angle in the external world [00:23:56]. Humans create these concepts, and then discover interesting features about them [00:24:13].
Most mathematicians reject this idea because they base the validity of their work on searching for external, pre-existing truths [00:24:22]. However, the counter-argument is that the Pythagorean theorem only has meaning when it resonates within a mind that can understand it [00:24:41]. If no thinking structures remain in the distant future, the theorem would cease to “exist” [00:24:50]. To suggest that mathematics exists independently of us is considered by some as a belief akin to believing in a deity [00:25:05].
Mathematics and Truth
Mathematics is considered a tool to capture objective truth about the physical processes in the universe [00:20:20]. These are truths related to the properties of the external world that science attempts to describe [00:20:15]. This contrasts with subjective truths, which are personal beliefs and values that deeply matter to an individual but are not universally objective [00:20:47]. Distinguishing between these external objective truths and internal subjective truths is considered extremely important [00:21:38].