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I have been thinking about how physics has evolved since the time of Galileo . Back then physical laws could be describe using axioms which could be comprehended by anyone who reads them. But currently physics is done in a whole different manner. The laws are written mathematically. The language of mathematics is deeply encrypted in the study of physics. For example, the theory of general relativity requires the idea of tensors, black holes are deeply mathematical and so on. I just wanted to know why physics is done using mathematics? Cant it be done without mathematics - for instance, by only doing only experiments?

Qmechanic
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Sillyasker
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    Have you done any research into this yourself? E.g. on Wikipedia – Marius Ladegård Meyer Nov 01 '23 at 10:09
  • Related: https://physics.stackexchange.com/q/267455/2451 , https://physics.stackexchange.com/q/223387/2451 and links therein. – Qmechanic Nov 01 '23 at 10:55
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    " [The universe] cannot be read until we have learnt 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." — Galileo, Opere Il Saggiatore. – PM 2Ring Nov 01 '23 at 12:25
  • Axioms, if properly stated, are a kind of mathematics by themselves. Spinoza uses axioms, not the way modern mathematics does, but I consider it a kind of mathematics non the less. – Gyro Gearloose Nov 01 '23 at 18:38
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    You need mathematics to properly interpret experimental data as well. – Andrew Nov 01 '23 at 19:17

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Without mathematics you can make statements like "Things tend to fall down". With mathematics you can make statements like "the height of an object in free fall follows the equation $h = ut - \frac{1}{2}a t^2$". This contains far more information than the previous statement. It tells you the maximum height the object will reach. It tells you the time it will hit the ground. It tells you where the object will be at each point in between.

Indeed asking any questions like "When will this object hit the ground?" imply quantitative numerical answers, so if you want to ask these types of questions formulating your theory in mathematical terms becomes a very natural thing to do

By Symmetry
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I just wanted to know why physics is done using mathematics? Cant it be done without mathematics - for instance, by only doing only experiments?

The reason why is because mathematics is the language that expresses the results of experiments. Or, in some cases, influences the designs of experiments (e.g., with the intent of extending the validity or adjusting parameters of the model).

But suppose you don't want to produce a mathematical model of the experiment you've performed, what would you do with the results?
Build a set of data points? What good would that do for you and others?
Describe it in words? How would that differ from using an equation instead?


On the more practical side, if you are concerned with the level of maths involved in the more advanced subjects in physics, note that such maths are not given to 1st year students in physics. As is the case with all learning, foundations need to be laid before getting into the deeper subject matter.

Kyle Kanos
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You said: "Cant it be done without mathematics - for instance, by only doing only experiments?"

Yes, it can, but how would you describe the experiments and there results? How to connect them? If there was no mathematics, you'll had to invent it once again.

Gyro Gearloose
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