Steven Weinberg - Is Mathematics Invented or Discovered?

Mathematics describes the real world of atoms and acorns, stars and stairs, with remarkable precision. So is mathematics invented by humans just like chisels and hammers and pieces of music?

[mikefm]

The channel is literally a gift to humanity. Having such deep genuine conversations about so much in a way nearly everyone can understand

[erickcruz]

Rest in peace professor Weinberg, Nobel prize in physics and great teacher

[tme]

This is probably the most realistic and honest discussion of physics you'll find on youtube.

[emilcioran]

He just passed away. What a wonderful and bright person he was

[GH-oijf]

I like the way Weinberg dealt with this question. He didn’t answer it directly, but, rather, explained the relationship of mathematics to physics. His approach is practical, where the question provides an opportunity for a lot of philosophical mumbo-jumbo.

[geshtu]

Mathematics in its most general form is a language for describing relationships between things. If math can describe the world, all it really means is that things in the world are related and that there are regularities (such that these relationships have ongoing practical value - if they only happened once math might be of limited use). In order to find a world where math wasn't useful, you'd need a universe where life such as ours could arise and yet everything be disorderly or unpredictable. Not sure that is possible.

[suncat]

I enjoy listening to Professor Weinberg's explanations tremendously! He seems to be a truly outstanding teacher, in addition to being a genius level physicist.

[NoActuallyGo-KCUF-Yourself]

It is important to not confuse the things studied- quantities and the relationships between quantities - and the way that they are studied - the notation and language of mathematics.

One is discovered, and the other is invented to talk about what is discovered, and to help make more discoveries.

[bryanx]

Well I'm on Team Discovered. These principles are just there. Whether we found them or not, they are there...

[mikepctv]

Good explanation in saying that math is the tool for pictures not the picture itself.

[sdal]

knowing so much and still being humble.

[markmartens]

"Dirac, I think, was responsible for exalting mathematics to a level I don't think it really deserves."

[kevintedder]

The laws of nature have always existed; since the big bang "created" them. But only when humans discovered them did they need to invent a language to represent them.
The circumference of a circle divided by its diameter always gives the answer 3.14159... (Pi) We needed a simpler way to express this to others. So we invented the language of maths to be able to say C/D=Pi for any circle, no matter what size.
A maths formula simply tells us how different attributes of the universe are related. Einstein showed us that energy and mass have a relationship via the speed of light (E=M*C2).

[guineapig]

Physics is the study of one possible world.
Math is the study of all possible worlds.

[valentin]

This video has the most accurate to the content title I ever seen on YouTube and I don't think Weinberg took any side in answering this question . [as he should]

[inkland]

Weinberg is my hero. The presenter did a great job by giving Weinberg enough time to talk without unnecessary interruptions.

[MoneyMotivation]

To me it’s discovered. If you find a map to treasure that changes your life, you didn’t invent the map. Math has been here the whole time we just had to intellectually discover it.

[JohnDoe-nmhs]

I think I agree with Weinberg on the principle that mathematics cannot be an explanation of the real world by itself. 1+1 does not give you enough information to describe the two objects that are being combined, and I believe the same analogy can be made for any mathematical equation. Mathematics is obviously a real and fundamental part of the universe, but it can't be the only part, that wouldn't make sense. You need non-mathematical ingredients to make a full explanation. Mathematics involves the _interaction_ between matter and particles and anything that seems to exist within our universe, but it cannot give all of the answers on its own.

I believe there must be some fundamental smallest state to the building blocks of the universe (a building block which is made of no parts, quarks and electrons may be like that as far as we know today, or there may be something smaller that we haven't discovered yet), and those cannot be explained mathematically, you can only explain the interaction between them in a mathematical way.You cannot say "this building block exists because X * Y = Z" if it is not made of any parts.

The only way that mathematics could explain everything is if we are made of infinitely small stuff, that is we could keep breaking up the smallest building blocks into parts an infinite amount of times (there's no end to how small it is!). But I find that so hard to believe given that our very existence depends on the fact that there are finite sizes and distances, the universe wouldn't make sense if there was no "smallest length" or "smallest size" to the building blocks.

[ChristnThms]

I heard someone say, and latched onto,

"Math is a written language, used to describe things that are inherently true."

It has symbols with specific meaning. It has syntax. It can be spoken. It can be used to describe many things in life. But if used to describe something that is NOT empirically true, it is NO LONGER math.

Unfortunately, pseudo-math is used by many.

[MagnusAnand]

We use mathematics to describe the world. But the world doesn’t fit to mathematics, it’s the other way around.