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The final factor is, in this scenario, do all human capable of reaching the same intellectual level? Do they born equal in that regard? Or for example every hundredth people has high enough intellect?

The envisioned technology level of (modern) also changes to final number. Steam-engines are easier to understand than nuclear. A possibly future automation could reach fully automated factories with a few overseer required.

To calculate an accurate number without these factors, is beyond my capability. At guess, a few hundred thousand or million, highly specialized human blessed with great intellectual capability could, in theory, all over the world operate and maintain the necessary machinery to keep it going.

 Note: Not all of them has to be the above mentioned specialized, very smart human. Only, everyone has to be smart enough to be able to do their jobs well. My answer to determine the lowest necessary number require higher percentage of technologically well educated and smart people (various engineers and scientists mostly), than simply hard-laborers.

The final factor to account in this scenario, do all human capable of reaching the same intellectual level? Do they born equal in that regard? Or for example every hundredth people has high enough intellect? I can't be trained to be a Quantum Physicist. People's view vary in this regard, so I will leave this as a simple multiplier.

They are pointers for a reasonably close estimate. My very rough guess, a few hundred thousand or most a million can maintain an inherited and hastily retrofitted modern technological world.

NOTE: In my view, they have to be highly specialized in various technological fields, and preferable the cream of the crop in intellectual ability, among other things. Mostly, because this will lower the necessary number. Not ALL of them have to be like that, but a significant percentage. Depending on the level of automation and mechanization, this percentage may vary. (Look at Factorio) Also, my assumption is that a hard-laborer can't be retrained (in reasonable time and capacity, views may vary) to be a rocket scientist, nuclear reactor operator and so on...

What we DON'T need

Let's start the answer in reverse. Who we can dismiss? Who we don't need to maintain modern technological levels. A good part of humanity if I says so. No offense for anyone.

• Employees of huge companies who provide service to the masses? They can be significantly down-scaled. If functionality, the maintaining of technology instead of profit the purpose, only their engineering team. You can scrap their HR, sales, and so on departments.
• Most services and its workers too - you don't need 20 kind of chips and cars and so on, to maintain modern technology levels.
• Any kind of Media related profession - SCRAP!
• Governmental bodies - Significantly downscaled, based on the situation and type of government.
• Homeless, unemployed, and so on... they don't contribute to modern technology, so they too can be dismissed.

Other factors: Human intellect, productivity, automation

• Automation - we are heading towards a heavily automated world, most mundane task can be or will be replaced by robots.
• Human intellect - Automation means, you can dismiss almost all the heavy-lifters. You will however need highly educated and intelligent people to operate and maintain the machinery.
• Productivity - much depends on the disposition of the people. Are they lazy? Hard-workers? Do you need police to manage big masses of them and so on. This too will affect the final number.

The final factor is, in this scenario, do all human capable of reaching the same intellectual level? Do they born equal in that regard? Or for example every hundredth people has high enough intellect?

The envisioned technology level of (modern) also changes to final number. Steam-engines are easier to understand than nuclear. A possibly future automation could reach fully automated factories with a few overseer required.

To calculate an accurate number without these factors, is beyond my capability. At guess, a few hundred thousand or million, highly specialized human blessed with great intellectual capability could, in theory, all over the world operate and maintain the necessary machinery to keep it going.

Quick edited note here: My answer, as I understood the question, is aimed at what is required to maintain modern technological levels. I answered this way, because in my understanding, that is the required foundation for modern life and in my view civilization is too subjective and broad to be answered. For that, I could say US or Europe or Japan, with automatized colonies around the globe for rare resources.

What we DON'T need, to only maintain modern technology

Let's start the answer in reverse. Who we can dismiss? Who we don't need to maintain modern technological levels. A good part of humanity if I says so. No offense for anyone. I'm part of the "dismissed".

• Employees of huge companies who provide service to the masses? They can be significantly down-scaled. If functionality, the maintaining of technology instead of profit the purpose, only their engineering team. You can scrap their HR, sales, and so on departments.
• Most services and its workers too - you don't need 20 kind of chips and cars and so on, to maintain modern technology levels.
• Any kind of Media related profession - SCRAP!
• Governmental bodies - Significantly downscaled, based on the situation and type of government.
• Homeless, unemployed, and so on... they don't contribute to modern technology, so they too can be dismissed.

Other factors: Human intellect, productivity, automation

• Automation - we are heading towards a heavily automated world, most mundane task can be or will be replaced by robots.
• Human intellect - Automation means, you can dismiss almost all the heavy-lifters. You will however need highly educated and intelligent people to operate and maintain the machinery.
• Productivity - much depends on the disposition of the people. Are they lazy? Hard-workers? Do you need police to manage big masses of them and so on. This too will affect the final number.

The final factor is, in this scenario, do all human capable of reaching the same intellectual level? Do they born equal in that regard? Or for example every hundredth people has high enough intellect?

The envisioned technology level of (modern) also changes to final number. Steam-engines are easier to understand than nuclear. A possibly future automation could reach fully automated factories with a few overseer required.

To calculate an accurate number without these factors, is beyond my capability. At guess, a few hundred thousand or million, highly specialized human blessed with great intellectual capability could, in theory, all over the world operate and maintain the necessary machinery to keep it going.

Note: Not all of them has to be the above mentioned specialized, very smart human. Only, everyone has to be smart enough to be able to do their jobs well. My answer to determine the lowest necessary number require higher percentage of technologically well educated and smart people (various engineers and scientists mostly), than simply hard-laborers.

What we DON'T need

Let's start the answer in reverse. Who we can dismiss? Who we don't need to maintain modern technological levels. A good part of humanity if I says so. No offense for anyone.

• Employees of huge companies who provide service to the masses? They can be significantly down-scaled. If functionality, the maintaining of technology instead of profit the purpose, only their engineering team. You can scrap their HR, sales, and so on departments.
• Most services and its workers too - you don't need 20 kind of chips and cars and so on, to maintain modern technology levels.
• Any kind of Media related profession - SCRAP!
• Governmental bodies - Significantly downscaled, based on the situation and type of government.
• Homeless, unemployed, and so on... they don't contribute to modern technology, so they too can be dismissed.

Other factors: Human intellect, productivity, automation

• Automation - we are heading towards a heavily automated world, most mundane task can be or will be replaced by robots.
• Human intellect - Automation means, you can dismiss almost all the heavy-lifters. You will however need highly educated and intelligent people to operate and maintain the machinery.
• Productivity - much depends on the disposition of the people. Are they lazy? Hard-workers? Do you need police to manage big masses of them and so on. This too will affect the final number.
• (It's not PC so I'll edit it out if its offending, but there is a reason Wakanda is fiction, Germany and Japan isn't.)

The final factor is, in this scenario, do all human capable of reaching the same intellectual level? Do they born equal in that regard? Or for example every hundredth people has high enough intellect?

The envisioned technology level of (modern) also changes to final number. Steam-engines are easier to understand than nuclear. A possibly future automation could reach fully automated factories with a few overseer required.

To calculate an accurate number without these factors, is beyond my capability. At guess, a few hundred thousand or million, highly specialized human blessed with great intellectual capability could, in theory, all over the world operate and maintain the necessary machinery to keep it going.

What we DON'T need

Let's start the answer in reverse. Who we can dismiss? Who we don't need to maintain modern technological levels. A good part of humanity if I says so. No offense for anyone.

• Employees of huge companies who provide service to the masses? They can be significantly down-scaled. If functionality, the maintaining of technology instead of profit the purpose, only their engineering team. You can scrap their HR, sales, and so on departments.
• Most services and its workers too - you don't need 20 kind of chips and cars and so on, to maintain modern technology levels.
• Any kind of Media related profession - SCRAP!
• Governmental bodies - Significantly downscaled, based on the situation and type of government.
• Homeless, unemployed, and so on... they don't contribute to modern technology, so they too can be dismissed.

Other factors: Human intellect, productivity, automation

• Automation - we are heading towards a heavily automated world, most mundane task can be or will be replaced by robots.
• Human intellect - Automation means, you can dismiss almost all the heavy-lifters. You will however need highly educated and intelligent people to operate and maintain the machinery.
• Productivity - much depends on the disposition of the people. Are they lazy? Hard-workers? Do you need police to manage big masses of them and so on. This too will affect the final number.

The final factor is, in this scenario, do all human capable of reaching the same intellectual level? Do they born equal in that regard? Or for example every hundredth people has high enough intellect?

The envisioned technology level of (modern) also changes to final number. Steam-engines are easier to understand than nuclear. A possibly future automation could reach fully automated factories with a few overseer required.

To calculate an accurate number without these factors, is beyond my capability. At guess, a few hundred thousand or million, highly specialized human blessed with great intellectual capability could, in theory, all over the world operate and maintain the necessary machinery to keep it going.