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Here's my answer:

microwave oven (initially I thought the answer was simply microwaves, but the title ("child of the atomic age") and the last clue ("I think 75 is more than 100") lead me to think the correct answer is the oven.

A miracle of modern science, I have always been everywhere.

Microwave radiation is part of the electromagnetic spectrum (though not exploited by scientists until the first half of the 20th century).

My cancerous cousin foments mistrust, but I promise not to linger.

Other radiation can cause cancer, but microwaves are safe (supposedly).

Wartime genesis gives way to peaceful delights.

The modern microwave oven was developed from radar technology used in World War II.

But do not cross me, for I can make water explode

People have gotten getting seriously burned by trying to boil water in their microwave, and then when they remove the container from the oven, the water explodes in their face because it got superheated. See https://www.stevespanglerscience.com/lab/experiments/exploding-water-in-the-microwave/

I shine bright, but you can never see me

You can't see the microwaves. "Shine bright" might mean the light bulb inside the oven, but I'm not sure about this.

I'm mathematically precise, yet everything is a guessing game – and I think 75 is more than 100!

On some microwave ovens, setting a cook time of 75 means 75 seconds, while a cook time of 1:00 means 1 minute (i.e. 60 seconds).

Here's my answer:

microwave oven (initially I thought the answer was simply microwaves, but the title ("child of the atomic age") and the last clue ("I think 75 is more than 100") lead me to think the correct answer is the oven.

A miracle of modern science, I have always been everywhere.

Microwave radiation is part of the electromagnetic spectrum (though not exploited by scientists until the first half of the 20th century).

My cancerous cousin foments mistrust, but I promise not to linger.

Other radiation can cause cancer, but microwaves are safe (supposedly).

Wartime genesis gives way to peaceful delights.

The modern microwave oven was developed from radar technology used in World War II.

But do not cross me, for I can make water explode

People have gotten getting seriously burned by trying to boil water in their microwave, and then when they remove the container from the oven, the water explodes in their face because it got superheated. See https://www.stevespanglerscience.com/lab/experiments/exploding-water-in-the-microwave/

I shine bright, but you can never see me

You can't see the microwaves. "Shine bright" might mean the light bulb inside the oven, but I'm not sure about this.

I'm mathematically precise, yet everything is a guessing game – and I think 75 is more than 100!

On some microwave ovens, entering a cook time of 75 means 75 seconds, while entering a cook time of 100 means 1 minute 00 seconds (i.e. 60 seconds).

Here's my answer:

microwaves (or microwave ovens)

A miracle of modern science, I have always been everywhere.

Microwave radiation is part of the electromagnetic spectrum (though not exploited by scientists until the first half of the 20th century).

My cancerous cousin foments mistrust, but I promise not to linger.

Other radiation can cause cancer, but microwaves are safe (supposedly).

Wartime genesis gives way to peaceful delights.

The modern microwave oven was developed from radar technology used in World War II.

But do not cross me, for I can make water explode

People have gotten getting seriously burned by trying to boil water in their microwave, and then when they remove the container from the oven, the water explodes in their face because it got superheated. See https://www.stevespanglerscience.com/lab/experiments/exploding-water-in-the-microwave/

I shine bright, but you can never see me

You can't see the microwaves. "Shine bright" might mean the light bulb inside the oven, but I'm not sure about this.

I'm mathematically precise, yet everything is a guessing game – and I think 75 is more than 100!

On some microwave ovens, setting a cook time of 75 means 75 seconds, while a cook time of 1:00 means 1 minute (i.e. 60 seconds).

Here's my answer:

microwave oven (initially I thought the answer was simply microwaves, but the title ("child of the atomic age") and the last clue ("I think 75 is more than 100") lead me to think the correct answer is the oven.

A miracle of modern science, I have always been everywhere.

Microwave radiation is part of the electromagnetic spectrum (though not exploited by scientists until the first half of the 20th century).

My cancerous cousin foments mistrust, but I promise not to linger.

Other radiation can cause cancer, but microwaves are safe (supposedly).

Wartime genesis gives way to peaceful delights.

The modern microwave oven was developed from radar technology used in World War II.

But do not cross me, for I can make water explode

People have gotten getting seriously burned by trying to boil water in their microwave, and then when they remove the container from the oven, the water explodes in their face because it got superheated. See https://www.stevespanglerscience.com/lab/experiments/exploding-water-in-the-microwave/

I shine bright, but you can never see me

You can't see the microwaves. "Shine bright" might mean the light bulb inside the oven, but I'm not sure about this.

I'm mathematically precise, yet everything is a guessing game – and I think 75 is more than 100!

On some microwave ovens, setting a cook time of 75 means 75 seconds, while a cook time of 1:00 means 1 minute (i.e. 60 seconds).

Here's my answer:

microwaves

A miracle of modern science, I have always been everywhere.

Microwave radiation is part of the electromagnetic spectrum (though not exploited by scientists until the first half of the 20th century).

My cancerous cousin foments mistrust, but I promise not to linger.

Other radiation can cause cancer, but microwaves are safe (supposedly).

Wartime genesis gives way to peaceful delights.

The modern microwave oven was developed from radar technology used in World War II.

But do not cross me, for I can make water explode

People have gotten getting seriously burned by trying to boil water in their microwave, and then when they remove the container from the oven, the water explodes in their face because it got superheated. See https://www.stevespanglerscience.com/lab/experiments/exploding-water-in-the-microwave/

I shine bright, but you can never see me

You can't see the microwaves. "Shine bright" might mean the light bulb inside the oven, but I'm not sure about this.

I'm mathematically precise, yet everything is a guessing game – and I think 75 is more than 100!

On some microwave ovens, setting a cook time of 75 means 75 seconds, while a cook time of 1:00 means 1 minute (i.e. 60 seconds).

Here's my answer:

microwaves (or microwave ovens)

A miracle of modern science, I have always been everywhere.

Microwave radiation is part of the electromagnetic spectrum (though not exploited by scientists until the first half of the 20th century).

My cancerous cousin foments mistrust, but I promise not to linger.

Other radiation can cause cancer, but microwaves are safe (supposedly).

Wartime genesis gives way to peaceful delights.

The modern microwave oven was developed from radar technology used in World War II.

But do not cross me, for I can make water explode

People have gotten getting seriously burned by trying to boil water in their microwave, and then when they remove the container from the oven, the water explodes in their face because it got superheated. See https://www.stevespanglerscience.com/lab/experiments/exploding-water-in-the-microwave/

I shine bright, but you can never see me

You can't see the microwaves. "Shine bright" might mean the light bulb inside the oven, but I'm not sure about this.

I'm mathematically precise, yet everything is a guessing game – and I think 75 is more than 100!

On some microwave ovens, setting a cook time of 75 means 75 seconds, while a cook time of 1:00 means 1 minute (i.e. 60 seconds).