Baby's drink, mathematician's think$\ $

Question

There are two people I must absolutely thank. @Mithrandir made this a rhyme in the first place, and @Rubio guided and helped me in making this puzzle a lot.

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In chemistry, this is a thing.
It makes the mathematicians sing.
A baby may know it as well
but not the same way, you can tell.

For the baby likes to think of drinks
and mathematicians prefer the thought of thinks.
Engineers use them, yes they do
but not for trains, no no to you.

Einstein used an E and C
the baby prefers the milk, you see.
And in yet another way
your mother used it, in a separate way.

In the kitchen, as you may find
but not the ones that stretch your mind.

What am I?

Answer 1

Is it

Formula?

In chemistry, this is a thing.

Refers to a chemical formula, with elements and such.

It makes the mathematicians sing.

Mathematical formulas for equations!

A baby may know it as well / but not the same way, you can tell.

There are bottle formulas for feeding to babies.

For the baby likes to think of drinks / and mathematicians prefer the thought of thinks.

Of course, baby formula and equation formulas are quite different--one is a drink, and the other is something you think up.

Engineers use them, yes they do / but not for trains, no to you.

Engineers do use formulas to find values, but train engineer is the term for people who handle/drive trains, so they don't use formulas to derive answers to their particular problems. (Thanks to @Mithrandir for the tip on this one!)

Einstein used an E and C

Referring to E = mc^2

the baby prefers the milk, you see. / And in yet another way / your mother used it, in a separate way.

Though babies may prefer their mothers' milk, mothers often use formula instead.

In the kitchen, as you may find / but not the ones that stretch your mind.

You might find baby formula in the kitchen, but probably not a mathematical formula.

And of course, the title "Baby's drink, mathematician's think" refers to

The difference between the mix for feeding to infants, and the formulas that mathematicians find and prove.

Answer 2

Are you

Avogadro's number: 6.022 x 10^23 ?

In chemistry, this is a thing. It makes the mathematicians sing.

Avogadro's number is often used in chemistry, and written in scientific notation, which is mathematical.

A baby may know it as well but not the same way, you can tell.

Baby food is often made of mushy vegetables like Avocados, which to a baby sounds almost the same as Avogadro.

For the baby likes to think of drinks and mathematicians prefer the thought of thinks.

Babies don't typically think about much other than food.

Engineers use them, yes they do but not for trains, no to you.

Engineers may sometimes need to use moles to calculate densities of things maybe? Not for big projects like trains probably.

Einstein used an E and C the baby prefers the milk, you see.

Einstein used the speed of light constant, c, where Avogadro's constant is usually Na.

And in yet another way your mother used it, in a separate way.

There's the 'separate way' thing again, talking about Avocados, or perhaps mole, which is just a sauce.

In the kitchen, as you may find but not the ones that stretch your mind.

You use Avocados and Mole in the kitchen, but not Moles (well, technically those are everywhere too, but we don't count them all the time)