From Perton Maths Department, try their Valentine puzzles.

From Desmos, send one of their great math-o-grams to your mathematical friends!
For an alternative source of Valentine’s cards, we can turn to NASA! Take your pick from this post or these fabulous NASA images. (And don’t forget that NASA provides us with many Mathematics resources.)
From @OCR_Maths, we could try this puzzle.
OCR often share some great maths puzzles, look out for them.
Here’s a Valentine logic starter from Transum.
The excellent Maths Careers site is managed and maintained by the Institute of Mathematics and its Applications. If your students wonder where Mathematics is used they will find plenty of answers here. See for example Who employs mathematicians?

For Valentine’s day we have an appropriate article from Maths Careers, did you know that 6 is a kissing number?! And for your Further Mathematicians, What is the equation for a heart?
Also from Maths Careers, see this post with instructions on how to make this wonderful pair of linked Möbius hearts.

If you wish to get creative and try this I advise watching the Numberphile video carefully; following the instructions worked as you can see from my creation here! I can verify that unless you follow the instruction to make sure the twist in each strip is in a different direction you will end up with a mess! Quite an interesting mess but certainly not two hearts!….
Note the Desmos graphs on my strips. I created a file in Word valentine-mobius-hearts (or pdf: valentine-mobius-hearts) with Desmos images in a table. Adding dotted borders to the table gives guidelines for cutting. I began each cut by using the end of a paperclip to pierce the paper.
To create my strips I printed the document and then printed again on the reverse. I then cut out and trimmed the strips so there was no white space at the end – the picture here has been made using strips 10 cells long.
From the MEI Archives, the February 2015 edition of the MEI Monthly Maths Magazine includes some connections between maths and Valentine’s Day. On page 7 note the article “A Happy Ending” which includes references to some Numberphile videos, Professor Ron Graham discusses the Happy Ending Problem and from Dr Emily Riehl, The Stable Marriage Problem. We also have a great Parametric Heart spreadsheet from Think Maths.
This edition of the magazine includes some lovely activities which link paper folding and proof.…………………………………………………..
Remaining with the loving theme you can express your feelings for WolframAlpha!

and from the WolframAlpha archives, Computing Valentine’s Day.