Sample Additional Highlights for Existing Mathematica Users
(Except as noted, all features are available for both desktop and cloud.)

Math

Constants of integration

Automatic generation of integration, summation, etc. constants

Unlimited limits

Multivariate limits, lim sup, sequence limits and all that

"By hand" equation manipulation

AddSides, MultiplySides, DivideSides, etc. (but always correct)

Asymptotic analysis »

Big O, little o, WKB, asymptotic solutions and all that

Prove it!

Generate symbolic proofs from axioms with FindEquationalProof

Complex number plots »

Complex plane, complex values; 2D, 3D; functions, data

Unintimidating roots

Simpler formatting for Root[] objects

Formal but less dotty

etc. to indicate formal variables more elegantly

Visualization

Scaled plots

Give your own scaling function (log, probability, etc.)

Stacked plots »

Show multiple datasets in stacked, percentile, etc. form

Multipanel plots »

Arrays of plots with common axes

Labeling is automatic

Callout, Labeled, etc. to automatically label points, lines, surfaces, features, etc.

Geometry

Way beyond Platonic solids »

Full computational treatment of polyhedra (served beveled, snubbed, ...)

Polygons: the full story »

Polygons that wind, cross, have holes, etc.

Region[] is now a thing »

Automatically visualized regions (implicit, explicit, ...)

Automated Euclid (and geometric drawing)

Euclid-style geometry (CircleThrough, Midpoint, ...) solved with FindGeometricConjectures etc.

All the basic geometric measures

Perimeter, SurfaceArea, PlanarAngle, SolidAngle, ...

Turtles in space

AnglePath3D for 3D "turtle-like" paths

Data, Computation & New Directions

Numbers with uncertainty »

x ± dx for computation, visualization, etc.

Building in industrial-strength systems engineering

SystemModel, SystemModelSimulate, SystemModelPlot, ... for machines, circuits, pathways

Industrial convex optimization »

Quadratic, semidefinite, conic, ... optimization for problems big and small

Molecules are symbolic expressions too »

Visualization and computation with arbitrary (organic) molecules

Join the blockchain revolution »

Read, write, analyze, transact on Bitcoin, Ethereum, etc.

Language Conveniences

ReverseSort »

Now there is a single function to sort largest first

Graphs keep their properties

Properties are automatically inherited when graph operations are done

Information[] on everything »

Standardized way to get information on objects (images, audio, cloud objects, entities, ...)

Granular dates »

Specify a day, week, month, etc. as well as a moment in time

Name that cellular automaton! »

Association-based specifications for cellular automaton rules

More operator forms (AKA currying)

Map, Select and more have operator forms, and Curry makes any function an operator

Notebook Innovations

In + Out labeled forever

In[•] and Out[•] to label input and output, even without a kernel

Iconize! »

Store code and data directly in a notebook, formatting only as an icon

Out-of-notebook storage

Summaries of Audio, SparseArray, etc. give a choice of storage location

Give your presentations with notebooks »

New Presenter Notebooks for rich screen size–adaptive interactive presentations

Mac front end is 64 bit!

Full support of modern 64-bit Cocoa for notebooks on the Mac (> 2 GB etc.)

Do you see that closed cell group?

Automatic indicators to make it easier to notice closed cell groups

Headless Linux notebooks

Qt 5 support, enabling rendering without an X server

Geo

Bubble visualization

GeoBubbleChart to visualize values on maps

Random places

RandomGeoPosition for random points in any region (country etc.)

Satellite imagery of everywhere

GeoImage for high-resolution imagery, not just of Earth

Vectors on Earth

Winds, paths, etc.: GeoVector, GeoStreamPlot, etc.

Machine Learning

Attention, transformers

AttentionLayer etc. integrated into the symbolic neural net framework

Did you expect that? »

Automatic anomaly detection for all forms of data

The world of feature space

FeatureSpacePlot, FeatureSpacePlot3D... and lots of built-in feature extractors

Multi-GPU and all that

State-of-the-art, high-efficiency neural net training

Watch that machine learn!

Fully interactive machine learning dashboard for training and more

Visualize that neural net

Automatic visualization of neural net structures (with drill down)

Export your neural net

MXNet export of core neural net structures

All the latest neural nets

The Wolfram Neural Net Repository with immediately computable nets for NetModel

A distribution of cat pictures

LearnDistribution for distribution of any type of data

Image Computation

Screen capture »

Not just from a camera, but also what is on the screen

Find those faces

FacialFeatures for finding faces and their features in an image

Paint like van Gogh

ImageRestyle for automatic restyling of images

Vectorizing bitmap graphics

ImageGraphics to heuristically convert bitmaps to vector graphics

Make that hue blue

ImageRecolor, ColorsNear, etc. to manipulate and recolor images

Audio

Find that sound!

WebAudioSearch, AudioIdentify, etc.

Record that audio!

Capture sound to an Audio[] object

Audio from spectrograms

Infer audio from a spectrogram image with InverseSpectrogram

iPhone audio formats

M4A import and export

Use voice input (and get text)

Transcribe text from speech audio with SpeechRecognize

Speak and compute »

Synthesize speech from text as computable audio

Natural Language Processing

Faster, Smaller, Stronger...

Knowledgebase

Systems & Developer

No more init.m!

Programmatically settable initialization of values

Digital signatures for anything »

Create and verify digital signatures

WolframScript editor

Create and edit .wl and .wls files from File > New

Asynchronous tasks »

In a session, on your machine or in the cloud

Communicate through byte arrays

Import, export, string-convert, etc. directly with byte arrays

PersistentValue: persist anything anywhere »

This notebook, this machine, this user, ...: persist code and data anywhere

Fire-and-forget web operations

Asynchronously submit to a URL, with callbacks

How much memory do I have left?

MemoryAvailable for programmatic access to memory limits

Serialize anything with WXF »

Efficiently store and transmit any expression in binary form

External Operations

Seamless remote file operations

Use RemoteFile in CopyFile etc., authenticating as you need

It is a mail client/analyzer too! »

Connect to any IMAP server and read/analyze/modify mail folders

Built-in SSH

RemoteRun etc. to run processes through SSH on remote machines

What is running on my machine?

Programmatic access to ps-like data on running processes

Symbolic network analyzer »

Capture network packets going to and from your machine

Talking to Databases

MongoDB

Read and write data in MongoDB

Terabyte databases are no problem

Full symbolic layer for seamlessly accessing SQL databases

SPARQL, RDF, IRIs & all that »

Programmatically access graph databases and triplestores

Bringing in Data

Interacting with the Outside

Go autonomous with microcontrollers »

Deploy control systems and filters directly to microcontrollers

Python cells, right in a notebook

Use > to start a Python cell, then get results back in the Wolfram Language

Puppet your web browser »

Programmatically interact with a web browser

Evaluate Python, JavaScript, ...

ExternalEvaluate to call code directly from the Wolfram Language

Authenticate that external service

OAuth etc. to authenticate access to external services

Make a game for Unity »

Create geometry, get telemetry... or programmatically make a full game

Send yourself a text »

SMS, MMS: programmatically send text messages

In the Cloud